research methodology analysis definition

Techniques or tools used for gathering research data include:

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Research Methodologies

• What are research designs?

What are research methodologies?

Quantitative research methodologies, qualitative research methodologies, mixed method methodologies, selecting a methodology.

• What are research methods?
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According to Dawson (2019),a research methodology is the primary principle that will guide your research.  It becomes the general approach in conducting research on your topic and determines what research method you will use. A research methodology is different from a research method because research methods are the tools you use to gather your data (Dawson, 2019).  You must consider several issues when it comes to selecting the most appropriate methodology for your topic.  Issues might include research limitations and ethical dilemmas that might impact the quality of your research.  Descriptions of each type of methodology are included below.

Quantitative research methodologies are meant to create numeric statistics by using survey research to gather data (Dawson, 2019).  This approach tends to reach a larger amount of people in a shorter amount of time.  According to Labaree (2020), there are three parts that make up a quantitative research methodology:

• Sample population
• How you will collect your data (this is the research method)
• How you will analyze your data

Once you decide on a methodology, you can consider the method to which you will apply your methodology.

Qualitative research methodologies examine the behaviors, opinions, and experiences of individuals through methods of examination (Dawson, 2019).  This type of approach typically requires less participants, but more time with each participant.  It gives research subjects the opportunity to provide their own opinion on a certain topic.

Examples of Qualitative Research Methodologies

• Action research:  This is when the researcher works with a group of people to improve something in a certain environment.  It is a common approach for research in organizational management, community development, education, and agriculture (Dawson, 2019).
• Ethnography:  The process of organizing and describing cultural behaviors (Dawson, 2019).  Researchers may immerse themselves into another culture to receive in "inside look" into the group they are studying.  It is often a time consuming process because the researcher will do this for a long period of time.  This can also be called "participant observation" (Dawson, 2019).
• Feminist research:  The goal of this methodology is to study topics that have been dominated by male test subjects.  It aims to study females and compare the results to previous studies that used male participants (Dawson, 2019).
• Grounded theory:  The process of developing a theory to describe a phenomenon strictly through the data results collected in a study.  It is different from other research methodologies where the researcher attempts to prove a hypothesis that they create before collecting data.  Popular research methods for this approach include focus groups and interviews (Dawson, 2019).

A mixed methodology allows you to implement the strengths of both qualitative and quantitative research methods.  In some cases, you may find that your research project would benefit from this.  This approach is beneficial because it allows each methodology to counteract the weaknesses of the other (Dawson, 2019).  You should consider this option carefully, as it can make your research complicated if not planned correctly.

What should you do to decide on a research methodology?  The most logical way to determine your methodology is to decide whether you plan on conducting qualitative or qualitative research.  You also have the option to implement a mixed methods approach.  Looking back on Dawson's (2019) five "W's" on the previous page , may help you with this process.  You should also look for key words that indicate a specific type of research methodology in your hypothesis or proposal.  Some words may lean more towards one methodology over another.

Quantitative Research Key Words

• How satisfied

Qualitative Research Key Words

• Experiences
• Thoughts/Think
• Relationship
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data analysis , the process of systematically collecting, cleaning, transforming, describing, modeling, and interpreting data , generally employing statistical techniques. Data analysis is an important part of both scientific research and business, where demand has grown in recent years for data-driven decision making . Data analysis techniques are used to gain useful insights from datasets, which can then be used to make operational decisions or guide future research . With the rise of “Big Data,” the storage of vast quantities of data in large databases and data warehouses, there is increasing need to apply data analysis techniques to generate insights about volumes of data too large to be manipulated by instruments of low information-processing capacity.

Datasets are collections of information. Generally, data and datasets are themselves collected to help answer questions, make decisions, or otherwise inform reasoning. The rise of information technology has led to the generation of vast amounts of data of many kinds, such as text, pictures, videos, personal information, account data, and metadata, the last of which provide information about other data. It is common for apps and websites to collect data about how their products are used or about the people using their platforms. Consequently, there is vastly more data being collected today than at any other time in human history. A single business may track billions of interactions with millions of consumers at hundreds of locations with thousands of employees and any number of products. Analyzing that volume of data is generally only possible using specialized computational and statistical techniques.

The desire for businesses to make the best use of their data has led to the development of the field of business intelligence , which covers a variety of tools and techniques that allow businesses to perform data analysis on the information they collect.

For data to be analyzed, it must first be collected and stored. Raw data must be processed into a format that can be used for analysis and be cleaned so that errors and inconsistencies are minimized. Data can be stored in many ways, but one of the most useful is in a database . A database is a collection of interrelated data organized so that certain records (collections of data related to a single entity) can be retrieved on the basis of various criteria . The most familiar kind of database is the relational database , which stores data in tables with rows that represent records (tuples) and columns that represent fields (attributes). A query is a command that retrieves a subset of the information in the database according to certain criteria. A query may retrieve only records that meet certain criteria, or it may join fields from records across multiple tables by use of a common field.

Frequently, data from many sources is collected into large archives of data called data warehouses. The process of moving data from its original sources (such as databases) to a centralized location (generally a data warehouse) is called ETL (which stands for extract , transform , and load ).

• The extraction step occurs when you identify and copy or export the desired data from its source, such as by running a database query to retrieve the desired records.
• The transformation step is the process of cleaning the data so that they fit the analytical need for the data and the schema of the data warehouse. This may involve changing formats for certain fields, removing duplicate records, or renaming fields, among other processes.
• Finally, the clean data are loaded into the data warehouse, where they may join vast amounts of historical data and data from other sources.

After data are effectively collected and cleaned, they can be analyzed with a variety of techniques. Analysis often begins with descriptive and exploratory data analysis. Descriptive data analysis uses statistics to organize and summarize data, making it easier to understand the broad qualities of the dataset. Exploratory data analysis looks for insights into the data that may arise from descriptions of distribution, central tendency, or variability for a single data field. Further relationships between data may become apparent by examining two fields together. Visualizations may be employed during analysis, such as histograms (graphs in which the length of a bar indicates a quantity) or stem-and-leaf plots (which divide data into buckets, or “stems,” with individual data points serving as “leaves” on the stem).

Data analysis frequently goes beyond descriptive analysis to predictive analysis, making predictions about the future using predictive modeling techniques. Predictive modeling uses machine learning , regression analysis methods (which mathematically calculate the relationship between an independent variable and a dependent variable), and classification techniques to identify trends and relationships among variables. Predictive analysis may involve data mining , which is the process of discovering interesting or useful patterns in large volumes of information. Data mining often involves cluster analysis , which tries to find natural groupings within data, and anomaly detection , which detects instances in data that are unusual and stand out from other patterns. It may also look for rules within datasets, strong relationships among variables in the data.

• Open access
• Published: 09 July 2024

Academic resilience in nusing students: a concept analysis

• Yang Shen 1 ,
• Hanbo Feng 1 &
• Xiaohan Li 1  

BMC Nursing volume  23 , Article number:  466 ( 2024 ) Cite this article

106 Accesses

Metrics details

Academic resilience is a crucial concept for nursing students to cope with academic challenges. Currently, there is significant variation in the description of the concept attributes of academic resilience among nursing students, which impedes the advancement of academic research. Therefore, it is essential to establish a clear definition of the concept of academic resilience for nursing students.

The purpose of this paper is to report the results of concept analysis of academic resilience of nursing students.

The Rodgers evolutionary concept analysis was employed to test the attributes, antecedents, consequences and related concepts of academic resilience of nursing students. Walker and Avant’s method was utilized to construct a model case and provide empirical referents.

The findings indicate that the attributes of nursing students’ academic resilience include self-efficacy, self-regulation and recovery, and the antecedents include internal factors and external environmental factors. The consequences include adaptability, career maturity, adversity quotient level, probability of academic success, a sense of belonging to school and low levels of psychological distress.

The systematic understanding of academic resilience among nursing students provides a pathway for nursing educators and students to enhance academic resilience, promote academic success, and establish a foundation for the training of more qualified nurses.

Peer Review reports

Introduction

Nursing is a scientific discipline that studies nursing theory and technology in the process of health promotion and disease prevention, with the aim of equipping students with knowledge, attitudes, and skills essential to the nursing profession [ 1 ]. Compared with students in other majors, nursing students often experience great pressure from unfamiliar clinical environments, the gap between professional theory and practice, unexpected emergencies, strained relationship with patients and their families, exposure to infectious diseases, as well as heavy workloads [ 2 , 3 ]. The high levels of stress experienced by nursing students can negatively affect their overall well-being and academic performance [ 4 , 5 , 6 ], compromising their quality of life while increasing burnout rates [ 7 ]. Moreover, sustained pressure may impede critical thinking abilities, problem-solving skills, decision-making capabilities among nursing students thereby diminishing their motivation for learning and hindering academic achievement [ 4 , 6 , 8 ], ultimately failing to complete their professional learning. Students’ coping ability and academic success are closely related to their perception and handling of academic pressure. Therefore, it is particularly crucial to assist them in comprehending their academic pressure and difficulties and continuously enhancing nursing students’ psychological quality in order to cope with setbacks and achieve successful adaptation [ 9 , 10 ].

Resilience refers to experiencing significant traumatic events and difficulties and still achieving positive developmental outcomes [ 11 ]. It is the process of adapting to major stressors and negative factors, as well as the strength to recover from stressful life events or successfully cope with negative experiences [ 12 , 13 ]. There is evidence that resilience can effectively buffer the negative impact of individuals and contribute to improved individual happiness and life satisfaction [ 14 , 15 , 16 , 17 ]. It is essential for nursing students to possess a positive psychological quality in order to effectively cope with academic pressure [ 18 , 19 ]. As resilience research continues to expand and evolve, its scope, focus, and application have diversified across different fields [ 10 , 20 ].

Academic resilience is a relatively new concept. It is the manifestation of resilience in the field of education [ 3 ]. It can assist students in adapting to the demands of school and clinical settings, enabling them to overcome academic pressure [ 21 ]. Resilient students are able to maintain high academic achievement and perform well even when they are faced with the threat of failure or stressful situations [ 22 ]. Therefore, academic resilience is crucial for nursing students [ 23 , 24 , 25 ], and enhancing academic resilience may help students focus on their strengths and potentially reverse academic failure. Furthermore, it can also help more nursing students persist in their nursing education, thereby contributing much-needed nurses to the profession [ 3 ].

Academic resilience is a crucial concept for nursing students in managing academic challenges. However, there are significant differences in the depiction of the conceptual attributes of academic resilience among nursing students, which impedes the advancement of academic research [ 26 , 27 ]. It is necessary to clarify the attributes and connotations of the concept in order to establish a foundation for planning academic resilience intervention measures for nursing students. This will ultimately improve the quality of nursing education and better meet the needs of students. Currently, there is no conceptual analysis of the academic resilience of nursing students. Therefore, the aim of this study is to explore the concept of academic resilience among nursing students.

In this study, Rodgers [ 28 ] evolutionary concept analysis method was applied to explore and clarify the concept of academic resilience of nursing students. The main steps were to determine the concept evolution, application, definition, conceptual attributes, antecedents, consequences of nursing students’ academic resilience, distinguish related concepts of nursing students’ academic resilience. Walker and Avant’s [ 29 ] method was employed to construct a model case and provide empirical referents. The researchers initially read the articles included, focus on the context of the concept, surrogate and related terms, the attributes, antecedents, consequences, and examples, and then analyze the data collected.

Search strategy

Search PubMed, Scopus, Embase, CINAHL, PsycINFO, Web of Science, ProQuest, Science Direct, CNKI, Wanfang Database, VIP database. Full search strategy can be found in the supplemental material.

Selection criteria

Literature inclusion criteria: (1) The subjects were nursing students who were studying in schools or practicing in hospitals. (2) The research contents include the concept, defining characteristics, attributes, antecedents, influencing factors and consequences of academic resilience. Exclusion criteria: (1) The full text cannot be obtained. (1) Repeated reports. (2) Non-Chinese or non-English literature.

Literature screening

The publications were imported into EndNote 20.0 software for de-duplication, the articles was selected independently by two researchers according to inclusion and exclusion criteria. If there was any disagreement, the two researchers would discuss it or invite a third researcher to join the discussion, and the included articles were ultimately determined.

Search results

A total of 918 literature were obtained. Among them, there are 741 English papers and 177 Chinese papers. After screening and exclusion according to the selection criteria, 22 literature were finally included. See Fig.  1 for PRISMA Diagram.

The 22 articles included in this study were published between 2015 and 2023 and were conducted in 8 countries, including 7 in Chinese, 5 in South Korea, 3 in the United Kingdom, 3 in Iran, 1 in Turkey, 1 in Saudi Arabia, 1 in the Philippines, and 1 in Indonesia. Most studies were cross-sectional (70%), with quantitative studies (86%) ranging from 106 to 1339 nursing students and qualitative studies (9%) ranging from 13 to 19 nursing students.

PRISMA diagram of literature search

Conceptual evolution

The development of academic resilience is based on resilience theory [ 30 ]. Due to researchers’ varying perspectives, several different concepts have emerged in the field of education after the introduction of the concept of resilience. Wang et al. [ 31 ]. first proposed this concept and defined it as follows: despite early traits, conditions and experiences creating an unfavorable environment, there is an increased probability of success in school. Based on previous literature, some researchers [ 32 ] have concluded that traditional academic resilience research has primarily focused on students who have suffered severe life experiences (such as changes in their living environment, illness, parental divorce, poverty, discrimination, etc.) during their early years. Despite enduring such adversity for an extended period of time, these students still managed to achieve good academic performance. The significance of academic resilience in recent risk factors (such as unsatisfactory academic performance, academic pressure, etc.) was ignored. Martin [ 22 ] et al. pointed out that academic pressure is a prevalent issue in the daily learning of any school-age student. Every student will encounter recent risk factors such as academic setbacks and pressure. Therefore, the research on academic resilience should shift from the previous minority and special groups to ordinary students. The academic resilience of this group refers to students’ ability to adjust in time after encountering academic setbacks or challenges (including poor academic performance, high levels of academic pressure, etc.) during their daily learning process, while still achieving good academic outcomes [ 33 ].

Application of concepts

The application of academic resilience in the nursing field basically adopted the definition of academic resilience provided by Martin et al. [ 33 ]. This focuses on the role of academic resilience in the proximal influencing factors (the academic pressure perceived by nursing students in their daily learning process). In the field of nursing, these proximal influencing factors generally include adapting to unfamiliar clinical practice environments and interpersonal relationships, feelings of helplessness caused by the gap between theory and practice [ 34 ], fear of infectious diseases, and heavy workloads [ 35 ]. Jeong et al. [ 36 ] believe that academic resilience can serve as a resource for nursing students to protect their mental health from the impact of stress. It is also the ability to attain high academic achievement and sustain strong motivation and enthusiasm for university life even under stressful conditions. Li et al. [ 10 ] argue that academic resilience is specific to the academic situation, referring to students’ ability to overcome setbacks and challenges in their schoolwork. Yang et al. [ 37 ] define academic resilience as the application of resilience within the field of education. In the context of education (usually referring to schools), students are able to effectively adapt to and manage various pressures encountered during the learning process, such as setbacks and failures. This crucial ability enables them to achieve positive learning outcomes. Wang et al. [ 38 ] propose that academic resilience refers to students’ ability to recover from stressful academic situations, enabling them to effectively navigate the challenges associated with the academic achievement process. It is defined as an individual’s capacity to confidently handle, adapt to, or manage important sources of interaction in a stressful learning environment and transform negative clinical learning experiences into positive evolving outcomes. Luo et al. [ 39 ] believe that academic resilience means that nursing students can leverage personal strengths and mobilize external resources when encountering academic difficulties, ultimately leading to a positive adaptation process and successful outcomes. Shi et al. [ 39 ] define academic resilience as the ability of students to successfully cope with typical academic setbacks in school daily learning activities, reflecting their perseverance and learning capability. According to Shahidi et al. [ 40 ], academic resilience is a crucial quality of nursing students, enabling them to overcome academic pressure and adapt to the demands of both learning and clinical practice.

In summary, after conducting in-depth research on academic resilience of nursing students, researchers have presented various viewpoints. However, an exact and comprehensive definition has not yet been established.

Definition of nursing student’s academic resilience

After conducting a thorough review and analysis of the literature, this study found that the academic resilience of nursing students is affected by a complex interaction of various factors, including internal factors of nursing students and external environmental factors. Through the analysis of the attributes, antecedents and consequences of nursing students’ academic resilience, the following definitions were obtained: when faced with academic challenges, nursing students maintain a belief in their capacity to overcome these obstacles. They proactively regulate their cognition and behavior, leverage their personal and external resources to adapt effectively to both school educational and clinical settings, ultimately achieving positive learning outcomes.

