Group‐based trajectory modeling of body mass index and body size over the life course: A scoping review

Abstract Background Group‐based trajectory modeling has been applied to identify distinct trajectories of growth across the life course. Objectives of this study were to describe the methodological approaches for group‐based modeling of growth across the life course and to summarize outcomes across studies. Methods A scoping review with a systematic search of Medline, EMBASE, CINAL, and Web of Science was conducted. Studies that used a group‐based procedure to identify trajectories on any statistical software were included. Data were extracted on trajectory methodology, measures of growth, and association with outcomes. Results A total of 59 studies were included, and most were published from 2013 to 2020. Body mass index was the most common measure of growth (n = 43). The median number of identified trajectories was 4 (range: 2–9). PROC TRAJ in SAS was used by 33 studies, other procedures used include TRAJ in STATA, lcmm in R, and Mplus. Most studies evaluated associations between growth trajectories and chronic disease outcomes (n = 22). Conclusions Group‐based trajectory modeling of growth in adults is emerging in epidemiologic research, with four distinct trajectories observed somewhat consistently from all studies. Understanding life course growth trajectories may provide further insight for population health interventions.

similarities in growth patterns may be differentially at risk for development of chronic diseases later in life.
Several approaches can be used to measure growth over the life course. Characterization of growth can be done using growth curves that assess individual change over time, or through group-based methods, which identify groups of individuals who share underlying characteristics. 6,7 The use of group-based procedures to categorize patterns of growth is an emerging method in epidemiology; however, the methods associated with generating group-based trajectories vary. Two common methods include latent class growth analysis or growth mixture modeling which are finite mixture modeling approaches that identify groups of individuals who share underlying characteristics. 8 The advantages of using group-based procedures to understand growth over the life course are the potential identification of sensitive or critical periods of exposure. There are periods of accelerated growth in childhood and the incidence and remission of obesity changes with age. 9 Understanding the impact of accumulation of risk or change in risk of obesity across the life course may help to better understand the risk of disease various chronic diseases. 7 A previous systematic review of group-based trajectory modeling for BMI trajectories only in childhood, starting at birth, found that most studies identified three or four distinct trajectories; however, there were several inconsistencies in terms of methodologies used to identify trajectories. 10 A limitation of the previous review is that it only included studies that had a measure of growth at birth and only those that used BMI as the anthropometric measure. There have been no reviews that included measures of growth for adults over the age of 18. Thus, the primary objective of this study is to review the methodological approaches and results of groupbased modeling studies of growth across the life course. A secondary objective is to describe the outcomes associated with growth trajectories.

| Study design
A systematic scoping review was conducted. This protocol review was registered with PROSPERO (CRD-42019129356). The preferred reporting items for systematic reviews and meta-analyses extension for scoping reviews guidelines were followed for the reporting of this study.

| Eligibility criteria
Studies were included if a group-based approach to construct trajectories of anthropometric measures were used. Inclusion criteria were that all studies had at least three repeated anthropometric measures taken over a period of at least 1 year, and at least 1 measure had to be recorded while the participant was >18 years of age. According to Medical Subject Headings 11 and World Health Organization, 12 growth is defined as a gradual increase or development in cells that results in changes in body weight or height.
Therefore, any anthropometric measures to assess growth (e.g., BMI, height, weight, waist circumference, body size, waist-to-hip, and skinfold thickness) were included. Any exposures or outcomes evaluated in relation to the growth trajectories were eligible for inclusion into the review. Studies were excluded if they focused on a specific clinical population, for example, only people with diabetes, spinal cord injuries, or who were pregnant. Studies that looked at growth velocity or modeled weight gain or weight loss after a medical procedure were also excluded. Any year of publication or study design were included; however, only studies published in English and primary studies were included (abstracts and review papers were excluded).  Table 1. Search strategies for the remaining databases can be found in the Tables A1-A3. The reference lists of included studies were reviewed to determine any further studies that were eligible for inclusion into the study.

| Study selection
Once searches were conducted in all databases, studies were imported into Covidence. Covidence is a web-based software used to maintain records throughout the various stages of conducting a systematic review. 13 All duplicates were identified and then removed prior to beginning screening. Studies were screened at title and abstract level, and then at full text by three independent reviewers (Vanessa De Rubeis, Alessandra Andreacchi, Isobel Sharpe). Conflicts at both title and abstract level and full-text level were resolved by the reviewers and a final decision was then made regarding inclusion of the study.

| Data extraction
All eligible studies had data extracted by two independent abstractors (Vanessa De Rubeis, Alessandra Andreacchi, Isobel Sharpe). Any conflicts that arose during data extraction were resolved by a third reviewer (Vanessa De Rubeis, Alessandra Andreacchi, Isobel Sharpe).
A data extraction template on Microsoft Excel was used to organize the information extracted from each study. Data on the general DE RUBEIS ET AL. characteristics of the study, including the author, year of publication, name of study, sample size, and population were extracted. Data were also extracted on the methodology used to generate trajectories, including statistical modeling methods, statistical software used, and model fit criteria. Trajectory details were also extracted, which included the number of trajectories, the shape of trajectories (e.g., cubic, quadratic), names of trajectories, and proportion of people in each trajectory. The measures of growth used to identify the trajectories, the number of measures, and the period of life course which the trajectories encompass were also extracted. Finally, details regarding if the growth trajectories were considered as an exposure or outcome were extracted, and in studies where growth trajectories were the exposure, associations with outcomes were extracted.

