Trajectory analysis in obesity epidemiology: a promising life course approach

The prevalence of obesity has been increasing in the past few decades across the world.[1] This trend is expected to continue owing to the rising pandemic of “Western diet” and sedentary lifestyle in the low and middle-income regions. High body mass index (BMI, the weight in kilograms divided by the square of the height in meters) has been established as a risk factor for numerous chronic diseases, including cardiovascular disease, type 2 diabetes, many cancers, chronic kidney disease, and an array of musculoskeletal disorders.

Because the incidence of these diseases typically increases with age and excess adiposity tends to accrue during early and middle adulthood, increasing epidemiologic studies have begun to assess how weight change over the life course may influence disease risk independently of the baseline body weight.[2] Leveraging the repeatedly and prospectively collected adiposity data, these studies have examined weight change at different windows of life, mostly from early to middle adulthood and in some cases during middle and late adulthood. Besides corroborating causality for the role of adiposity in disease pathogenesis, such investigations are also important in elucidating the critical window during which excess body fatness may exert most of its adverse effects. This has critical implications, not only for understanding disease etiology but also for development of effective public health strategies. For example, studies of colorectal cancer indicate a predominant risk-elevating effect of weight gain from early adulthood to midlife compared to that from midlife to older age, supporting the importance of early prevention.[3, 4]

However, because of its segmented examination of weight change at different time points, this approach is limited in its ability to capture the dynamic changes of body weight across a broader range of lifespan. More importantly, it becomes challenging to separate and interpret the effect of early adiposity from later weight gain (Table 1), because the two are correlated in a complex manner and together contribute to excess body weight in midlife when chronic disease risk starts to rise rapidly.[5] To overcome these limitations, the group-based trajectory modeling (GBTM) approach has been increasingly used to study the health impact of adiposity from a life course perspective (Figure 1).[6–10] Moreover, the approach has been used to investigate the predictors[11] and influences on intermediate biomarkers[12, 13] of body weight trajectories over an extended period of time. Herein, I provide an overview about the GBTM approach in obesity research. I start with the rationales and principles, and then briefly describe the methods and common applications. I conclude with some critical questions that need to be addressed to fully realize the power of this relatively new method in obesity epidemiology.

Table 1.

Comparison of different approaches in epidemiologic studies of adiposity at different ages in relation to disease risk

Exposure of study	Typical questions to be addressed	Example model specification (only primary exposures shown)	Potential limitations
Adiposity status at certain ages or time points	Is adiposity at each specific age independently associated with disease risk?	Y=BMI_age1+BMI_age2	• Collinearity,  because of tracking  of early-life weight  status into  adulthood. • Over-adjustment,  because  BMI at later life is  likely a mediator for  the effect of  adiposity  at a young age.
Weight change during certain period of time	Is weight change associated with disease risk, independently of baseline weight?	Y=Baseline_weight+weight change	• Difficult to  simultaneously  study weight  change at multiple  periods of time. • Challenging to  separate and  interpret the effect  of baseline weight  from later weight  gain.
Trajectory of body fatness during certain period of time	Does the disease risk differ between individuals with different trajectories?	Y=trajectory_groups	• A limited number of  trajectories are  typically derived  that may not  accurately reflect  each person’s  profile of body  fatness. • Generalizability:  results can be  difficult to compare  between studies.

Figure 1.

Framework of trajectory analysis in epidemiologic research

Assumption and principles of the trajectory analysis

Since its development by Daniel Nagin in 1999,[14] GBTM has been widely used in psychology and criminology to study population differences in individual-level developmental trajectories of behaviors. It is intended to provide a flexible and easily applied approach for identifying distinctive clusters of individual trajectories within the population and for profiling the characteristics of individuals within the clusters. A fundamental assumption of GBTM is that the population is composed of a mixture of distinct groups defined by their developmental trajectories. This assumption distinguishes GBTM from other trajectory modeling methods, such as growth curve modeling (GCM) which assumes that all individuals in the population follow a similar functional form of development and growth mixture modeling (GMM) which assumes that the population is composed of literally distinct subpopulations.[15] Therefore, compared to GCM that is useful to describe how patterns of growth vary continuously throughout the population and GMM to characterize distinct yet unobservable subpopulations in the course of development, GBTM provides a unique statistical tool to classify individuals into relatively homogeneous groups based on their trajectories and in turn approximate the continuous population distribution of trajectories of unknown shape. This principle makes GBTM well suited for biomedical research, because of the well-recognized between-person variation in the development and progression of a wide range of human traits, disorders, and related symptoms and treatment responses.

For obesity research, the trajectory approach can be particularly useful because it respects the continuity of body growth and fat accumulation over time. Compared to the traditional weight change analysis that partitions time into intervals, GBTM takes a holistic approach to studying the evolution of body fatness over time, allows a close scrutiny of the population heterogeneity in change of body fatness over the life course, and permits direct comparison of the disease risk across different trajectory groups.[7] By doing so, it circumvents the difficulty in disentangling the independent effect of early- versus late-life adiposity and addresses a different but more tangible question about the relative disease risk of people who experience different developmental courses of body fatness (Table 1).