Attributes are a set of features or components of a concept. Clarifying the defining attributes of a concept helps to deepen the understanding of the concept, which is an important aspect of concept analysis [ 41 ]. Through literature analysis and induction, this study summarized three core attributes of nursing students’ academic resilience, including self-efficacy, self-regulation and recovery.

Self-efficacy.

Self-efficacy is confidence and belief [ 42 ], which refers to an individual’s belief in their ability to control outcomes, successfully complete tasks, and possess the necessary skills to accomplish those tasks [ 43 ]. It is one of the internal attributes and driving force of nursing students’ academic resilience. Improving the self-confidence of nursing students is the initial step of constructive learning, particularly when faced with academic challenges. Confidence enables students to seize learning opportunities, actively analyze and assess dilemmas they encounter, and positively impacts their ability to cope with academic pressure [ 38 , 44 ].

Self-regulation.

Self-regulation is one of the important elements of resilience [ 45 ], which refers to the regulation of thinking, emotion, behavior and attention through deliberate or specific mechanisms. This enables individuals to effectively manage their activities over time and environmental changes [ 46 ], as well as helping them to control emotions and actions under pressure. This attribute includes cognitive regulation and behavioral regulation. Cognitive regulation: When facing academic setbacks, nursing students can positively view setbacks by cognitive reconstruction, emotional adjustment, reconstructing negative thoughts and re-attribution [ 47 ], thereby enhancing their self-efficacy to overcome difficulties. Behavioral adjustment: In the face of academic pressure or challenges, individuals have to adjust their original coping strategies, assess their own advantages, mobilize available resources within their reach, re-integrate personal resources and social resources, make the most of all available resources to overcome academic difficulties [ 48 , 49 ].

Recovery is defined as the outcome of becoming well again after an illness or injury, according to the Oxford Dictionary. As one attribute of academic resilience, it refers to the outcome that nursing students rebound from adversity, and return to the right track or enter a new balance in this paper [ 38 , 44 ].

Antecedents

Antecedents refer to the events or situations that should exist prior to the development of a concept [ 41 ]. Based on Kumpfer’s psychological resilience model [ 49 ], a review of previous studies has identified two categories of antecedents for nursing students’ academic resilience: individual internal factors and external factors.

Studies have indicated that the academic resilience of nursing students is influenced by various internal factors. (1) social demographic factors: research has demonstrated that as age [ 40 ] and grade [ 39 , 50 , 51 ] levels increase, along with a higher educational background among nursing students [ 52 ], there is a corresponding enhancement in academic resilience. Additionally, studies have revealed that female nursing students exhibit greater academic resilience compared to male students [ 3 , 50 ], while rural students tend to demonstrate higher levels of academic resilience than urban students [ 52 ]. Moreover, it has been found that non-only-child students generally display higher academic resilience when compared to only-child students [ 53 ]. (2) Spiritual factors: Studies have shown that nursing students with an optimistic attitude [ 44 , 54 ], high levels of mindfulness [ 38 , 51 ], strong self-confidence [ 44 ], effective self-control ability [ 37 , 44 ], high learning engagement [ 55 ] and strong religious coping ability [ 56 ] are conducive to the development of academic resilience. Furthermore, nursing students who independently choose to study nursing as their major demonstrate higher academic resilience than those recommended by relatives and friends or those who are transferred into the major [ 52 ]. Additionally, nursing students with role models exhibit higher academic resilience than those without role models [ 3 ]. (3) Emotional factors: Research has indicated that higher levels of emotional intelligence [ 44 , 54 ] is linked to increased academic resilience among nursing students. In addition, when faced with academic setbacks, nursing students may employ different coping styles [ 36 ], which can also impact their academic resilience. (4) Cognitive factors: Literature has shown that nursing students with high levels of academic performance [ 3 , 36 , 40 , 57 ], scholarship [ 52 ], self-directed learning ability [ 54 ] and skill level [ 38 ] also have high academic resilience. (5) Physical factors: Nursing students with good subjective health status demonstrate higher academic resilience than those with poor subjective health status [ 54 ]. (6) Behavioral factors: Nursing students’ interpersonal communication ability [ 57 ] are also influential factors in their academic resilience.

The level of nursing students’ academic resilience is not only affected by internal factors of individuals, but also restricted by external factors. (1) school factors: Studies have indicated that high pressure in school life [ 54 ] and low professional satisfaction [ 3 , 36 , 54 ] are hindering factors for nursing students’ academic resilience. Moreover, a positive clinical work atmosphere [ 38 ], strong interpersonal relationships at school [ 3 ], encouragement and support from teachers [ 38 , 44 ], as well as support from patients and their families [ 38 ] and recognition [ 38 ] during clinical practicum were promoting factors of academic resilience. (2) Family factors: Literature has shown that high levels of family relationship satisfaction [ 3 ], effective family communication mode [ 57 ] and strong family support [ 38 ] contribute to the improvement of academic resilience. (3) Peer group factors: Peer support [ 38 , 58 ] and good peer’s interpersonal relationship [ 3 ] can also promote the enhancement of nursing students’ academic resilience.

Consequences

Consequences refer to the events or situations caused by the concept [ 41 ]. Studies [ 21 , 38 , 39 , 52 , 55 , 59 ] have indicated that academic resilience plays a significant role in enhancing nursing students’ adaptability during the school period, career maturity, adversity quotient level, probability of academic success and a sense of belonging to school. Additionally, it has been found to reduce the degree of psychological distress experienced by nursing students. “Career maturity” refers to the extent to which individuals are able to accomplish tasks that are coordinated with their stage of career development [ 52 ]. “Adversity quotient level” refers to an individual’s ability to cope with setbacks and adversity [ 39 ].

Related concepts

Related concepts refer to words that share commonalities with concepts but do not possess identical characteristics. Academic buoyancy refers to a student’s capacity to successfully cope with the academic setbacks and challenges typical of school life. Unlike academic resilience, academic buoyancy is more closely related to how a student handles the everyday stressors commonly experienced by students, such as tight deadlines, challenging assignments, exam stress, and unexpected or persistent low grades. However, resilience plays a role when students suffer from long-term poor performance, overwhelming anxiety that they cannot bear, truancy, and significant setbacks due to dissatisfaction [ 60 ]. Academic hardiness is defined as the ability to prepare oneself to confront academic problems. It comprises three components: control (the ability to manage different life situations), commitment (willingness to engage) and challenge (the ability to understand that changes in life are normal), emphasizing individuals’ endurance in the face of difficulties [ 61 , 62 ].

The concept analysis of model case is beneficial to better understand and identify the connotation of concepts [ 41 ]. Although Rodgers does not suggest the creation of a model case, in order to better understand the concept, we used Walker and Avant’s [ 29 ] method to construct a model case as follows.

Lucy, 22 years old, is a member of a family consisting of four members (father, mother and brother), with very harmonious family relations. As a junior student, Lucy has a passion for medicine and has taken the initiative to study nursing at university in pursuit of a bachelor’s degree. After three years of theoretical study, she entered a large hospital to begin clinical practice and complete the final stage of her undergraduate education. Lucy’s first internship took place in the emergency ward of a hospital. Faced with an unfamiliar clinical environment, heavy medical workloads, anxious patients and their families, as well as sudden situations (such as the rescue of patients and unexpected deaths, etc.), Lucy experienced significant pressure. Due to the gap between theoretical knowledge and clinical practice and inexperienced nursing skills, Lucy was afraid of providing nursing interventions for patients and making mistakes. Every day when she went to the hospital for her internship, Lucy felt extremely anxious. During conversations with her family members, Lucy confided in them about her troubles. Her family listened patiently to Lucy’s difficulties and offered positive affirmation and encouragement. They believed that Lucy would overcome the current difficulties and become a qualified nurse. With the encouragement of her family, Lucy recalled her initial decision to pursue a career in nursing voluntarily, aspiring to be someone who could alleviate patients’ suffering like Florence Nightingale. She then adjusted her mindset and earnestly contemplated how to confront and surmount the present difficulties with a positive outlook. She firmly believed that she could triumph over the current predicament through her diligent efforts. Lucy took the initiative to contact the senior students and inquire about their experiences in adapting to the clinical environment during their internship. Drawing on their experience, she utilized her solid theoretical knowledge from the initial three years of study for understanding new knowledge in clinical work. Throughout her internship, Lucy carefully observed the operations of her mentor, diligently recorded any challenges encountered, sought clarification when needed, and dedicated herself to repeated practice. The mentor also affirmed Lucy’s efforts and gave timely feedback to her operation, which significantly enhanced Lucy’s nursing skills and bolstered her confidence. In order to maintain a healthy physical state for clinical work, Lucy conscientiously balanced her study and rest time. Additionally, she incorporated mindfulness exercises into her routine to relax both body and mind while improving focus and reducing distress related to professional challenges. Through her efforts, Lucy earned recognition from patients and their families while experiencing a profound sense of accomplishment when performing patient care procedures. Finally, she successfully completed her internship tasks and obtained a bachelor’s degree in nursing.

Lucy’s case exemplifies the three attributes of nursing students’ academic resilience, namely self-efficacy, self-regulation and recovery. Upon entering the clinical practice stage, Lucy experienced significant pressure but maintained a belief in her ability to overcome challenges through diligent effort. She actively analyzed her current station and seized learning opportunities, reflecting the first attribute of academic resilience, self-efficacy. Through cognitive reconstruction and emotional adjustment, Lucy approached her difficulties with a positive attitude and effectively utilized her strengths to navigate the challenges she faced. For instance, she has established a solid foundation for theoretical learning, confided her difficulties with her family, sought assistance from her seniors and mentors, maintained good health, utilizing available internal and external resources around her. By regulating one’s own cognition and behavior to overcome academic challenges, demonstrating the second attribute of academic resilience, self-regulation. By actively analyzing the dilemma she faced, adjusting her own thoughts and behaviors, integrating internal and external resources, Lucy successfully rebounded from adversity. She adapted to the clinical pressure environment and ultimately completed the internship task. This reflects the third attribute recovery of academic resilience. The stress induced by clinical practice, Lucy’s optimistic attitude, high levels of mindfulness, independent choice of nursing major, role model, high levels of emotional intelligence, positive coping style, good academic achievement, healthy physical state, high self-directed learning ability, self-control ability, interpersonal communication ability, skill level, support from mentors, family members, patients and their family members, peers all contribute to the enhancement of Lucy’s academic resilience. The improvement of Lucy’s adaptability, career maturity, adversity quotient level and the reduction of her psychological distress during her clinical internship are the consequences of her academic resilience.

Empirical referents

In order to gain a better understanding of the concept, we used Walker and Avant’s [ 29 ] method to provide empirical referents. Currently, there are two primary tools for evaluating nursing students’ academic resilience. One is the Nursing Student Academic Resilience Inventory (NSARI) developed by Iranian scholar Ali-Abadi [ 27 ], which comprises a total of 24 items. The six dimensions include optimism (5 items), communication (4 items), self-esteem/evaluation (4 items), self-awareness (3 items), trustworthiness (4 items) and self-regulation (4 items). The scale employed a 5-point Likert scale ranging from completely agree (5 points) to completely disagree (1 point), with scores requiring conversion into standardized scores. Higher scores indicate higher levels of academic resilience. The intraclass correlation coefficient of the scale was 0.903, and the Cronbach’ α coefficient of the scale was 0.66–0.78, indicating good reliability and validity. This instrument was developed with undergraduate nursing students as the research subjects and specifically used to measure the academic resilience of nursing students. It has been applied to undergraduate nursing students in Iran [ 40 ]. Additionally, Turkish scholar Enes Ucan [ 63 ] et al. conducted cross-cultural adaptation of the tool.

The other is Academic Resilience Inventory for Nursing Students (ARINS) developed by Li Chengjie [ 10 ], a scholar from Taiwan, China. The scale contains a total of 15 items, including three dimensions: cognitive maturity (5 items), emotional regulation (3 items) and help-seeking resources (7 items). The 5-point Likert scale ranging from “very inconsistent” (1 point) to “very consistent” (5 points) was employed, with higher scores indicating higher levels of academic resilience. The Cronbach’s α coefficient of the total scale was 0.929. The Cronbach’s α coefficients of the three dimensions of cognitive maturity, emotional regulation and help-seeking resources were 0.926, 0.801 and 0.855, respectively. The theoretical model exhibited a good fit with the observation data. The total scale demonstrated excellent reliability and validity. Originally designed to measure the academic resilience of nursing students holding junior college degrees in Taiwan. Additionally, it has been applied in undergraduate nursing students in Chinese mainland [ 37 , 55 ] while showing good reliability and validity. However, further investigation is required to determine these tools’ applicability among nursing students at different educational levels.

Disscussion

The conceptual model of nursing students’ academic resilience.

Through a comprehensive analysis and synthesis of literature, this study has developed a conceptual model of nursing students’ academic resilience, as shown in Fig.  2 . In essence, the academic resilience of nursing students is shaped by the interplay between internal and external factors when they encounter setbacks or challenges in their academic pursuits. This interaction ultimately fosters the development of academic resilience among nursing students and yields positive outcomes. Nursing students with high levels of academic resilience are able to view academic setbacks positively, enhance their problem-solving skills, and effectively navigate through academic difficulties, thereby successfully completing their studies and go to the future nursing position [ 42 ].

Model of nursing student’s academic resilience

The significance of the role of nurses for the nursing students’ academic resilience

The definition and attributes of nursing students’ academic resilience proposed in this study emphasize the characteristics of nurses’ working environment and learning environment of nursing students. Nurses play a crucial role as providers of healthcare services, taking on important medical tasks with increasingly complex professional responsibilities. They possess multifaceted roles as healthcare providers, strategists, administrators, educators, and coordinators [ 64 , 65 ]. This necessitates not only a solid foundation of professional knowledge and skills but also profound critical thinking and judgment abilities, astute observational and analytical capabilities, decisive decision-making prowess, and exceptional interpersonal communication aptitude [ 66 ]. These qualities enable them to effectively manage busy and high-pressure clinical tasks within an increasingly tense doctor-patient relationship, ultimately providing satisfactory medical services to patients and their families. As the reserve army of the nursing team, nursing students are expected to quickly acquire these knowledge and abilities during their theoretical learning and clinical practice, thereby imposing significant academic pressure on them [ 67 ]. Simultaneously, it is these qualities that distinguish nursing from other specialties and healthcare disciplines. It is hoped that the results of this concept analysis will inspire further research into effective measures aimed at enhancing the academic resilience of nursing students, in order to improve their ability to cope with academic setbacks and increase retention rates of nurses.

Implications and recommendations

Currently, there are relatively few studies on the academic resilience of nursing students, and there are significant discrepancies in the definition of conceptual attributes among nursing students’ academic resilience in the existing literature. This study addresses this gap by providing a comprehensive conceptualization of academic resilience of nursing students by combing the related concepts, attributes, antecedence and consequences of nursing students’ academic resilience. The findings offer a theoretical foundation for future research.

Academic resilience plays a crucial role in regulating individuals’ pressure levels, enhancing their problem-solving abilities, and supporting nursing students in successfully completing their academic studies and transitioning into future nursing positions [ 42 ]. This study provides a conceptual framework for nursing schools and hospitals to design academic resilience training curricula and programs for nursing students. It is essential to thoroughly investigate these relationships based on the nursing context through appropriate measures. This process can clearly define attributes, antecedence, and consequences of nursing students’ academic resilience. Nursing educators can begin by focusing on the antecedence and attributes of nursing students’ academic resilience. This can be achieved through targeted training programs or specialized courses aimed at improving emotional intelligence, interpersonal communication skills, self-directed learning capabilities, self-control, self-regulation, and self-efficacy among nursing students. In addition, nursing educators can also consider external environmental factors. This includes creating a conducive learning and working atmosphere for nursing students, providing training for professional teachers and clinical instructors, setting a professional example for nursing students, offering timely guidance, feedback and encouragement to support students’ learning. Moreover, it’s important to guide nursing students to think positively, helping them build self-confidence, and enhance their academic confidence. Additionally, peer support programs can be designed. Existing research [ 68 ] suggests that interaction and practice among nursing students with similar knowledge, skills, and experience can promote the effective learning. The experience of other students in internship and studies can help build confidence and resilience in academic research while reducing concerns about academic issues and clinical practice. It is helpful for nursing students to improve their self-esteem and confidence in academic success which can enhance their resilience.