| RESULTS
A total of 7170 studies were identified from the search and three additional studies were identified from the reference lists of the included studies. Six hundred and seventy-three duplicates were identified and removed. There were 6497 studies that were screened at title and abstract level and 158 of these studies were screened for eligibility at full-text level. A total of 59 papers met the inclusion criteria and were included in this review. A detailed description of the screening process can be found in Figure 1

| Description of studies
A summary of study characteristics can be found in Table 2 25 Table A4 in the Appendix outlines more detailed characteristics of the included studies. Table 3 summarizes the growth measures and methods that were used to identify trajectories. BMI was the most commonly used growth measure (n ¼ 43). Two studies estimated distinct trajectories for more than one measure of growth. 26,36 Of the 43 studies that used BMI, 27 (63%) relied on self-report, and the remaining 16 (37%) used directly measured height and weight by trained research assistants. Eleven studies used body shape as the growth measure. To measure body shape, studies used pictures or somatotypes, ranging from lean to overweight, which assist in recall of past or current body size. Two studies 26,37 used measured weight (unadjusted for height) to estimate trajectories. Body fat percentage, 38 total lean mass, 26 total body fat mass, 26 skinfold thickness, 36 and waist circumference 39 were also used to estimate trajectories in one study each. One study 40 modeled percent change of BMI from the baseline measure at 20 years of age. No studies used height only as a measure growth.

| Growth measures used and period of life
The number of growth measures used to estimate trajectories ranged from 3 to 16, with a mean of 6.2 (SD ¼ 2.7). The mean trajectory duration (time between first and last anthropometric measurement) was 29.2 years (SD ¼ 17.1). 22 studies that began growth assessment in childhood 5,14,18,20,22,30-32,36,38,41- Of these 37 studies that only reported growth measures in T A B L E 1 EMBASE search strategy 1 "Latent growth model*".mp OR "latent class growth mixture model*".mp OR "growth mixture model*".mp OR "latent growth model*".mp OR "latent class growth analysis". mp OR "latent class growth analyses".mp OR "group based trajectory model*".mp OR "group based trajectory analysis".mp OR "group based trajectory analyses".mp OR "group based model*".mp OR "latent growth mixture model*".mp OR "group based trajectory*".mp adulthood, six studies 26,[61][62][63][64]70 only included measures during the older adulthood period of life (≥60 years of age).

| Statistical approach
As described in Table 3, most studies (n ¼ 33) used the statistical software SAS with the procedure PROC TRAJ 73 to estimate trajectories. Mplus was used by 11 studies and three of these stated full information maximum likelihood (FIML) was used, two stated general mixture modeling was used, and the others did not specify the specific procedure in Mplus. Only four studies used the statistical software R 74 to estimate trajectories, and all fit latent class mixed models using the extended mixed models using latent classes and latent processes (lcmm) package. 75 The final software that was used to estimate trajectories was STATA, TRAJ procedure 76 (n ¼ 11).

| Model fit criteria
The studies used various model fit criteria to determine the number of trajectories that optimally fit the data. The most commonly method was the Bayesian Information Criteria, which was used by almost all studies (n ¼ 54). Studies also used a combination of the Akaike's Information Criteria, Lo-Mendell-Rubin likelihood ratio test, odds of correct classification, posterior probability, significance of polynomial terms, and a priori knowledge to inform the creation of trajectories. Only nine studies included entropy as a criterion for model fit, with the most commonly reported cutoff of >1%. The most common polynomial terms that were found to be significant were quadratic and cubic polynomial terms (Table 3).

| Number and naming of identified trajectories
The number of trajectories that studies identified ranged from 2 to 9.
Most studies (56%) found the optimal number of trajectories was 4.
Fifteen studies identified five trajectories, and 11 studies identified three trajectories to best fit the data. A sample plot illustrating a 5-trajectory model from an included study 35 can be found in Figure 2.
The names that were given to the trajectories varied greatly across all studies; however, names were commonly generated based on visual assessments. Most studies used terms such as "normal," "normative," "low," or "stable" to describe the trajectory defined by the lowest weight/BMI throughout the life course. Other common terms used to name trajectories include, "increasing," "decreasing," "overweight," "obese," and "persistent". Five studies did not name their identified trajectories, and only referred to the trajectories by group or class number. A detailed description of the various names used to describe the trajectories in each study can be found in Table 3.
The prevalence of the identified trajectories varied, for example the "normal" or "lean stable" trajectory ranged from 14% to 91% of the study populations. Whereas the trajectory with the lowest prevalence was most often the highest growth trajectory, often defined as "persistent obesity" and ranged from 0.8% to 10  inform where future studies When comparing the studies that used the same study populations, it was evident that differences did exist.
However, this may be related to differences in the objectives of the studies leading to slightly different participants in the study.
For instance, the NLSY was used by five studies. Three of these studies [20][21][22] reported four trajectories, whereas the remaining two studies reported three 80  Using life course trajectories provides a much more comprehensive understanding of the impact of differential growth patterns.
Group-based trajectory modeling is a novel approach to identify various patterns of growth throughout the life course. The findings from this review may inform future epidemiologic research on the commonly used methodologies and approaches used to generate DE RUBEIS ET AL.