This study has discovered that academic resilience of nursing students is associated with several key outcomes, including academic success, career maturity, adversity quotient and school sense of belonging. Additionally, it has been found to have a positive impact on reducing psychological distress among nursing students. As a result, nursing educators can consider targeting academic resilience as an intervention strategy in order to indirectly improve these outcomes for students.

Limitations

Due to language limitations, only English and Chinese literature were included in this study. Although the relevant literature was searched as comprehensively and scientifically as possible, grey literature sources were not included. In addition, due to limitations of some database resources, 14% of the literature was not obtained in full text. Nevertheless, this study explored the concept, attributes, antecedents and consequences of nursing students’ academic resilience through the obtained studies and achieved the research purpose.

This study applied Rodgers’ evolutionary concept analysis method to clarify the conceptual attributes, antecedents, consequences and related concepts of academic resilience among nursing students, and combined with model case to help understand the concept. The clear definition of nursing students’ academic resilience is beneficial for both nursing educators and nursing students themselves. It allows them more accurately assess the level of academic resilience and explore effective intervention measures to improve the level of academic resilience and increase the probability of academic success of nursing students.

Data availability

All data generated or analyzed during this study is included in this published article.

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Home » Data Analysis – Process, Methods and Types

Data Analysis – Process, Methods and Types

Table of Contents

Data Analysis

Definition:

Data analysis refers to the process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, drawing conclusions, and supporting decision-making. It involves applying various statistical and computational techniques to interpret and derive insights from large datasets. The ultimate aim of data analysis is to convert raw data into actionable insights that can inform business decisions, scientific research, and other endeavors.

Data Analysis Process

The following are step-by-step guides to the data analysis process:

Define the Problem

The first step in data analysis is to clearly define the problem or question that needs to be answered. This involves identifying the purpose of the analysis, the data required, and the intended outcome.

Collect the Data

The next step is to collect the relevant data from various sources. This may involve collecting data from surveys, databases, or other sources. It is important to ensure that the data collected is accurate, complete, and relevant to the problem being analyzed.

Clean and Organize the Data

Once the data has been collected, it needs to be cleaned and organized. This involves removing any errors or inconsistencies in the data, filling in missing values, and ensuring that the data is in a format that can be easily analyzed.

Analyze the Data

The next step is to analyze the data using various statistical and analytical techniques. This may involve identifying patterns in the data, conducting statistical tests, or using machine learning algorithms to identify trends and insights.

Interpret the Results

After analyzing the data, the next step is to interpret the results. This involves drawing conclusions based on the analysis and identifying any significant findings or trends.

Communicate the Findings

Once the results have been interpreted, they need to be communicated to stakeholders. This may involve creating reports, visualizations, or presentations to effectively communicate the findings and recommendations.

Take Action

The final step in the data analysis process is to take action based on the findings. This may involve implementing new policies or procedures, making strategic decisions, or taking other actions based on the insights gained from the analysis.

Types of Data Analysis

Types of Data Analysis are as follows:

Descriptive Analysis

This type of analysis involves summarizing and describing the main characteristics of a dataset, such as the mean, median, mode, standard deviation, and range.

Inferential Analysis

This type of analysis involves making inferences about a population based on a sample. Inferential analysis can help determine whether a certain relationship or pattern observed in a sample is likely to be present in the entire population.

Diagnostic Analysis

This type of analysis involves identifying and diagnosing problems or issues within a dataset. Diagnostic analysis can help identify outliers, errors, missing data, or other anomalies in the dataset.

Predictive Analysis

This type of analysis involves using statistical models and algorithms to predict future outcomes or trends based on historical data. Predictive analysis can help businesses and organizations make informed decisions about the future.

Prescriptive Analysis

This type of analysis involves recommending a course of action based on the results of previous analyses. Prescriptive analysis can help organizations make data-driven decisions about how to optimize their operations, products, or services.

Exploratory Analysis

This type of analysis involves exploring the relationships and patterns within a dataset to identify new insights and trends. Exploratory analysis is often used in the early stages of research or data analysis to generate hypotheses and identify areas for further investigation.

Data Analysis Methods

Data Analysis Methods are as follows:

Statistical Analysis

This method involves the use of mathematical models and statistical tools to analyze and interpret data. It includes measures of central tendency, correlation analysis, regression analysis, hypothesis testing, and more.

Machine Learning

This method involves the use of algorithms to identify patterns and relationships in data. It includes supervised and unsupervised learning, classification, clustering, and predictive modeling.

Data Mining

This method involves using statistical and machine learning techniques to extract information and insights from large and complex datasets.

Text Analysis

This method involves using natural language processing (NLP) techniques to analyze and interpret text data. It includes sentiment analysis, topic modeling, and entity recognition.

Network Analysis

This method involves analyzing the relationships and connections between entities in a network, such as social networks or computer networks. It includes social network analysis and graph theory.

Time Series Analysis

This method involves analyzing data collected over time to identify patterns and trends. It includes forecasting, decomposition, and smoothing techniques.

Spatial Analysis

This method involves analyzing geographic data to identify spatial patterns and relationships. It includes spatial statistics, spatial regression, and geospatial data visualization.

Data Visualization

This method involves using graphs, charts, and other visual representations to help communicate the findings of the analysis. It includes scatter plots, bar charts, heat maps, and interactive dashboards.

Qualitative Analysis

This method involves analyzing non-numeric data such as interviews, observations, and open-ended survey responses. It includes thematic analysis, content analysis, and grounded theory.

Multi-criteria Decision Analysis

This method involves analyzing multiple criteria and objectives to support decision-making. It includes techniques such as the analytical hierarchy process, TOPSIS, and ELECTRE.

Data Analysis Tools

There are various data analysis tools available that can help with different aspects of data analysis. Below is a list of some commonly used data analysis tools:

• Microsoft Excel: A widely used spreadsheet program that allows for data organization, analysis, and visualization.
• SQL : A programming language used to manage and manipulate relational databases.
• R : An open-source programming language and software environment for statistical computing and graphics.
• Python : A general-purpose programming language that is widely used in data analysis and machine learning.
• Tableau : A data visualization software that allows for interactive and dynamic visualizations of data.
• SAS : A statistical analysis software used for data management, analysis, and reporting.
• SPSS : A statistical analysis software used for data analysis, reporting, and modeling.
• Matlab : A numerical computing software that is widely used in scientific research and engineering.
• RapidMiner : A data science platform that offers a wide range of data analysis and machine learning tools.

Applications of Data Analysis

Data analysis has numerous applications across various fields. Below are some examples of how data analysis is used in different fields:

• Business : Data analysis is used to gain insights into customer behavior, market trends, and financial performance. This includes customer segmentation, sales forecasting, and market research.
• Healthcare : Data analysis is used to identify patterns and trends in patient data, improve patient outcomes, and optimize healthcare operations. This includes clinical decision support, disease surveillance, and healthcare cost analysis.
• Education : Data analysis is used to measure student performance, evaluate teaching effectiveness, and improve educational programs. This includes assessment analytics, learning analytics, and program evaluation.
• Finance : Data analysis is used to monitor and evaluate financial performance, identify risks, and make investment decisions. This includes risk management, portfolio optimization, and fraud detection.
• Government : Data analysis is used to inform policy-making, improve public services, and enhance public safety. This includes crime analysis, disaster response planning, and social welfare program evaluation.
• Sports : Data analysis is used to gain insights into athlete performance, improve team strategy, and enhance fan engagement. This includes player evaluation, scouting analysis, and game strategy optimization.
• Marketing : Data analysis is used to measure the effectiveness of marketing campaigns, understand customer behavior, and develop targeted marketing strategies. This includes customer segmentation, marketing attribution analysis, and social media analytics.
• Environmental science : Data analysis is used to monitor and evaluate environmental conditions, assess the impact of human activities on the environment, and develop environmental policies. This includes climate modeling, ecological forecasting, and pollution monitoring.

When to Use Data Analysis

Data analysis is useful when you need to extract meaningful insights and information from large and complex datasets. It is a crucial step in the decision-making process, as it helps you understand the underlying patterns and relationships within the data, and identify potential areas for improvement or opportunities for growth.

Here are some specific scenarios where data analysis can be particularly helpful:

• Problem-solving : When you encounter a problem or challenge, data analysis can help you identify the root cause and develop effective solutions.
• Optimization : Data analysis can help you optimize processes, products, or services to increase efficiency, reduce costs, and improve overall performance.
• Prediction: Data analysis can help you make predictions about future trends or outcomes, which can inform strategic planning and decision-making.
• Performance evaluation : Data analysis can help you evaluate the performance of a process, product, or service to identify areas for improvement and potential opportunities for growth.
• Risk assessment : Data analysis can help you assess and mitigate risks, whether it is financial, operational, or related to safety.
• Market research : Data analysis can help you understand customer behavior and preferences, identify market trends, and develop effective marketing strategies.
• Quality control: Data analysis can help you ensure product quality and customer satisfaction by identifying and addressing quality issues.

Purpose of Data Analysis

The primary purposes of data analysis can be summarized as follows:

• To gain insights: Data analysis allows you to identify patterns and trends in data, which can provide valuable insights into the underlying factors that influence a particular phenomenon or process.
• To inform decision-making: Data analysis can help you make informed decisions based on the information that is available. By analyzing data, you can identify potential risks, opportunities, and solutions to problems.
• To improve performance: Data analysis can help you optimize processes, products, or services by identifying areas for improvement and potential opportunities for growth.
• To measure progress: Data analysis can help you measure progress towards a specific goal or objective, allowing you to track performance over time and adjust your strategies accordingly.
• To identify new opportunities: Data analysis can help you identify new opportunities for growth and innovation by identifying patterns and trends that may not have been visible before.

Examples of Data Analysis

Some Examples of Data Analysis are as follows:

• Social Media Monitoring: Companies use data analysis to monitor social media activity in real-time to understand their brand reputation, identify potential customer issues, and track competitors. By analyzing social media data, businesses can make informed decisions on product development, marketing strategies, and customer service.
• Financial Trading: Financial traders use data analysis to make real-time decisions about buying and selling stocks, bonds, and other financial instruments. By analyzing real-time market data, traders can identify trends and patterns that help them make informed investment decisions.
• Traffic Monitoring : Cities use data analysis to monitor traffic patterns and make real-time decisions about traffic management. By analyzing data from traffic cameras, sensors, and other sources, cities can identify congestion hotspots and make changes to improve traffic flow.
• Healthcare Monitoring: Healthcare providers use data analysis to monitor patient health in real-time. By analyzing data from wearable devices, electronic health records, and other sources, healthcare providers can identify potential health issues and provide timely interventions.
• Online Advertising: Online advertisers use data analysis to make real-time decisions about advertising campaigns. By analyzing data on user behavior and ad performance, advertisers can make adjustments to their campaigns to improve their effectiveness.
• Sports Analysis : Sports teams use data analysis to make real-time decisions about strategy and player performance. By analyzing data on player movement, ball position, and other variables, coaches can make informed decisions about substitutions, game strategy, and training regimens.
• Energy Management : Energy companies use data analysis to monitor energy consumption in real-time. By analyzing data on energy usage patterns, companies can identify opportunities to reduce energy consumption and improve efficiency.

Characteristics of Data Analysis

Characteristics of Data Analysis are as follows:

• Objective : Data analysis should be objective and based on empirical evidence, rather than subjective assumptions or opinions.
• Systematic : Data analysis should follow a systematic approach, using established methods and procedures for collecting, cleaning, and analyzing data.
• Accurate : Data analysis should produce accurate results, free from errors and bias. Data should be validated and verified to ensure its quality.
• Relevant : Data analysis should be relevant to the research question or problem being addressed. It should focus on the data that is most useful for answering the research question or solving the problem.
• Comprehensive : Data analysis should be comprehensive and consider all relevant factors that may affect the research question or problem.
• Timely : Data analysis should be conducted in a timely manner, so that the results are available when they are needed.
• Reproducible : Data analysis should be reproducible, meaning that other researchers should be able to replicate the analysis using the same data and methods.
• Communicable : Data analysis should be communicated clearly and effectively to stakeholders and other interested parties. The results should be presented in a way that is understandable and useful for decision-making.

Advantages of Data Analysis

Advantages of Data Analysis are as follows:

• Better decision-making: Data analysis helps in making informed decisions based on facts and evidence, rather than intuition or guesswork.
• Improved efficiency: Data analysis can identify inefficiencies and bottlenecks in business processes, allowing organizations to optimize their operations and reduce costs.
• Increased accuracy: Data analysis helps to reduce errors and bias, providing more accurate and reliable information.
• Better customer service: Data analysis can help organizations understand their customers better, allowing them to provide better customer service and improve customer satisfaction.
• Competitive advantage: Data analysis can provide organizations with insights into their competitors, allowing them to identify areas where they can gain a competitive advantage.
• Identification of trends and patterns : Data analysis can identify trends and patterns in data that may not be immediately apparent, helping organizations to make predictions and plan for the future.
• Improved risk management : Data analysis can help organizations identify potential risks and take proactive steps to mitigate them.
• Innovation: Data analysis can inspire innovation and new ideas by revealing new opportunities or previously unknown correlations in data.

Limitations of Data Analysis

• Data quality: The quality of data can impact the accuracy and reliability of analysis results. If data is incomplete, inconsistent, or outdated, the analysis may not provide meaningful insights.
• Limited scope: Data analysis is limited by the scope of the data available. If data is incomplete or does not capture all relevant factors, the analysis may not provide a complete picture.
• Human error : Data analysis is often conducted by humans, and errors can occur in data collection, cleaning, and analysis.
• Cost : Data analysis can be expensive, requiring specialized tools, software, and expertise.
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Muhammad Hassan

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• Open access
• Published: 13 July 2024

A compartmental model for smoking dynamics in Italy: a pipeline for inference, validation, and forecasting under hypothetical scenarios

• Alessio Lachi 1 , 2 ,
• Cecilia Viscardi 1 , 3 ,
• Giulia Cereda 1 , 3 ,
• Giulia Carreras 4 &
• Michela Baccini 1 , 3  

BMC Medical Research Methodology volume  24 , Article number:  148 ( 2024 ) Cite this article

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We propose a compartmental model for investigating smoking dynamics in an Italian region (Tuscany). Calibrating the model on local data from 1993 to 2019, we estimate the probabilities of starting and quitting smoking and the probability of smoking relapse. Then, we forecast the evolution of smoking prevalence until 2043 and assess the impact on mortality in terms of attributable deaths. We introduce elements of novelty with respect to previous studies in this field, including a formal definition of the equations governing the model dynamics and a flexible modelling of smoking probabilities based on cubic regression splines. We estimate model parameters by defining a two-step procedure and quantify the sampling variability via a parametric bootstrap. We propose the implementation of cross-validation on a rolling basis and variance-based Global Sensitivity Analysis to check the robustness of the results and support our findings. Our results suggest a decrease in smoking prevalence among males and stability among females, over the next two decades. We estimate that, in 2023, 18% of deaths among males and 8% among females are due to smoking. We test the use of the model in assessing the impact on smoking prevalence and mortality of different tobacco control policies, including the tobacco-free generation ban recently introduced in New Zealand.

Peer Review reports

Smoking is a significant risk factor for many common chronic diseases, including cancer, cardiovascular, cerebrovascular and respiratory diseases, diabetes, and a leading preventable cause of premature death [ 1 , 2 ]. Also, smoking reduces length and quality of life [ 3 ], and contributes to health inequities [ 4 ]. The Global Burden of Disease study [ 5 ] reports that in 2019 smoking was responsible for around 8,709,000 deaths in the World (15.4% of all deaths), 907,000 in Europe, and 96,000 in Italy.

The importance of Tobacco Control Policies (TCP) has been firmly established within the World Health Organization’s (WHO) Framework Convention on Tobacco Control (FCTC), an international treaty that came into force in 2005 and has been ratified by 182 countries. Specifically, tobacco control has been included as one of the global development goals, recognized as crucial and necessary to achieve a one-third reduction in premature mortality by 2030 [ 6 ].

Focusing on Italy, data from the Italian surveillance system PASSI (Progressi delle Aziende Sanitarie per la Salute in Italia) highlighted that in 2021 23.7% of Italians (27.2% in men and 20.2% in women) described themselves as current smokers [ 7 ]. Among adolescents, smoking prevalence stalled in the last years, with a prevalence of current smokers between 27.3% and 32.4% in young people aged 13-16 years [ 8 , 9 ].

Dynamic simulation models are widely used to describe and project the evolution of smoking habits in the population over time and to estimate the impact of past and hypothetical future TCPs. Since the 2000s, several models have been proposed [ 10 , 11 , 12 , 13 ], some of which developed within the Cancer Intervention and Surveillance Modelling Network (CISNET), a consortium of investigators funded by the National Cancer Institute, that uses mathematical modelling to study the impact of cancer control interventions [ 14 ]. These models are mainly of two types: compartmental models and agent-based models. Compartmental models, starting from a baseline year, perform macro-simulations so that the population evolves through deaths, births and changes in smoking habits [ 10 , 11 , 12 ]. The SimSmoke model [ 15 ] is the most used compartmental model [ 16 ], implemented for a wide number of countries including Italy [ 17 , 18 , 19 , 20 ]. Agent-based models, also called micro-simulation models, simulate individual life trajectories and interactions with a view to assessing their effects on the system as a whole [ 21 , 22 ].

In this paper, grounding on previous works [ 12 , 23 , 24 , 25 ], we developed a compartmental model that describes the evolution of smoking habits in Tuscany, a region of Central Italy, from 1993 to 2019, and forecasts them until 2043. The model assumes that at each point in time, the population is divided into non-overlapping groups called compartments, defined according to smoking status (never, current, and former smokers), age and sex [ 26 ]. Transitions between compartments are described by simple probabilistic rules and the evolution of the size of the compartments is governed by a system of differential equations.

While some of the transition parameters in the model were assumed as fixed, we estimated via a two-step calibration the age-specific probabilities of starting and quitting smoking, modelled in a flexible way through cubic regression splines [ 27 ], the probability of relapsing smoking, modelled as a nonlinear function of the time from quitting [ 28 ], and the mortality rate. We calibrated the model on the observed prevalence of never, current, and former smokers for the years from 1993 to 2019, arising from yearly local surveys.

Once we estimated the transition parameters, we predicted the prevalence of never, current, and former smokers in the regional population over time, and quantified the impact of smoking in terms of the number of smoking-attributable deaths (SAD) and population attributable fraction (PAF). With simple examples, we also illustrated the use of the compartmental model to predict the future impact of hypothetical interventions that act on the probabilities of starting and quitting smoking.

Compared to previous studies that dealt with the same problem, we aimed at presenting some methodological advances both in the modelling and estimation strategies. First of all, grounding on a formal definition of the model equations, we addressed the problem of accounting for sampling variability and provided confidence intervals for the estimates of the parameters and compartment sizes. To this end, due to the unavailability of the likelihood function associated with the model, we relied on a parametric bootstrap procedure [ 29 , 30 ]. Also, we introduced a flexible modelling of the probabilities of starting and stopping smoking, usually assumed as constant, allowing them to change over time as functions of age. Moreover, we assessed the predictive performance of the model using cross-validation on a rolling basis. Finally, we assessed parameter identifiability through Global Sensitivity Analysis (GSA) [ 31 ].

The analyses relied on data from heterogeneous sources. We used data from the National Institute of Statistics (ISTAT) Multipurpose Surveys “Aspect of Daily Life" (AVQ) ( www.istat.it/it/archivio/91926 ), which every year collect fundamental information related to the daily life of individuals and families in Italy, enrolling about 25,000 families distributed in about 800 Italian municipalities of different population sizes. Specifically, we obtained from the ISTAT AVQ surveys an estimate of the distribution by smoking habit (never, current, and former smokers) of the population residing in Tuscany for each year from 1993 to 2019, separately for males and females and by age class (14-17, 18-19, 20-24, 25-34, 35-44, 45-54, 55-59, 60-64, 65-74, 75+). We obtained from the same surveys the smoking intensity distribution for current smokers, by sex and age class.

We used data from the ISTAT Multipurpose Surveys European Health Survey (EHIS) ( www.istat.it/it/archivio/167485 ), a survey on the main aspects of public health carried out every 5 years from 1980 in all member states of the European Union, to obtain an estimate of the smoking intensity distribution among former smokers, as well as information about time since smoking cessation, separately for males and females and by the same age classes reported above. In particular, we considered the surveys for 1994, 1999, 2004, and 2013.

We obtained the size of the Tuscany population on January 1st 1993 and January 1st 2005, by age and sex, from the ISTAT website ( www.istat.it ). From the same website, we got the mortality rates by age and sex and the number of new births in Tuscany for the period 1993-2019. The relative risks (RRs) of death for smokers and ex-smokers versus never smokers are those reported in the Appendix of [ 32 ].

Model specification

We specified a compartmental model for smoking habit dynamics in the population, which we call Smoking Habits Compartmental (SHC) model. In order to better present the SHC model adopted for the analysis, we first introduce a simpler version of it, and then proceed step by step, adding elements of complexity.

The starting model assumes that at each time the alive population is divided into the following non-overlapping compartments: never ( N ), current ( C ), and former ( F ) smokers. We consider only cigarette smoking. Never smokers can become current smokers, current smokers can become former smokers, and former smokers may restart smoking (smoking relapse). The compartments C and F are further divided into sub-compartments denoted by \(C_i\) and \(F_i\) , where \(i\in \{l,m,h\}\) indicates the level of smoking intensity, corresponding to low (<10 cigarettes/day), medium ( \(\ge\) 10 and <20 cigarettes/day), and high ( \(\ge\) 20 cigarettes/day) smoking intensity, respectively. During their life, individuals can change their smoking status, but, for the sake of simplicity, we assume that they cannot change their level of smoking intensity. The model admits deaths and new births. From each compartment, subjects can transit to a deceased compartment denoted by the letter D and a subscript corresponding to the compartment of origin. New births ( \(\nu (t)\) is the number of new births at time t ) increase the size of the compartment N . Transitions of the individuals from a given compartment to another one determine flows regulated by the transition parameters, among which the rates of starting smoking ( \(\gamma _i^*\) ), stopping smoking ( \(\epsilon _i^*\) ), and relapsing into smoking after having stopped ( \(\eta _i^*\) ). Note that these rates can depend on the level of smoking intensity i . Death happens with different rates for never ( \(\delta ^*_N\) ), current ( \(\delta ^*_{C_i}\) ), and former ( \(\delta ^*_{F_i}\) ) smokers. For current and former smokers, the mortality rates may depend also on smoking intensity. This compartmental model, graphically represented in Fig.  1 , is expressed by the following system of differential equations for each \(i\in \{l,m,h\}\) :

where \(\gamma ^*=\gamma ^*_l+\gamma ^*_m+\gamma ^*_h\) is the overall transition rate from the status of never smoker to the status of current smoker. The initial conditions of the system, i.e. the sizes of the compartments at time 0, set to the 1 \(^{st}\) of January 1993, are \(N(0)=n_0\) , \(D_N(0)=0\) , \(F_i(0)=f^i_0\) , \(C_i(0)=c^i_0\) and \(D_{C_i}(0)=D_{F_i}(0)=0\) \(\forall i \in \{l,m,h\}\) , where \(n_0\) is the number of never smokers in the considered population on the first day of the study period, and \(f^i_0\) and \(c^i_0\) are the number of ex-smokers and current smokers with smoking intensity i .

Smoking Habits Compartmental model in its simplest form

For computational reasons, it is convenient to discretise the system of differential equations in Eq. ( 1 ), assuming that the size of the compartments is constant during 1-year time steps. Hereafter, t will denote discrete time, with the year as a time-unit ( \(t\in \{1,...,T\}\) ), and we replace the system in Eq. ( 1 ) with a system of difference equations, where the annual probability of stopping smoking ( \(\epsilon _i\) ), and the annual probabilities of smoking relapse ( \(\eta _i\) ) are derived from the corresponding rates in Eq. ( 1 ), as well as the annual probabilities of death for never ( \(\delta _{N}\) ), current ( \(\delta _{C_i}\) ), and former ( \(\delta _{F_i}\) ) smokers. In particular, \(\delta _N=1-\exp (-\delta ^*_{N})\) , and \(\epsilon _i=1-\exp (-\epsilon _i^*)\) , \(\eta _i=1-\exp (-\eta _i^*)\) , \(\delta _{C_i}=1-\exp (-\delta ^*_{C_i})\) , \(\delta _{F_i}=1-\exp (-\delta ^*_{F_i})\) with \(i \in \{l,m,h\}\) . Regarding the probabilities of starting smoking for never smokers, the overall annual probability \(\gamma\) comes from the corresponding rate, \(\gamma =1-\exp (-\gamma ^*)\) , while \(\gamma _i=\pi _{C_i}\gamma\) , where \(\varvec{\pi }=(\pi _{C_l}, \pi _{C_m}, \pi _{C_h})\) is the distribution of the level of smoking intensity among the new current smokers. Notice that, if \(\lambda\) is the rate of occurrence of an event, the probability of experiencing at least one event in the time unit is \(1-\exp (-\lambda )\) . The resulting system of discretised equations for each \(i\in \{l,m,h\}\) and \(t\in \{1,..., T\}\) is:

where \(\nu (t)\) denotes the newborns in the year t . The initial conditions of the system coincide with those of the previous model in Eq. ( 1 ).

The SHC model extends the system in Eq. ( 2 ) to account for two additional discrete time axes: age and time since smoking cessation. The final model is a compartmental model with separate compartments for each discrete age ( a ), where also a stratification by years since smoking cessation ( c ) is introduced for former smokers. Two separate SHC models are specified by sex. The final SHC model is defined by the following system of equations for each \(i\in \{l,m,h\}\) and \(t\in \{1,..., T\}\) :

The initial conditions of the system are obtained by generalizing those of the model in Eq. ( 2 ), to take into account the stratification by age for current smokers, and the stratification by age and time since cessation for former smokers.

For simplicity, \(\nu (t)\) was assumed to be constant over time. The age a takes values from 0 to 100. We set \(\gamma (a)\) to 0 until 13 and from 35 years of age, and, in order to account for the possible non-linearity between 14 and 34, we modelled the logit transformation of \(\gamma (a)\) through a natural cubic regression spline of age, with 2 equidistant internal knots. Similarly, we set \(\epsilon (a)\) to 0 until 19 years of age; we introduced a natural cubic regression spline with 2 equidistant internal knots to model non-linearity for \(a\ge 20\) . The resulting functions are the following:

where \(\varvec{\psi }=(\psi _0,\psi _1,\psi _2,\psi _3)\) and \(\varvec{\phi }=(\phi _0,\phi _1,\phi _2,\phi _3)\) are vectors of unknown parameters governing the probabilities of starting and quitting smoking, respectively. The relapsing rate, \(\eta ^*(c)\) , was modelled as a negative exponential function of the time since cessation, with parameters \(\varvec{\omega }=(\omega _0,\omega _1\) ):

where \(\omega _0\) governs the lifetime probability of no relapse and \(\omega _1\) tunes how fast the rate of smoking relapse declines with the time from cessation [ 12 , 23 , 28 , 33 ]. Both \(\omega _0\) and \(\omega _1\) are assumed to be positive so that \(\eta ^*(c)\) is a positive, decreasing function of c . The assumptions on which the SHC model is based are summarized in Section Model assumptions , Supplemental Material.

Estimation strategy

An important issue in compartmental models concerns parameter identifiability [ 30 ]. Complex models with many compartments, such as the model in Eq. ( 3 ), have many parameters governing the admitted transitions, but unfortunately observed data are often insufficient to estimate all of them. To overcome this problem we fixed some of the parameters to values from the literature or external data, leaving as unknown the mortality risks and the spline coefficients \(\varvec{\phi }\) and \(\varvec{\psi }\) , and \(\varvec{\omega }\) . Regarding the initial size of the compartments, it was obtained by combining the population size at the beginning of the study period with estimated prevalences arising from the ISTAT AVQ and EHIS surveys. Details on the values assigned to the fixed parameters and the initial size of the compartments are provided in Section S2, Supplemental Material. The unknown parameters have been estimated following the two step-procedure described in the next section.

Two-step estimation

In order to estimate the unknown parameters, we adopted a two-step procedure. Both steps use as observed data the prevalence of never, current and former smokers from ISTAT AVQ, here denoted by \(p^{obs}(t;a^*)=\left( p^{obs}_C(t;a^*),p^{obs}_N(t;a^*),p^{obs}_F(t;a^*)\right)\) , where t denotes the year and \(a^*\) the age class. In particular, we considered years from 1993 to 2019 and age classes \(a^*\in \{14-17, 18-19, 20-24, 25-34, 35-44, 45-54, 55-59, 60-64, 65-74, 75+\}\) . According to the ISTAT AVQ survey, current smokers are defined as individuals who reported being smokers at the time of the interview, while former smokers as those who reported having quitted.

First step.

We estimated the age-specific risks of mortality for never smokers \(\delta _N(a)\) using the prevalence values, as well as relative risks coming from the literature. In particular, the age-specific risks of dying for current and former smokers in the population at time t are respectively \(\delta _C(t;a)=RR_{C}\times \delta _{N}(t;a)\) and \(\delta _F(t;a)=RR_{F}\times \delta _{N}(t;a)\) , with \(RR_{C}\) and \(RR_{F}\) the relative risks of dying for current smokers and former smokers versus never smokers. Let \(p(t;a)=\left( p_N(t;a), p_C(t;a), p_F(t;a)\right)\) be the distribution of never, current and former smokers in the population. The overall mortality at age a in the year t , \(\delta _{pop}(t;a)\) , is a weighted average of \(\delta _N(t;a)\) , \(\delta _C(t;a)\) , and \(\delta _F(t;a)\) with weights p ( t ;  a ). Thus, \(\delta _N(t;a)\) can be derived as the ratio:

Therefore, separately for each year t in the period 1993-2019, we obtained an estimate of \(\delta _N(t;a)\) , plugging into Eq. ( 4 ) the mortality risk at age a reported for Tuscany, the relative risks for current and former smokers versus never smokers [ 32 ], and the observed age-specific prevalence of never, current and former smokers \(p^{obs}(t;a^*)\) . Finally, we averaged the year-specific \(\hat{\delta }_N(t;a)\) over t , obtaining the overall estimate \(\hat{\delta }_N(a)\) . The risks of dying for current and former smokers by i and c were then derived as:

Second step.

After fixing the mortality risks to the values computed at the first step, \(\hat{\varvec{\delta }}(a,c)\) , we calibrated the model on the observed prevalence \(p^{obs}(t;a^*)\) to estimate the vector of parameters which were still unknown, \(\varvec{\theta }=(\varvec{\psi },\varvec{\phi },\varvec{\omega })\) . Let \(p(t;a^*,\varvec{\theta })=\left( p_{C}(t;a^*,\varvec{\theta }),p_{N}(t;a^*,\varvec{\theta }),p_{F}(t;a^*,\varvec{\theta })\right)\) be the vector of the prevalence of never, current and former smokers belonging to the class of age \(a^*\) at time t , calculated on the population predicted by the model in Eq. ( 3 ), given a specific value of \(\varvec{\theta }\) . With calibration, we searched for the value of \(\varvec{\theta }\) that leads to predicted prevalences as close as possible to the observed ones. To compare observed and simulated trajectories, we considered the following objective function, where \(H(\cdot ,\cdot )\) denotes the Hellinger distance [ 34 ] between two discrete probability distributions:

where \(A^*\) is the number of age classes \(a^*\) . We minimized the objective function in Eq. ( 5 ) over \(\varvec{\theta }\) via a global optimization procedure, resorting to the JULIA package Optim.jl [ 35 ]. It is well-known that, in the context of compartmental models, optimization results often depend on the chosen starting points of the algorithm [ 36 , 37 ]. To avoid the problem of getting stuck in local minima, we performed several optimizations using different starting points, then we selected the solution that brought to the minimum Hellinger distance [ 30 , 36 ]. The two-step procedure was performed separately by sex, obtaining different estimates for males and females and sex-specific evolution of the compartment sizes. We estimated the compartment sizes up to 2043 by projecting the model dynamics, assuming that parameters and model structure do not change after 2019.

Parametric bootstrap procedure

We quantified the sampling variability around point estimates and projections by using a parametric bootstrap procedure [ 29 , 30 ]. Let \(\hat{\varvec{\theta }}\) be the vector of parameters minimizing the objective function in Eq. ( 5 ) and \(p(t;a^*,\hat{\varvec{\theta }})\) the corresponding estimated vector of prevalence for never, current and former smokers of age \(a^*\) in the population at time t . Let \(n(t;a^*)\) be the number of subjects belonging to the age class \(a^*\) , enrolled in the ISTAT AVQ in the year t in Tuscany (i.e. the denominator of the observed prevalence \(p^{obs}(t;a^*)\) ). The bootstrap procedure consisted of the following steps:

for each \(a^*\) and t , we sampled a vector of prevalence from a Dirichlet distribution:

we considered the collection of these sampled vectors as the observed values and performed the two-step estimation, computing the vector \(\varvec{\delta }^b(a,c)\) and finding \(\varvec{\theta }^b\) that minimized the objective function;

we repeated the previous two steps \(B=1000\) times, collecting a sample of B bootstrap estimates of \(\varvec{\delta }(a,c)\) and \(\varvec{\theta }\) to be used to estimate as many curves describing the transition parameters and compartment size trajectories;

we calculated the \(90\%\) confidence intervals for the quantities of interest as the 5 \(^{th}\) and 95 \(^{th}\) percentiles of the bootstrap estimates; pointwise confidence intervals were calculated for the curves.

Model validation

In order to evaluate the predictive performance of the estimation procedure described in Estimation strategy section, we applied cross-validation (CV) on a rolling basis. We started defining the first 3 years of the period 1993-2019 as the training set, and the subsequent q years as the test set. Then, we calibrated the compartmental model in Eq. ( 3 ) on the training set and used the estimated model to forecast the prevalence of never, current and former smokers in the years belonging to the test time window. The discrepancy between observed and projected prevalence was evaluated in terms of absolute percentage error. Then, we progressively extended the length of the training set by adding one year at a time, and we obtained the projections for the q subsequent years every time. We stopped when the last training set considered the years between 1993 to 2019- q . We finally computed the Mean Absolute Percentage Error (MAPE), by averaging the absolute percentage errors across different types of smokers over time, age classes, and training sets. Note that in general, for a set of n observations, MAPE is defined as \(\frac{100}{n}\sum \nolimits _{i=1}^{n}{\frac{|O_i-E_i|}{O_i}}\) , where \(O_i\) is the observed value and \(E_i\) is the expected one for unit i . We calculated the MAPE for different forecasting horizons by setting \(q=3,6,9,12\) years.

Sensitivity analysis

A key assumption of our model is that the dynamics of the studied phenomenon, particularly the transition probabilities between compartments, remain constant from 1993 to 2019 (and continue to do so until 2043). To verify its appropriateness, we conducted two separate analyses, first calibrating the model on the period 1993-2004 and then on the period 2005-2019, and compared the results. Notice that in the analysis 2005-2019 the initial sizes of the compartments were set to values obtained from 2005 surveys (see Section Details on the fixed parameters , Supplemental Material).

Another crucial point concerns the fact that the inference results could be affected by the model parameters assumed as fixed. To address this issue, we utilized a variance-based approach to Global Sensitivity Analysis (GSA) [ 31 ]. Given \(K_X\) mutually independent inputs \((X_1, X_2,..., X_{K_X})\) and a model which, given the inputs, returns \(K_Y\) outputs \((Y_1, Y_2,..., Y_{K_Y})\) , this approach quantifies the relative importance of each input to the model’s outcomes by propagating uncertainty from the inputs to the outputs and computing variance indices. In our application, given the model in Eq. ( 3 ), we considered as inputs all the parameters, both fixed and unknown, and the Hellinger distance in Eq. ( 5 ) as the output Y . Note that, considering the Hellinger distance as the output, we directly measure the influence of the inputs on the discrepancy between observed and predicted data, thus, ultimately, on the inference results. Then we calculated, for each input \(X_i\) , the so-called total variance index, which  \(S^{tot}_i\) measures the overall effect of the i -th input on the output Y , including all the interactions of \(X_i\) with the other inputs. This index corresponds to the expected variance of Y that would be left on average when all the parameters but \(X_i\) , \(X_{\sim i}\) , are fixed:

A total variance index close to zero indicates that the parameter \(X_i\) does not influence Y , and therefore, the inference results. Conversely, a large total variance index indicates that the parameter does have an impact on them. In the former case, the parameter can be fixed without affecting our estimates, or in other words, our model and data do not provide information on this parameter. The computation of \(S^{tot}_i\) relies on Monte Carlo simulations [ 38 ]. We simulated \(K=10,000\) different combinations of the model inputs, then, for each of them, we predicted the prevalence values via the model in Eq. ( 3 ) and calculated the corresponding Hellinger distance. Specifically, we draw the model parameters from the distributions reported in Table S3.1, Supplemental Material, adopting a quasi-random numbers sampling which provides a more efficient exploration of the sample space [ 39 , 40 ]. On the basis of the simulated Hellinger distance and the combination of the parameters, we computed the total variance indices as described in [ 38 ]. It is worth noting that in the GSA we did not include the age-specific mortality rates, \(\delta _{pop}(t;a)\) , among the model inputs. It is reasonable, as done elsewhere [ 23 ], to treat these parameters as not affected by uncertainty, given that they were estimated based on the entire population.

Health impact assessment

The impact of smoking on population health was quantified in terms of attributable deaths. We calculated the Smoking-Attributable Deaths (SADs) in the year t as the difference between the number of deaths occurring in that year under the actual scenario, i.e. the number of deaths predicted by the model in Eq. ( 3 ) given \(\hat{\varvec{\theta }}\) and \(\hat{\varvec{\delta }}(a)\) , and the deaths we would observe under a specific counterfactual condition. We considered the counterfactual condition where current smokers and former smokers in the year t were never smokers. Therefore, for each age a , we applied to the size of the compartments of smokers or ex-smokers the excess risk relative to never-smokers. The excess risk is defined as the difference between risks. For example, the excess risk of current smokers of age a and smoking intensity i relative to never-smokers is \(\delta _{C_i}(a,c)-\delta _N(a)\) . Thus, for the year t , the number of SADs among people of age a was calculated as:

The age-specific \(\text {SAD}(t;a)\) can be summed over a to obtain the total number of attributable deaths in population or in a certain class of age: \(\text {SAD}(t)=\sum \limits _a\text {SAD}(t;a)\) . The impact of smoking on population health can be expressed also in terms of Population Attributable Fraction (PAF), defined as the proportion of deaths that would be avoided if all current and former smokers in the population or in a subset of it were never smokers [ 41 ]. For details, see Section Population Attributable Fraction computation , Supplemental Material. We calculated SADs and PAFs over the period 1993-2043, separately by sex and for the ages 35+ and 65+.

Impact of future hypothetical policies

In order to illustrate the use of the compartmental model to assess the impact of hypothetical TCPs on SAD, we focused on three policies acting on the rates of starting and stopping smoking, \(\gamma ^*(a)\) and \(\epsilon ^*(a)\) . We assumed that all the defined policies are implemented in 2023 and that, in the absence of policies, the smoking habit dynamics would not change.

Taking inspiration from [ 42 ], and from a recent policy introduced in New Zealand ( www.bbc.com/news/world-asia-63954862 ) we defined the following hypothetical TCPs starting from 2023:

TCP1, a policy able to reduce the rate of starting smoking by 25% in 10 years for subjects between 14 and 34 years of age; for simplicity, we assumed a linear decrease, starting with a decrease of 2.5% the first year, a decrease of 5% the second one and so on, up to a final decrease of 25% after 10 years;

TCP2, a policy able to increase the rate of stopping smoking by 25% in 10 years for subjects between 25 and 100 years of age; for simplicity, we assumed a linear growth, starting with an increase of 2.5% the first year, an increase of 5% the second one and so on, up to a final increase of 25% after 10 years;

TCP3, a policy that imposes a complete smoking ban on cohorts born since 2009.

For each policy, we calculated the evolution of smoking prevalence and the number of avoided deaths expected from its implementation, taking the scenario without policies as a reference (TCP0). To better appreciate the impact of policies in terms of SAD, limited to this analysis, we extended the projections up to 2063.

The Tuscany population in 1993 counted 1,697,495 million males and 1,824,090 million females, and the proportions of never, current, and former smokers estimated from the ISTAT AVQ survey were respectively 35%, 34%, 31% for males and 67%, 20%, 13% for females.

Figure  2 , Panel (a) and (b) show, separately for males and females, the estimates of the parameters left unknown in the SHC model in Eq. ( 3 ), with their 90 \(\%\) confidence intervals (CI), as obtained from the two-step estimation procedure and bootstrap. In particular, Panel (b) compares the estimated risk of death for never smokers with the one in the general population. It is worth noting that while the two risks are similar for females (the mortality among never-smokers is \(8\%\) lower than among the general population), a not negligible difference is observed for males ( \(25\%\) lower) as noted also in [ 43 ].

Results of the two-step estimation procedure for males in blue and females in red, with their bootstrap \(90\%\) confidence intervals: parameters tuning the probabilities of starting ( \(\varvec{\psi }\) ) and stopping smoking ( \(\varvec{\phi }\) ), and the probability of smoking relapse ( \(\varvec{\omega }\) ) ( a ), age-specific mortality for never smokers and for the general population ( b ), probabilities of starting ( \(\gamma (a)\) ), and stopping smoking ( \(\epsilon (a)\) ) and probability of smoking relapse ( \(\eta (c)\) ) ( c ), observed and predicted prevalence for never ( N ), current ( C ) and former ( F ) smokers ( d ), Population Attributable Fraction (PAF) and Smoking Attributable Deaths (SAD) for people over the age of 35 ( e ) and 65 ( f )

Figure  2 , Panel (c) shows the estimates of the probabilities of starting and quitting smoking and the probability of smoking relapse, derived from the estimated coefficients in Panel (a). Table 1 reports some summaries of the curves. Males are more likely to start and quit smoking than females. In particular, the probability of starting smoking has a peak around 19.9 years of age for males and 19.1 for females, with a maximum of just over 9% for males and just over 6% for females. The mean age of initiation is 20.7 for males and 20.5 for females. The probability of stopping smoking increases after 50 years of age, reaching a maximum of 29.5% for males and a maximum of 24.0% for females. The probability of smoking relapse is affected by large sampling variability. However, our results seem to indicate that it is about 80% after 1 year, then declines to about 40% after two years and progressively becomes negligible after 3 years (Fig.  2 ). On average, former smokers relapse into smoking after 1.7–1.5 years, for males and females respectively (Table 1 ).

Panel (d) shows the estimated prevalence of never, current, and former smokers among those over 14 years old from 1993 to 2043, predicted through the SHC model, together with the observed data used to calibrate the model (blue and red dots respectively for males and females with their 90% CI). The model fit appears to be adequate, with the predicted values close to the observed ones. Our forecasts, starting from 2020, suggest that the smoking prevalence will decrease in the coming years. Panels (e) and (f) show the predicted SAD and PAF over the period 1993-2043, separately for males and females, calculated for the population over 35 years of age and for the population over 65 years of age. The impact on males is higher than on females both in absolute and relative terms. However, while a clear reduction of the attributable deaths is expected in the coming years for males, for females they slightly decline only after having reached a maximum around 2030 [ 44 ]. Note that the majority of attributable deaths in the population over 35 are due to deaths in individuals over 65, as shown by the similarity of the curves.

Tables 2 and 3 report the percentages of never, current, and former smokers, the SAD and PAF, estimated every 10 years from 1993 to 2043, with their 90% confidence intervals. As an example, we estimated that in Tuscany in 2023 smoking was responsible for 4,070 (90% CI:3,795-4,247) deaths among men over 35 years old (one death per 745 people over the age of 35) and 1,976 (90% CI:1,741-2,407) deaths among women in the same age class (one death per 1655 people over the age of 35), corresponding to a PAF of 18% and 8%, respectively. Most of the attributable burden, however, was on people older than 65 (3,497 SAD for men and 1,765 for women).

Regarding the CV procedure, the average values of MAPE for different prediction horizons are lower than 30% (Table 4 ), indicating that the predictive performance of the model is adequate, even if not optimal [ 45 ]. The MAPE is lower for the model on the male population than for the model on the female one.

Figure  3 reports the results of the two separate calibrations of the SHC model, one on the prevalence data from 1993 to 2004 and one on the prevalence data from 2005 to 2019. The confidence bands are wider in the second period of calibration than in the first one. For males, there is evidence of a downward shift of age corresponding to the maximum probability of starting smoking. For females, calibrating the model in the first years brought a lower projection of the prevalence of never smokers, which likely reflects a change over time in the smoking habits among women. Apart from these differences, the two calibrations provided qualitatively similar results. For numerical details see Tables S5.1-S5.6, Supplemental Material and Figures S5.1 and S5.2, Supplemental Material.

Results of the two-step estimation procedure for males in blue and females in red, by period of calibration (from 1993 to 2004 in a light colour and from 2005 to 2019 in a dark colour): probabilities of starting ( \(\gamma (a)\) ) and stopping smoking ( \(\epsilon (a)\) ), and probability of smoking relapse ( \(\eta (c)\) ), with 90% confidence bands, ( a ) and ( c ); prevalence of never ( N ), current ( C ) and former ( F ) smokers, with 90% confidence bands, ( b ) and ( d )

The total variance indices derived from the GSA (Table 5 ) reveal that the primary factor contributing to the variability of the Hellinger distance is the probability of starting smoking and its interaction with the other model inputs, resulting in \(S_i^{tot}\) values of 0.58 for males and 0.76 for females. This is followed by the probability of quitting smoking, with values of 0.36 for males and 0.21 for females, and by the probability of smoking relapse, with values of 0.15 for males and 0.09 for females. Conversely, the parameters assumed to be fixed have a negligible impact on the Hellinger distance, with total variance indices very close to 0. This latter result indicates that fixing the aforementioned parameters to specific values does not significantly affect the calibration results, and consequently the prevalence estimates, demonstrating their robustness against variations in \(\varvec{\pi }\) , \(\nu\) , and RRs specifications.

Figure  4 compares the evolution of smoking habits in the male and female populations under three alternative scenarios that simulate hypothetical tobacco control policies. These scenarios are compared with the status quo, corresponding to the absence of actions to reduce tobacco consumption (TCP0). We assumed that the TCPs are applied since 2023. They have no substantial effect on the prevalence of never, former, and current smokers during the 10 years following their implementation. TCP3 has the largest impact: in 2043 it is expected to increase by 12 percentage points the prevalence of never-smokers among males and by 8 among females, compared with TCP0 (see Table 6 ).

Estimated prevalence of never ( N ), current ( C ) and former ( F ) smokers under different tobacco control policies (TCP) with \(90\%\) confidence bands, for males ( a ) and females ( b )

In order to better appreciate the impact of the TCPs on mortality, we extended the forecasting horizon up to 2063. Table 7 reports the predicted number of attributable deaths every 10 years, from 2023 to 2063, for both males and females under different TCPs, for the classes of age 35+ and 65+. TCP2, which increases the probability of stopping smoking, is the policy that most impact mortality in both classes of age. TCP3, which bans access to smoking to the new generations, despite its effectiveness in reducing current smokers, does not reduce SADs within the time window considered. Indeed, this policy is expected to have a longer-term impact, which is not visible before 2063. Additional Tables and Figures are reported in Section Additional results , Supplemental Material.

Interesting findings emerged from our analysis. We found that the probability of starting smoking reaches its maximum, just over 9% for males and just over \(6\%\) for females, between 19 and 20 years of age. Considering that younger people have a large probability of becoming stable smokers [ 46 ], these probabilities are quite worrying. The difference in the mean age of initiation between males and females is lower than one year, confirming what is reported for high-income countries [ 47 ]. Regarding the probability of stopping smoking, we found that it increases after 50 years of age and has a maximum of 29.5% for males and 24.0% for females, even if the confidence bands around these curves are quite wide. The 80% of ex-smokers relapse into smoking after 1 year, in line with the results of the Italian surveillance system PASSI for the years 2020-2021 ( www.epicentro.iss.it/passi/dati/SmettereFumo ). On average, former smokers relapse into smoking during the second year from cessation (after 1.7 and 1.5 years for males and females, respectively).

According to our model, in 2023 in Tuscany, 23% of men smoke, while 35% are ex-smokers. These percentages are lower among women: 16% smoke and 24% are ex-smokers. The prevalence of smokers estimated by our model is lower than the one reported in the PASSI survey for the period 2020-2021 (26.1% and 20.5% in the age class 18-69 for males and females, respectively), but consistent if we consider that our estimates are calculated on all population, while PASSI focuses on the age class 18-69 ( www.epicentro.iss.it/passi/pdf2020/Scheda-fumo-PASSI-regione-2016-2019.pdf ).

We estimated that, in 2023, 18% of deaths among males and 8% among females are due to smoking, corresponding to 4,070 and 1,976 deaths, respectively. These PAFs are in line with those estimated by the Global Burden of Disease Study for Italy in 2019 ( https://vizhub.healthdata.org/gbd-results/ ), 20.5% (CI: 19.5-21.7) in males and 8.17% (CI: 7.51-9.02) in females, slightly lower than those reported for Italy by the Tobacco Atlas initiative ( https://tobaccoatlas.org/challenges/deaths/ ), and overall coherent with previous results for Italy and Tuscany ([ 48 ]; www.deathsfromsmoking.net ).

As shown by the cross-validation results, the model produces quite reliable predictions of prevalence. Thus, subject to the assumption that all mechanisms underlying smoking dynamics and demographic evolution do not change in the future, we projected the dynamics. For the next two decades, we estimated an evident decrease in the prevalence of current smokers for males, due to an increase in the percentage of never-smokers. For females, substantial stability is expected. Similar considerations apply to PAFs: a decrease is observed for males and stability for females. These results confirm that Italy is in the fourth stage of the tobacco epidemic model, characterized by a continuing slow decline of smoking prevalence in both men and women with converging rates between sex [ 49 , 50 ]. The robustness of the long-term predictions to events that could change the described dynamics over time could be assessed by implementing a specific GSA procedure. However, in this work, we used the GSA only to assess the sensitivity of the inference results to changes in the parameters treated as fixed.

The proposed model can be used for assessing the impact of alternative TCPs. For illustrative purposes, we considered the impact of three policies aimed at reducing smoking in the population. The first two policies are completely hypothetical and defined in terms of their effect on the probability of starting (TCP1) and stopping (TCP2) smoking. They are not real policies but represent the intentions of the legislator to change the rates of smoking initiation and cessation. The third one (TCP3), which bans smoking in new cohorts since 2009, is inspired by the tobacco-free generation real intervention implemented in New Zealand as part of a plan for the tobacco endgame, including also additional strategies aimed at decreasing the affordability and availability of smoking, reducing the levels of nicotine in tobacco products, and restricting sales to designated tobacco outlets. We evaluated the expected marginal impact that this tobacco-free generation intervention would have in Tuscany, assuming complete compliance of new generations to the smoking ban. The results indicate that under TCP1 and TCP2 the prevalence of current smokers is reduced by a few percentage points either for women or men. On the contrary, TCP3 produces a clear increase in never-smokers, thus a reduction in smoking prevalence, which is expected to decrease in ten years by 9 and 6 percentage points among males and females, respectively. The impact on mortality of the three policies, in particular TCP1 and TCP3, that act by increasing the number of never smokers, can be appreciated only by extending the time horizon of forecasting. Interventions able to increase the probability of stopping smoking, like TCP2, are expected to produce the largest reduction of SADs in the medium term, especially among the over-65s. However, this kind of policy does not contribute to reducing smoking among the youngest, thus effectively stopping the tobacco epidemic.

From a methodological point of view, we introduced several elements of novelty. First of all, we provided a formal definition of the equations that describe the system dynamics and made explicit assumptions on the distribution of the involved random variables. We also introduced cubic regression splines for modelling in a flexible way the probabilities of starting and quitting smoking as functions of age, thus obtaining more realistic trajectories. Furthermore, we included in the model dependencies from the smoking intensity, which may allow assessing the impact of personalized TCPs specific for heavy or moderate smokers, such as lung cancer screening, use of pharmacological treatment, or smoking cessation campaigns.

Regarding the inference on the unknown parameters, we proposed a two-step estimation strategy to estimate the curves describing the probability of starting and stopping smoking and the probability of smoking relapse, as well as the mortality risk among never, current and former smokers. At the second step of the estimation procedure, we defined the calibration objective function in terms of a Hellinger distance between observed and predicted prevalence, instead of the widely used sum of squares function. The use of this discrepancy measure is relatively new in this framework and allowed handling a bounded loss function, defined in [0, 1], that is simple to minimise and to be interpreted. Finally, we provided confidence intervals/bands for the parameters/curves of interest. To the best of our knowledge, this is the first time that quantification of sampling variability is performed in this field. To this aim, we resorted to a parametric bootstrap procedure defined by adapting to our framework a method proposed for compartmental models describing infectious dynamics [ 30 ]. The assumed Dirichlet distribution enabled us to model the prevalence values complying with the constraint that their sum equals one. Furthermore, specifying appropriate values for the concentration parameters of the Dirichlet distributions, we were able to quantify the sampling variability accounting for the sample size of the surveys from which we derived the observed prevalence used in calibration. The estimation procedure has also limitations. We estimated the parameters in a deterministic way, in the sense that we considered the distributional assumptions on the prevalence only in the bootstrap procedure but not in the calibration phase. While likelihood-based approaches are unfeasible in this framework, likelihood-free inference methods such as Approximate Bayesian Computation algorithms would allow a full uncertainty quantification [ 25 ].

The reliability of the model’s results depends on several factors. First of all, it depends on the quality of the data used for calibration. In our case, we used data from yearly surveys conducted according to well-established methodology on reasonably large sample sizes. Secondly, it depends on the values of the fixed parameters, and we demonstrated, through the GSA, that the inference was robust to variations of the fixed parameters within plausible ranges of values. Lastly, the reliability of the results depends on the structural assumptions on which the model is based, not assessed via GSA. Underneath, we qualitatively review the main assumptions of the model and discuss the limitations that may arise from them. With respect to demographic dynamics, we assumed that the population was close to immigration and emigration and that the number of new births did not vary during the study period, effectively feeding the model with identical cohorts of subjects each year. For more realistic modelling, we could use the observed yearly number of births to create the new cohorts up to 2019. However, in light of the GSA, we expect that the impact of this choice on the results has not been significant. We also assumed that the age-specific mortality rates did not vary over the study period.

Regarding smoking dynamics, we assumed that the probabilities of starting and stopping smoking were functions of age and that the probability of smoking relapse was a function of time since cessation, but not of age. We did not allow any of these probabilities to vary over time. By defining the transition probabilities in this way, we have made a clear choice about which time axes were most important in our opinion to capture appropriately the smoking dynamics in the population. This choice is not without problems because in some cases there is evidence suggesting otherwise. For example, a decreasing trend in the probability of starting smoking has been reported for both males and females in Europe [ 51 ], while evidence of a dependence between age and risk of smoking relapse has been found in the US population [ 52 ]. However, if introducing multiple time-axes dependence in the transition probabilities could lead to more realistic results, this would be at the price of further complicating the model by introducing new unknown parameters to be estimated. We partially explored the goodness of the assumption of no calendar time dependence through a simple sensitivity analysis, which confirmed that the probabilities of starting and stopping smoking, and the probability of smoking relapse were quite similar when two separate calibrations were performed on the periods 1993-2004 and 2005-2019. It is worth stressing that, even if these two periods correspond to before and after the introduction of the so-called Sirchia law that banned smoking in all indoor public places in Italy, it was not our goal to speculate about the causal effect of this intervention on smoking dynamics. We also assumed that people could not change their smoke intensity during their entire life, that the probability of stopping and relapsing did not depend on smoking intensity, and, again, that the distribution of smokers by smoking intensity did not change over the study period.

In general, it is important to note that underlying all the simplifications introduced in model specification is the fact that adding details to a compartmental model goes along with the definition of new compartments and new transitions, and without available and reliable data, the model could become non-identifiable producing more uncertain and unstable results [ 53 ]. Moreover, microsimulation models or social network models, that explore smoking dynamics from an individual point of view, could be more suitable solutions to introduce detail and complexity, including those related, for example, to the course of disease [ 54 , 55 ], or to explore the exposure to second-hand smoke that, being related to the social network of the individuals, was not considered in our analysis.

Conclusions

We developed an approach for modelling smoking dynamics in the population that overcomes many of the limitations of previously proposed models. It includes validation tools like cross-validation on a rolling basis and GSA, aimed at checking the robustness of our results and supporting our findings.The model can be generalized and applied to other Italian regions changing the initial conditions of the system. The fact that the surveys we relied on provide information about all regions makes this extension easily feasible. The proposed approach can be straightforwardly applied also to other countries after a careful check of the validity of the model assumptions, which, however, can be mostly adapted to different contexts. Finally, it can be also used to assess the impact of other tobacco control policies on smoking prevalence and mortality, beyond those considered in this paper.

Availability of data and materials

Data are available on request from the corresponding author.

Code availability

Codes are available on request from the corresponding author.

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Acknowledgements

We thank Maria Chiara Malevolti for her contribution to data collection and validation, and all ACAB project participants for their support.

The present work is part of the Attributable Cancer Burden in Tuscany (ACAB) project, funded by Regione Toscana under the grant "Bando Ricerca Salute 2018" ( www.acab-toscana.it ). The funding body played no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript.

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Alessio Lachi, Cecilia Viscardi, Giulia Cereda & Michela Baccini

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Transferable preference learning in multi-objective decision analysis and its application to hydrocracking

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• Xinzhe Wang 2 ,
• Chao Jiang   ORCID: orcid.org/0000-0001-8106-4740 1 ,
• Yang Liu 2 ,
• Lianbo Ma 2 ,
• Cuimei Bo 3 &
• Quanling Zhang 1  

Hydrocracking represents a complex and time-consuming chemical process that converts heavy oil fractions into various valuable products with low boiling points. It plays a pivotal role in enhancing the quality of products within the oil refining process. Consequently, the development of efficient surrogate models for simulating the hydrocracking process and identifying appropriate solutions for multi-objective oil refining is now an important area of research. In this study, a novel transferable preference learning-driven evolutionary algorithm is proposed to facilitate multi-objective decision analysis in the oil refining process. Specifically, our approach involves considering user preferences to divide the objective space into a region of interest (ROI) and other subspaces. We then utilize Kriging models to approximate the sub-problems within the ROI. In order to enhance the robustness and generalization capability of the Kriging models during the evolutionary process, we transfer the mutual information between the sub-problems in the ROI. To validate the effectiveness as well as efficiency of our proposed method, we undertake a series of experiments on both benchmarks and the oil refining process. The experimental results conclusively demonstrate the superiority of our approach.

Avoid common mistakes on your manuscript.

Introduction

Hydrocracking is a vital process in the oil refining industry, converting low-quality feedstocks, exemplified by vacuum gas oil, into high-value transportation fuels under high temperatures and pressures [ 1 ]. This industrial process typically involves the use of two-bed catalytic reactors [ 2 ]. The first reactor, known as the hydro processor (HT), serves the purpose of decomposing sulfur- and nitrogen-containing compounds. On the other hand, the second reactor, the hydrocracker (HC), undertakes hydroisomerization and hydrocracking of the treated liquid fraction from the first reactor [ 2 ]. Hydrocracking offers numerous advantages, including excellent adaptability to various materials, flexibility in the production process, and the production of high-quality products. As a result, it has gained popularity in the production of low-sulfur, low-aromatics diesel fuel, as well as high-smoke point jet fuel [ 1 ].

From an optimization perspective, the hydrocracking process represents a typical multi-objective optimization problem (MOP). In the refining process, it is essential to optimize the operating conditions, such as cell feed flow, reaction pressure, and temperature, to meet the requirements for hydrocracking yield and improve the economic efficiency of refiners [ 3 ]. However, modeling the hydrocracking process as a complex simulation and evaluating the performance of new operating conditions on the simulation can be highly time-consuming and costly. The conventional approach to address this issue often involves speculations and commissioning operations by experienced engineers, which can be both unreliable and inefficient [ 3 ]. As a result, finding efficient and effective methods to handle the optimization of hydrocracking has become a growing concern within the refining industry. To obtain optimal operating conditions for industrial hydrocracking units, researchers have developed various mathematical models and attempted to optimize them. However, the optimization process of hydrocracking still requires improvement, primarily because evaluating the performance of operation units relies on complex simulation models using commercial engineering software, which is highly nonlinear and time-consuming [ 3 ]. Consequently, when the evaluation cost is high, these optimization problems are referred to as expensive multi-objective optimization problems (EMOPs). For evolutionary algorithms with a limited number of fitness evaluations, particularly in multi-objective scenarios, optimizing such problems becomes challenging.

Illustration of the hydrocracking process

Traditional MOEAs are typically designed to discover a wide and representative set [ 4 , 5 , 6 ], which is referred as Pareto set (PS). The decision-makers (DM) then select the final solution from this set based on their preferences. Nonetheless, within real-world optimization scenarios such as the hydrocracking process, providing the decision-maker (DM) with the entire of PS for a MOP is frequently impractical [ 7 ]. This limitation arises due to two main reasons: (1) Complex optimization problems: Practical optimization problems are often non-convex, nonlinear, and involve a great number of objective or decision variable dimensions. This poses significant challenges for traditional multi-objective evolutionary algorithms. For instance, in high-dimensional objective spaces, Pareto dominance-based MOEAs may struggle to distinguish the relationships between solutions [ 8 ]. Additionally, they can fail to converge to the true Pareto front (PF) due to the presence of Dominance Resistant Solutions (DRSs) [ 9 ]. (2) Costly evaluations: As previously mentioned, the endeavor to identify the entirety of the Pareto front may necessitate a substantial volume of evaluations, thereby incurring significant costs when applied to practical application problems. The cost of conducting too many evaluations is often unacceptable. Moreover, when MOEAs provide the DM with numerous solutions, it becomes challenging for them to choose the final preferred alternative.

In solving complex MOPs, preference-based MOEAs have gained significant attention [ 10 , 11 , 12 , 13 ], where the preference-driven algorithms incorporate the preference information from the DM into the optimization process, concentrating on one or several constrained regions of the PF, which are often termed as Regions of Interest (ROIs) [ 14 ]. Sandra et al. [ 15 ] come up with a new approach to approximate the ROI by means of aspiration and reservation points. Molina et al. [ 16 ] introduce the concept of g-dominance, which divides the objective space into subregions with varying priorities by setting reference points, guiding the algorithm to prioritize subregions with high importance. Said et al. [ 17 ] propose r-dominance, establishing a strict biased order among non-dominated individuals through distances between individuals and reference points as the second criterion for environmental selection. Yi et al. [ 18 ] merge r-domination and angular domination, further enhancing the performance of preference-based multi-objective evolutionary algorithms. Guo et al. [ 19 ] efficiently design a bolt supporting network in an interactive way, where the preferences from the DM are expressed by dynamically updating the ROI based on preferred solutions during the evolution. Tang et al. [ 20 ] propose a decomposition-based interactive evolutionary algorithm, which efficiently guides the population toward the ROI by transforming the originally evenly distributed reference vectors into a biased distribution. Palakonda et al. [ 21 ] propose an efficient and effective preference-inspired differential evolution algorithm for multi and many-objective optimization, where a preference-inspired mutation operator is designed to generate individuals with good performance and local knee points are acquired to articulate preferences in the mutation operator. Yu et al. [ 22 ] introduce LBD-MOEA, which is based on localized alpha-domination and knee point domination, demonstrating significant advantages in discovering knee point regions [ 23 ]. In summary, preference-based MOEAs offer two main advantages. Firstly, they conduct a targeted search towards the ROIs, avoiding exploration of uninterested regions and thus reducing computational resources. Secondly, the resulting solution set comprises a significantly reduced quantity of solutions compared to traditional methods, rendering the selection of preferred solutions by the DM a more straightforward endeavor [ 7 ]. Preference-based MOEAs can incorporate the DM’s preferences in three ways based on the timing of integration: (1) A priori: Preferences are provided before the search process begins. (2) Interactive: Preferences are incorporated interactively during the search. (3) A posteriori: Preferences are considered after the search is completed, and the final solution is chosen from the provided compromise solutions according to the preferences. Most traditional MOEAs are based on a posteriori approach. In this work, we will utilize a priori approach for preference incorporation in hydrocracking process, where the DM’s preferences are injected before the search begins.

In solving the issue of expensive evaluations, data-driven MOEAs have emerged as a prominent research focus in the discipline of multi-objective optimization [ 24 , 25 , 26 , 27 , 28 ]. These approaches considerably decrease the quantity of real evaluations by utilizing surrogate models. Various technologies have been proposed to build surrogate models, including polynomial response surface methods (PRSM) [ 29 ], radial basis functions (RBF) [ 30 ], and Kriging models [ 31 ], among others. Each surrogate model possesses unique characteristics. For instance, RBF models use appropriate coefficients for aggregating various basis functions, enabling them to simulate intricate design scenarios. In contrast, Kriging models treat the response of the input system as a stochastic process, making them suitable for predicting nonlinear problems [ 1 ].

In addition, some studies have embedded preferences into surrogate models to handle expensive MOPs. For example, Gibson et al. [ 32 ] define a novel acquisition function which considers the maximin distance from individuals to the PF and to the aspirational points chosen by the DM, which can effectively drive the population toward the preferred region. Wang et al. [ 33 ] propose an surrogate-assisted framework by integrating epsilon-dominance with iterative radial basis function, where the size of the ROI is controlled by the epsilon value. Tinkle et al. [ 34 ] successfully incorporate preference vectors from DM to Kriging-assisted evolutionary algorithm [ 27 ] for multiobjective shape design in a ventilation system. Besides, He [ 35 ] also incorporates the desirable objective function values into scalarising functions, and innovatively use generalised value distribution to approximate the scalarising function to get general surrogate models. In addition, Mohammad et al. [ 36 ] use achievement scalarising function [ 37 ] as the objective surrogate function, which is employed in generating solutions reflecting the preferences of the DM. Tang et al. [ 38 ] take the advantage of knee points [ 23 ] as their preference information for the Pareto front estimation, considering when the preference from the decision maker is not available. Yang et al. [ 39 ] design truncated expected hypervolume improvement as an infill criterion to effectively approximate preferred Pareto front.

Although recent studies have shown strong capability in handling expensive MOPs, different preference articulations are set for different scenarios, such as aspirational points, epsilon-dominance, preference vectors, achievement scalarising function, knee points, truncated expected hypervolume improvement. In handling the hydrocracking process, empirical studies have shown that the ranges of the objective values of the hydrocracking problem vary greatly on each objective. Especially, simply approximating the objectives or scalarising functions is not efficient as small number of solutions are around the preference vector. Hence, when we take account of the preference from the DM and the consumption of expensive evaluations, appropriate design of prefernece model is required. Accordingly, we come up with a new preference model composed of m +1 reference vectors, where m is the number of objectives. The model restrains the ROI through a preference vector and a parameter to control the size of ROI. Consequently, the development of efficient surrogates along the m +1 reference vectors can be easily built, which not only approximates the sub-problems within the ROI but also faciliate the DM to control the size of ROI. In addition, we can transfer the mutual information between the sub-problems to generate diverse solutions within the ROI. In this way, we theoretically and experimentally extend our recent work [ 40 ] and provide with a new way of multi-objective decision analysis in the oil refining process.

In summary, the contributions of this paper are as follows:

In our preference-based framework, we incorporate the Kriging model. Since the preference region typically constitutes only a small portion of the entire Pareto frontier, we leverage the exploration and exploitation capabilities of the Kriging model. Within ROI, we generate only \(m+1\) reference vectors. These reference vectors help guide the search within the ROI. The Kriging model is then employed to directly approximate the fitness values of individuals corresponding to these reference vectors. By doing so, we efficiently explore the ROI while effectively capturing the fitness landscape of the hydrocracking optimization problem.

To better explore the ROI, transfer learning is introduced into the search process to improve the surrogate model’s prediction ability and global exploration ability. It mainly includes two levels of transfer: (1) sample transfer: individuals who perform well on different sub-problems are involved in building surrogate models for other sub-problems. (2) parameter transfer: when building an surrogate model, information about the parameters of other surrogate models is consulted.

The subsequent sections of this paper are structured as follows. Section  Related works provides an overview of previous related research, encompassing fundamental notions of multi-objective optimization and Kriging models. Section  Proposed method is devoted to clarifying our divised algorithm and its implementation. Section  Experimental results and analysis presents and discusses the experimental results of our TPD-MOEA and the comparative algorithm for the benchmark problem and the refining process. Finally, Sect.  Conclusion summarizes this paper.

Related works

In this section, we begin by providing the definition of MOPs [ 41 ]. For the sake of convenience, our discussion will be confined to scenarios where all objectives are aimed at minimization, as the conversion of maximizing objectives to minimizing ones can be readily accomplished. Subsequently, we introduce the well-known Kriging model, which is utilized to approximate the value of the aggregation function.

Definition of MOPs

A minimization MOP takes the following form:

where \(\textbf{x} = \left( x_1, x_2,\ldots , x_d \right) ^T\) symbolizes the vector of decision variables, d represents the dimension of the decision vector, \(\Omega \in {R}^d\) is decision space, \(F:\Omega \rightarrow {R}^m\) denotes the objective vector, comprising m objective functions, \({R}^m\) is objective space, \(h_i\) and \(g_j\) is the equality and inequality constraints of the problem respectively, while \(n_h\) and \(n_g\) are the numbers of the equality and inequality constraints.

In MOPs, the objectives frequently exhibit conflicting characteristics, meaning that no solution can be optimal across all objectives concurrently. Instead, optimal solutions in MOPs represent a balance or compromise among the objectives, and these solutions are termed Pareto Solutions. The entirety of Pareto optimal solutions constitutes the Pareto set (PS) within the decision space, while the corresponding mapping of these solutions in the objective space is designated as the Pareto front (PF). When \(m > 3\) , MOPs are termed many-objective optimization problems (MaOPs).

Kriging model

In surrogate-assisted evolutionary algorithms (SAEAs), the Kriging model, also known as the Gaussian process, is a highly appealing mathematical regression model based on the optimal linear unbiased estimation method. It not only offers prediction values but also provides valuable uncertainty information about its predictions. This uncertainty information proves to be beneficial in achieving a balance between exploration and exploitation while managing the model. By incorporating the Kriging model in the optimization process, SAEAs can efficiently approximate the fitness functions and guide the search towards promising regions in the search space.

Kriging model treats the input x as a variable from Gaussian distribution [ 42 ], which can be formulated as:

where \(\mu \) is the prediction values of the Kriging model, \(\varepsilon \left( \textbf{x} \right) \) is a stochastic process characterized by a zero mean and a standard deviation \(\sigma \) :

To approximate the real function \(f\left( \textbf{x} \right) \) , Kriging model necessitates training through a set of samples. Considering a collection of N n -dimensional inputs denoted as \(X=\left. \left\{ \textbf{x}^1, \textbf{x}^2, \cdots ,\textbf{x}^N \right. \right\} ^T\) and their associated objective function values \(Y=\left. \left\{ y^1, y^2, \cdots ,y^N \right. \right\} ^T\) , there exists a multivariate Gaussian distribution on \(R^n\) . In general, For two arbitrary inputs \(\textbf{x}^i\) and \(\textbf{x}^j\) , Kriging model uses squared exponential correlation with additional hyperparameters to calculate their correlations \(R\left( \textbf{x}^i, \textbf{x}^j \right) \) :

where \(i,j = 1, \cdots , n\) . \(\theta _{k}\) and \(p_{k}\) are the hyperparameters. When there are N inputs, an \(N \times N\) covariance matrix S can be obtained:

The hyperparameter \(\theta _{k}\) denotes the importance of \(k\text {-th}\) dimension and can be estimated by maximizing the following likelihood function:

where \(\det \left( \cdot \right) \) is the determinant of a square matrix.

Variable \(\hat{\mu }\) and \(\hat{\sigma }\) can be estimated by

where \(\textbf{1}\) stands for an \(n \times 1\) vector comprised of ones.

Given a new input \({\bar{\textbf{x}}}\) , the prediction value \(\bar{y}\) and variance \(\bar{\sigma }^2\) of \(\bar{x}\) can be calculated by the following formulas:

where r represents an \(n \times 1\) vector containing the covariance values between \({\bar{\textbf{x}}}\) and all the training points.

Proposed method

In this section, we will describe the proposed TDP-MOEA. Specifically, the framework of the proposed algorithm is outlined first, and then the preference model and transfer learning models are elaborated in detail.

The overarching framework of the presented algorithm, i.e., a transfer learning-driven preference-inspired multi-objective evolutionary algorithm (TDP-MOEA), is presented in Algorithm 1, which includes four main phases:

Main Framework of TDP-MOEA

Preference articulation method (line 1): The proposed TDP-MOEA algorithm requires the DM to provide their preference vector and specify the desired region size. Using this information, we can determine the boundary of ROI. Within the ROI, we generate a set of uniform reference vectors. Notably, our approach stands out by generating only \(m + 1\) reference vectors, a unique feature that sets it apart from other methods. The process of determining the boundaries of preference regions and generating the reference vectors will be thoroughly discussed in Sect.  Preference model .

Initialization (lines 2–4): During this stage, our primary objectives are to generate the initial population and establish the initial surrogate models. Initially, the Latin hypercube sampling method [ 43 ] will be employed to produce N individuals. Subsequently, the real objective functions will evaluate all these individuals. Once evaluated, the individuals will be linked with the closest reference vector, determined by their angle with the reference vectors. Their fitness will then be calculated based on different vectors. All the evaluated individuals will be duplicated into an archive for storage. Among these archived individuals, we will select those demonstrating the highest fitness on this vector. These selected individuals will be utilized to train the Kriging model, which is employed in approximating the fitness of the individuals.

Evolving (lines 5–14): In each generation of the evolutionary process, offspring will be generated using the Kriging models and the Expected Improvement (EI) acquisition function. Subsequently, the newly created individuals will be evaluated using the real objective functions. They will then be associated with the closest reference vector and have their fitness calculated based on different vectors before being stored in the archive. To enhance the Kriging models, a transfer learning method will be employed, which encompasses two levels of transfer: sample transfer and parameter transfer. A detailed discussion of these transfer methods can be found in Sect.  Transfer learning model . The evolutionary process will persist until the maximum number of evaluations, denoted as MaxFEs , is reached.

Selection (lines 15–16): Finally, all non-dominated individuals in ROI form the final solutions.

Preference model

The ways in which DM express the preferences can be broadly categorized into two groups. The first category encompasses knee points, extreme points, or nadir points, while the second category involves goal attainment, reference vectors, preference relations, and other similar approaches. The key distinction lies in whether the preferences are explicitly stated [ 7 ].

In this work, we introduce a novel preference model based on reference vectors. Since ROI constitutes only a sub-region of the entire PF. As a result, the variation between different sub-problems within the ROI is smaller compared to that of the entire PF. Consequently, there is no need to generate an excessive number of reference vectors. Instead, we generate \(m + 1\) reference vectors to guide the direction of population evolution, where m represents the number of objectives of the test problems.

Illustration of the preference model

The method of generating reference vectors in this work is presented in Algorithm 2. Given the DM’s unit preference vector \(W_{pre} = \left\{ w_{1}, w_{2}, \cdots , w_{m} \right\} , \sum _{i}^{m}{w_{i}=1}\) , and the desired region size \(\epsilon \) , \( 0< \epsilon \le 1\) , the boundary vectors of ROI can be defined by follows:

where \(W_b\) consists m extreme vectors, e.g., (1,0,0), (0,1,0), and (0,0,1) in 3-objectives case. The larger the \(\epsilon \) is, the large the ROI will be. Once the m boundary reference vectors have been determined, the m reference vectors \(W_{ROI}\) will be calculated using equation 12 . These m reference vectors will then be combined with the preference reference vector \(W_{pre}\) . As a result, a total of \(m + 1\) reference vectors will be evenly distributed in ROI to guide the direction of the evolutionary search. For a visual representation of this process, please refer to Fig.  2 . In Fig.  2 , the intersection of the boundary vector, the extreme vector, and the preference vector with the hyperplane corresponds to the boundary point, the extreme point, and the preference point, respectively.

Reference_Vectors_Generation

Angle penalized distance [ 27 ] is employed as the fitness function, which can be calculated by equation 13 :

where \(\left\| f_j\right\| \) is the distance from the objective vector of the \(j\text {-th}\) individual to the origin point and \(\theta _{j}^{i}\) is the angle between the \(j\text {-th}\) individual and the reference vectors \(W_{ROI}[i]\) . \(P\left( \theta _{j}^{i}\right) \) is a penalty function, which is defined as follows:

where m is the number of objects, \(\alpha \) serves as a hyper-parameter employed to regulate the rate of change of the penalty function and we use the default setting of \(\alpha \) in [ 27 ], FEs is the number of evaluations that have been consumed, and MaxFEs is the maximum number of evaluations, \(\theta \) is the angle between the reference vectors, which is a constant value. During the initial phase of the evolutionary process, an emphasis on convergence is prioritized to draw individuals nearer to the PF. Once individuals have successfully converged to the PF, the focus shifts towards promoting diversity, leading to the dispersion of individuals along the PF.

Surrogate model

In data-driven evolutionary algorithms, surrogate models can replace real function evaluations, providing predictions for objective values. For example, the MOEA/D-EGO method treats the predicted objective values as independent variables and uses the additivity of the Gaussian distribution to generate a new Gaussian model (as mentioned in [ 25 ]). However, such may can accumulate errors in predicted values, leading to inaccuracies in fitness values. In addition, treating predicted objective values as independent variables may neglect critical information because of conflicting objectives.

Instead, we prefer the direct method, using surrogate models to directly approximate the aggregation function. However, this approach requires an increasing number of surrogate models with the inclusion of more reference vectors, making it computationally demanding. To handle this issue, in this work, \(m + 1\) Kriging models are trained to approximate the fitness of solutions on different reference vectors.

Expected improvement (EI) acquisition function [ 44 ] is used as the infill criterion for sampling promising offspring. For a minimization problem, it is given by

where \(\varPhi (\cdot )\) and \(\phi (\cdot )\) represent the normal cumulative distribution function and the probability density function, respectively. \(y_{min}\) denotes the minimum value in the current population. For a new individual \(\textbf{x}\) , \(\hat{y}(\textbf{x})\) and \(s(\textbf{x})\) represent the predicted value and uncertainty information, respectively, provided by the Kriging model.

Transfer learning model

In order to decrease the quantity of models, we adopt a strategy of generating \(m + 1\) reference vectors uniformly within ROI. This allows us to convert the original multi-objective problem into \(m + 1\) single-objective problems. Each sub-problem is then addressed using a surrogate model, which predicts the fitness values of individuals. However, using such a small number of reference vectors presents potential issues.

The first issue involves the accuracy of surrogate models. Initially, the reference vectors partition the objective space into \(m + 1\) sub-regions, with individuals in each sub-region forming a sub-population. These individuals are utilized for training the surrogate model, which can accurately predict fitness values within that specific sub-region. However, the predicted values might become less accurate for individuals located in other regions. To overcome this limitation, we propose a transfer learning method based on individuals in the evolving stage. For each \(W_{ROI}[i]\) reference vector, we select \(11 \cdot d -1 + 25\) individuals (suggested in [ 24 ]) with the best fitness value in that sub-problem to train the model. This inclusion of individuals from other sub-regions helps to enhance the model’s accuracy and expedite the algorithm’s convergence.

Additionally, even though the reference vectors are uniformly distributed, their small number may not adequately cover the entire Pareto front within the ROI. Consequently, the distribution of final solutions might be concentrated in a few points rather than evenly spread across the entire Pareto front, making it challenging to maintain a uniform distribution of populations.

Moreover, during the offspring selection process, the individual with the maximum EI value is chosen as the new offspring. This process strongly depends on the surrogate model’s parameters. The hyper-parameter \(\theta _i\) in the Kriging models represents the importance of the \(i\text {-th}\) feature (decision variable) and can be considered as the extracted characteristics. Given that ROI usually represents only a small fraction of the entire Pareto front, sub-problems within ROI may share many common characteristics. Transferring these parameters might be a viable approach to alleviate this problem. Transfer learning in Kriging models has been proposed by several researchers [ 45 , 46 ]. In this work, we adopt a feature selection-based parameter transfer learning method [ 47 ] to facilitate information sharing among models.

The transfer learning process is presented in Algorithm 3, encompassing two-level transfer learning, namely, individual-based transfer learning and parameter-based transfer learning. Initially, we select \(11 \cdot d - 1 + 25\) individuals with the best fitness for this sub-problem to train the model. Subsequently, these individuals are categorized into different classes based on the minimum angle of their objective vector to the reference vectors. The number of individuals in each class indicates the significance of the model’s parameters and is utilized in the parameter transfer process. To prevent negative transfer, we employ a binary particle swarm optimization algorithm based on filtered feature selection every five generations to discern the most pertinent subset of parameters for this sub-problem. Moving on to the parameter-based transfer process, let us consider the \(i\text {-th}\) trained model, and suppose that the index set of the most relevant variables related to the corresponding sub-problem is denoted as \(param_{index}\) . Let \(prop = \left\{ prop_{1}, prop_{2}, \cdots , prop_{m + 1} \right\} \) represent the set of proportions for each class. The new parameters of this model can be calculated as follows:

where \(j \in param_{index}\) , and \(\theta _i^{j}\) is j parameter of \(i\text {-th}\) Kriging model. \(\alpha \) is an adaptation parameter, which is used to assign adaptive weights of parameters of different models in the aggregation function, which is formulated as follows:

where MaxFEs and FEs denote the max number and the current number of the function evaluations using the real objective function, respectively. At the beginning of the optimization, the spaced areas between sub-regions are relatively large, so the utilization of knowledge from other models to generate more offspring within this region is preferable. As optimization proceeds, the spaced areas become smaller, so the model’s parameters will become increasingly important. Note that when updating the \(i\text {-th}\) model, if the percent of \(i\text {-th}\) class is less than p , we think the model has not extracted enough information in its response regions, so the model’s parameters will not be transferred. In this work, parameter p is set to \(1 / (m + 1) \cdot 0.5\) .

Transfer_Learning_Method

Experimental results and analysis

Experimental settings.

To evaluate the proposed algorithm’s performance, we conduct comparative studies with six representative reference or preference vectors driven algorithms, namely, K-RVEA [ 27 ], MOEA/D-EGO [ 25 ], r-NSGAII [ 17 ], MOEA-D-PRE [ 48 ], MCEA/D [ 49 ] and PB-RVEA [ 50 ]. For fair comparison, all algorithms are constrained to find the optimal solution within the same preference region, and use the same \(m + 1\) reference vectors generated in the ROI. The numerical experiments are performed on the popular ZDT benchmark [ 51 ] and DTLZ benchmark [ 52 ] for 2, 3, and 5 objectives. Each algorithm is independently run on each test problem 20 times. The number of decision variables is set to \(m + k\) , where m denotes the number of objectives, and k is set to 9. The population size and maximum number of fitness evaluations are set to 100 and 200, respectively, when \(m=2\) , and 105 and 300, respectively, when \(m=3\) , and 126 and 400, respectively, when \(m=5\) . The preference vector \(W_{pre}\) is set to \(\left\{ \frac{1}{m},\frac{1}{m},\cdots , \frac{1}{m} \right\} \) to ensure uniform preference across all objectives. All the test codes of compared algorithms and benchmark instances are provided in PlatEMO [ 53 ].

The distribution of the PF obtained by TDP-MOEA, TDP-MOEA-0, TDP-MOEA-1 and TDP-MOEA-2 on DTLZ-2

Different performance indicators are utilized for the experiment analysis and application results analysis. In the experiment analysis, we employ the inverted generation distance (IGD) [ 54 ], which assesses the average distance between the obtained front and the reference front, providing a comprehensive evaluation of both convergence and diversity. This metric allows for comparing the performance of different algorithms on benchmarks. When we calculate the IGD, we need to have the reference front in the ROI. The way to get the reference front in the ROI is as follows: (1) we need to get the reference points of the true PF of a test problem through PlatEMO [ 53 ]. (2) Following the preference model in Sect.  Preference model , all reference points of the true PF will be mapped to the space of preference/reference vectors. (3) On the basis of the given preference vector and the predefined desired region size ( \(\epsilon \) ), we can find the boundary points of the ROI. (4) Once the boundaries are determined, all solutions in the ROI are found and denoted by the reference front.

Additionally, we use the Hypervolume (HV) [ 55 ], another comprehensive metric, to measure the volume dominated by the obtained approximated front during the application results analysis. In general, superior algorithm performance is indicated by smaller IGD values and larger HV values. It’s worth noting that only individuals within ROI contribute to the calculation of performance indicators. For the experiment analysis, we set the number of reference points for IGD to 1000, 1540, and 1820, respectively. Regarding HV, we use a reference point of (10172, 0.25, 0.49, 0.7, 0.17), which is an empirical value derived from the oil refining process.

Performance comparison on benchmark

The results obtained by TDP-MOEA and other compared algorithms are presented in Tables 1 , 2 , 3 , providing the mean and standard deviation of the IGD values for the ZDT and DTLZ test suites with \(\epsilon =0.3\) , 0.5, and 0.7, respectively. In these tables, the symbol ‘NaN’ denotes cases where the algorithm failed to find a solution within ROI. Additionally, the symbols ‘+,’ ‘ \(\approx \) ’, and ‘-’ indicate that the compared algorithm performs significantly better, similarly to, or worse than TDP-MOEA. The highlight displays the best result for each test instance, while the statistical results are presented at the bottom of the table.

The distribution of the PF obtained by TDP-MOEA, TDP-MOEA-0, TDP-MOEA-1 and TDP-MOEA-2 on DTLZ-4

Several observations can be drawn from the above results. Firstly, the proposed algorithm TDP-MOEA consistently outperforms other algorithms and ranks first with the most best results on the test instances with different numbers of objectives and sizes of ROI, particularly on the ZDT test suites, DTLZ1, DTLZ2, DTLZ3 and DTLZ5. The results indicate that the proposed transferable preference learning technique is able to improve the searching efficiency of TDP-MOEA in handling expensive MOPs. However, on ZDT4 when \(\epsilon = 0.3\) , \(\epsilon = 0.5\) , and \(\epsilon = 0.7\) , and on DTLZ4 with 8 objectives when \(\epsilon = 0.3\) and \(\epsilon = 0.5\) , none of the algorithms can identify a preferred solution. This is because these test instances are exceedingly challenging to approximate their Pareto fronts, and the difficulty escalates with limited evaluations. By contrast, on DTLZ4 with 8 objectives when \(\epsilon = 0.7\) , TDP-MOEA, KRVEA, PB-RVEA are able to find the solutions in the ROI. This results may indicate that smaller ROI makes the optimization more difficult since a smaller number of solutions may be generated in the ROI during the optimization process. This phenomenon also happens in the statistical results. From Tables 1 , 2 , 3 , TDP-MOEA performs better than other algorithms on most instances, and the superiority of TDP-MOEA turns more apparent when the ROIs expand. In addition, on ZDT6 when \(\epsilon = 0.3\) , all algorithms except TDP-MOEA give results of ‘NaN’, which demonstrates that TDP-MOEA can find solutions within the preference region even when the preference region is small. Overall, the results in Tables 1 , 2 , 3 have demonstrated that the proposed transferable preference learning technique is able to assist in improving the searching ability of TDP-MOEA in handling expensive MOPs.

To assess the impact of the transfer learning method, we conducted an additional comparison experiment between the algorithm based on no transfer learning strategy (TDP-MOEA-0), the algorithm based on the individual-driven transfer learning strategy (TDP-MOEA-1), the algorithm based on the parameter-driven transfer learning strategy (TDP-MOEA-2), and the algorithm based on the mixture of the strategies (TDP-MOEA). Figures  3 , 4 illustrate the distribution of the non-dominated solutions generated by TDP-MOEA, TDP-MOEA-0, TDP-MOEA-1 and TDP-MOEA-2 on DTLZ-2 and DTLZ-4 test problems, respectively. In these figures, the red dots represent the non-dominated individuals, solid orange lines depict the reference vectors, and blue dashed lines outline the boundary of the preference region. In terms of the results, it can be seen that the variants with transfer learning strategies can generate more non-dominated solutions in the ROI compared with TDP-MOEA-0, proving that either of the individual-based and the parameter-based transfer learning strategies is able to improve the prediction ability of the model. Especially in Figs.  3 , 4 , TDP-MOEA with the mixture of the individual- and parameter-based transfer learning strategies generates more non-dominated solutions in the ROI compared with TDP-MOEA-0, TDP-MOEA-1 and TDP-MOEA-2, proving that the hybrid transfer learning strategies are able to effectively guide the evolutionary process toward the ROI.

Application on oil refining process

In this section, we apply TDP-MOEA to optimize the oil refining process and compare its performance with other methods. We use a 5-objective simulation model with eight decision variables [ 3 ], and Aspen HYSYS [ 56 ] is used for rigorous hydrocracking process simulation. The decision variables, optimization objective functions, and parameter settings (such as feed material properties, reactor design parameters, and recycled bottom conditions) are detailed in Tables 4 , 5 , 6 , 7 , 8 .

The maximum number of evaluations of the true objective function ( MaxFEs ) is set to 500, the initial population size is 126, and the prefrerence vector of DM \(W_{pre}\) is set to \(\left\{ 0.2, 0.2, 0.2, 0.2, 0.2\right\} \) . \(\epsilon \) is set to 0.5, as it yielded the best performance on the benchmarks. The parameters of the comparison algorithms are set to the recommended values from the corresponding literature.

For fairness, all comparison algorithms use the same \(m+1\) reference vectors generated in the ROI. We calculate HV(pre) and HV based on the non-dominated solutions within the ROI and the entire space, respectively. The statistical results for HV values on 30 independent runs are presented in Table 9 , showing that TDP-MOEA achieves the best results either within ROI or the entire space, while MCEA/D exhibits the poorest overall performance. Additionally, we also provide the visualization results in Fig.  5 . It illustrates the distribution of non-dominated fronts obtained by different algorithms. Red individuals represent solutions in the preference region, while the blue ones are the non-preferred solutions. The figures show that TDP-MOEA produces more non-dominated solutions in the preference regions compared to other methods. Moreover, MOEA/D-PRE and MCEA/D are unable to generate non-dominated solutions in the ROI. PB-RVEA and r-NSGAII generate sparse non-dominated solutions in the ROI. K-RVEA and MOEA/D-EGO perform better than the above algorithms. However, when they are compared with TDP-RVEA, they seem to be less effective than TDP-MOEA in finding preferred solutions in the region of interest and the results in Table 9 can also support this conclusion. Overall, TDP-MOEA shows its advantage in providing more choices in the ROI for the DM and helping them gain a clearer understanding of their preferences in handling the oil refining process problem.

The parallel coordinates of the PF by TDP-MOEA and other algorithms on hydrocracking optimization problem

In this paper, we present a novel transfer learning driven preference-inspired multi-objective evolutionary algorithm, named TDP-MOEA, designed to tackle EMOPs or EMaOPs in the context of the oil refining process. Our approach involves an in-depth analysis of various methods to construct surrogate models for individual fitness, comparing their performance, and proposing a new preference representation suitable for preference scenarios. To enhance the surrogate model’s accuracy and population diversity, we introduce a new transfer model that incorporates two-level transfers, including individual-based transfer and parameter-based transfer, considering the relationships among different sub-problems. The proposed TDP-MOEA is extensively tested on benchmark suites and successfully applied to real-world oil refining problem. The experimental results demonstrate that TDP-MOEA consistently outperforms classical algorithms used for comparison.

In scenarios where the preference region is small, the challenge of obtaining a preferred solution within that region increases significantly. Finding such solutions quickly, given a limited number of evaluations, becomes a critical concern. Moreover, the existence of numerous different preference expressions adds complexity. Our future research direction will focus on effectively integrating these expressions with surrogate models to enhance the optimization process.

Data availibility statement

There are no datasets used in this paper.

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Acknowledgements

This work was supported by National Natural Science Foundation of China No. 62103150, National Natural Science Foundation of China No. 62333010.

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Yu, G., Wang, X., Jiang, C. et al. Transferable preference learning in multi-objective decision analysis and its application to hydrocracking. Complex Intell. Syst. (2024). https://doi.org/10.1007/s40747-024-01537-6

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• How to Do Thematic Analysis | Step-by-Step Guide & Examples

How to Do Thematic Analysis | Step-by-Step Guide & Examples

Published on September 6, 2019 by Jack Caulfield . Revised on June 22, 2023.

Thematic analysis is a method of analyzing qualitative data . It is usually applied to a set of texts, such as an interview or transcripts . The researcher closely examines the data to identify common themes – topics, ideas and patterns of meaning that come up repeatedly.

There are various approaches to conducting thematic analysis, but the most common form follows a six-step process: familiarization, coding, generating themes, reviewing themes, defining and naming themes, and writing up. Following this process can also help you avoid confirmation bias when formulating your analysis.

This process was originally developed for psychology research by Virginia Braun and Victoria Clarke . However, thematic analysis is a flexible method that can be adapted to many different kinds of research.

Table of contents

When to use thematic analysis, different approaches to thematic analysis, step 1: familiarization, step 2: coding, step 3: generating themes, step 4: reviewing themes, step 5: defining and naming themes, step 6: writing up, other interesting articles.

Thematic analysis is a good approach to research where you’re trying to find out something about people’s views, opinions, knowledge, experiences or values from a set of qualitative data – for example, interview transcripts , social media profiles, or survey responses .

Some types of research questions you might use thematic analysis to answer:

• How do patients perceive doctors in a hospital setting?
• What are young women’s experiences on dating sites?
• What are non-experts’ ideas and opinions about climate change?
• How is gender constructed in high school history teaching?

To answer any of these questions, you would collect data from a group of relevant participants and then analyze it. Thematic analysis allows you a lot of flexibility in interpreting the data, and allows you to approach large data sets more easily by sorting them into broad themes.

However, it also involves the risk of missing nuances in the data. Thematic analysis is often quite subjective and relies on the researcher’s judgement, so you have to reflect carefully on your own choices and interpretations.

Pay close attention to the data to ensure that you’re not picking up on things that are not there – or obscuring things that are.

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Once you’ve decided to use thematic analysis, there are different approaches to consider.

There’s the distinction between inductive and deductive approaches:

• An inductive approach involves allowing the data to determine your themes.
• A deductive approach involves coming to the data with some preconceived themes you expect to find reflected there, based on theory or existing knowledge.

Ask yourself: Does my theoretical framework give me a strong idea of what kind of themes I expect to find in the data (deductive), or am I planning to develop my own framework based on what I find (inductive)?

There’s also the distinction between a semantic and a latent approach:

• A semantic approach involves analyzing the explicit content of the data.
• A latent approach involves reading into the subtext and assumptions underlying the data.

Ask yourself: Am I interested in people’s stated opinions (semantic) or in what their statements reveal about their assumptions and social context (latent)?

After you’ve decided thematic analysis is the right method for analyzing your data, and you’ve thought about the approach you’re going to take, you can follow the six steps developed by Braun and Clarke .

The first step is to get to know our data. It’s important to get a thorough overview of all the data we collected before we start analyzing individual items.

This might involve transcribing audio , reading through the text and taking initial notes, and generally looking through the data to get familiar with it.

Next up, we need to code the data. Coding means highlighting sections of our text – usually phrases or sentences – and coming up with shorthand labels or “codes” to describe their content.

Let’s take a short example text. Say we’re researching perceptions of climate change among conservative voters aged 50 and up, and we have collected data through a series of interviews. An extract from one interview looks like this:

In this extract, we’ve highlighted various phrases in different colors corresponding to different codes. Each code describes the idea or feeling expressed in that part of the text.

At this stage, we want to be thorough: we go through the transcript of every interview and highlight everything that jumps out as relevant or potentially interesting. As well as highlighting all the phrases and sentences that match these codes, we can keep adding new codes as we go through the text.

After we’ve been through the text, we collate together all the data into groups identified by code. These codes allow us to gain a a condensed overview of the main points and common meanings that recur throughout the data.

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Next, we look over the codes we’ve created, identify patterns among them, and start coming up with themes.

Themes are generally broader than codes. Most of the time, you’ll combine several codes into a single theme. In our example, we might start combining codes into themes like this:

At this stage, we might decide that some of our codes are too vague or not relevant enough (for example, because they don’t appear very often in the data), so they can be discarded.

Other codes might become themes in their own right. In our example, we decided that the code “uncertainty” made sense as a theme, with some other codes incorporated into it.

Again, what we decide will vary according to what we’re trying to find out. We want to create potential themes that tell us something helpful about the data for our purposes.

Now we have to make sure that our themes are useful and accurate representations of the data. Here, we return to the data set and compare our themes against it. Are we missing anything? Are these themes really present in the data? What can we change to make our themes work better?

If we encounter problems with our themes, we might split them up, combine them, discard them or create new ones: whatever makes them more useful and accurate.

For example, we might decide upon looking through the data that “changing terminology” fits better under the “uncertainty” theme than under “distrust of experts,” since the data labelled with this code involves confusion, not necessarily distrust.

Now that you have a final list of themes, it’s time to name and define each of them.

Defining themes involves formulating exactly what we mean by each theme and figuring out how it helps us understand the data.

Naming themes involves coming up with a succinct and easily understandable name for each theme.

For example, we might look at “distrust of experts” and determine exactly who we mean by “experts” in this theme. We might decide that a better name for the theme is “distrust of authority” or “conspiracy thinking”.

Finally, we’ll write up our analysis of the data. Like all academic texts, writing up a thematic analysis requires an introduction to establish our research question, aims and approach.

We should also include a methodology section, describing how we collected the data (e.g. through semi-structured interviews or open-ended survey questions ) and explaining how we conducted the thematic analysis itself.

The results or findings section usually addresses each theme in turn. We describe how often the themes come up and what they mean, including examples from the data as evidence. Finally, our conclusion explains the main takeaways and shows how the analysis has answered our research question.

In our example, we might argue that conspiracy thinking about climate change is widespread among older conservative voters, point out the uncertainty with which many voters view the issue, and discuss the role of misinformation in respondents’ perceptions.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Measures of central tendency
• Chi square tests
• Confidence interval
• Quartiles & Quantiles
• Cluster sampling
• Stratified sampling
• Discourse analysis
• Cohort study
• Peer review
• Ethnography

Research bias

• Implicit bias
• Cognitive bias
• Conformity bias
• Hawthorne effect
• Availability heuristic
• Attrition bias
• Social desirability bias

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