Statistical methods of the trajectory analysis

This section is intended to provide a nontechnical overview of the statistical basis of GBTM. Readers interested in the details are encouraged to refer to other excellent publications on the methods of GBTM.[14, 16, 17] A customized SAS procedure Proc Traj has been developed for GBTM analysis.[17, 18] GBTM represents an application of latent growth mixture model that fits longitudinal data as a discrete mixture of two or more latent trajectories and links age and the study trait through a polynomial relationship. Different statistical models can be specified for different types of data (e.g., Poisson model for count data, linear model for continuous data, and logistic model for binary data). In the case of body fatness analysis, GBTM uses BMI or other anthropometric data collected repeatedly across different ages as the input and classifies individuals into distinct trajectory groups, within which the pattern of adiposity evolution is similar. A cubic polynomial linear model can be specified as y_it^j = β₀^j + β₁^jAge_it + β₂^jAge_it² + β₃^jAge_it³, where y_it^jis the expected BMI (or other measurements of choice) of subject i at time t given membership in trajectory group j, Age_it is subject i’s age at time t, and Age_it² and Age_it³ are the square and cubic of subject i’s age at time t.

A key issue of GBTM analysis is model selection, which encompasses two tasks: (a) to determine the optimal number of trajectory groups and (b) to determine the appropriate order of the polynomial function used to model each group’s trajectory. A two-stage approach is typically undertaken to fulfill the two tasks, with the first stage to identify the optimal number of groups by using a quadratic form for all trajectory groups and the second stage to determine the optimal order of the polynomial function specifying the shape of each group. While various criteria have been proposed for model selection, the most commonly used one is the Bayesian information criteria (BIC), which provides a good balance of model complexity and goodness of fit to the data.[16]

Once the form of the final model is determined, trajectories can then be characterized as the product of maximum-likelihood estimation and plotted against age for intuitive interpretation. The derived trajectory groups can be named to describe their visual patterns. Another important product of the modeling process is the posterior membership probability for each individual, which reflects the probability of a person assigned to each of the identified groups. It provides an objective, data-based assignment rule for classification of individuals and post hoc evaluation of the GBTM model. Individuals are assigned to the group to which their posterior membership probability is largest. The resultant group membership assignments can be used as a categorical variable for downstream analyses.

The last step of GBTM analysis involves evaluation of model adequacy. It can be done by calculating the average posterior probability (AvePP) of assignment for each group. The higher the probability, the more adequate the model in describing the data. It has been recommended that an AvePP of at least 0.70 should be achieved for all groups.[9] Another useful diagnostic statistic is the odds of correct classification (OCC) for each group, calculated as the ratio of the odds of correct classification based on the maximum probability classification rule (AvePP/1-AvePP), and the odds of correct classification based on random assignment, which can be calculated using the proportion of individuals assigned to each group π (π/1 − π). If the maximum probability assignment rule has no predictive capacity beyond random chance, OCC=1. As AvePP approaches its ideal value of 1, OCC increases, indicating better assignment accuracy.[7]

Applications of the trajectory analysis

Once the trajectories are identified and individuals are assigned into different groups, subsequent analyses are straightforward and can in general proceed in two directions: to study either the predictors or consequences of the trajectories. The latter is most commonly employed in epidemiology by studying how the risk of diseases or levels of intermediate biomarkers may differ across different trajectories. Specifically, in the area of obesity epidemiology, trajectories of body fatness from early to middle life have been associated with risk of cardiovascular disease,[10] type 2 diabetes,[10] certain cancers,[6, 8, 19–22] and mortality,[7] as well as adulthood biomarkers of telomere length, mitochondrial DNA copy number[12] and the insulin-insulin-like growth factor (IGF) system.[13] Compared to individuals who are lean throughout life, those who are either persistently heavy over the life course or lean in early life and then gain substantial weight in midlife demonstrate a dramatically higher risk of cardiometabolic diseases, modestly increased risk of cancer (with variable associations by cancer types) and early death, and have the most undesirable profiles of biomarkers. These findings highlight a role in metabolic pathogenesis of adiposity across the lifespan, particularly weight gain from early to middle adulthood.

Besides the overall association analysis for all trajectories groups, targeted comparisons can also be made for specific groups to gain further insight into the role of the timing of adiposity in disease development. For example, in our analysis of breast cancer,[6] despite similar levels of achieved body fatness, women who started lean and became heavy later in life actually had a higher risk than those who were persistently heavy across the lifespan, indicating a potential benefit of early-life adiposity, which has been reported in other studies with BMI as the main exposure.

In addition to the “forward” analysis for predicting future events, the analysis can go “backward” to study potential determinants of trajectories using group membership assignments as a multinomial outcome. These analyses are informative for understanding how individual characteristics may influence the developmental course. For example, we recently analyzed the impact on the trajectories of body fatness of adult BMI-associated common genetic variants that have been identified from meta-analysis of genome-wide association studies.[11] We found that individuals with more genetic BMI variants were more likely to maintain a heavy body shape and gain further weight as they aged. The results indicate that the genetic impact is not restricted to shaping early-life adiposity but may extend over the life course.

The trajectory analysis can have important clinical applications to improve prediction rules and identify high-risk subgroups for targeted intervention by leveraging the longitudinal data that provides more information than a snapshot by single assessment. For example, a study assessed the trajectories of blood pressure in early adulthood from age 25 up to 50 years and calculated the probability of having subclinical atherosclerosis in middle age across different trajectories, which increased from 4% in the low-stable group to 25% in the elevated-increasing group, with an area under the ROC curve of 0.84.[23] Given the increasing use of electronic medical records in clinical practice and surging adoption of mobile health (e.g., wearable biometric sensors) in the general population, acquisition of detailed, large-scale longitudinal data is becoming feasible and less costly, which conceivably could increase the utility of trajectory approach in clinical and public health predictions. Also, by monitoring the longitudinal pattern of certain clinical characteristics, trajectories can facilitate identification of high-risk individuals for targeted and more aggressive interventions. For example, a study characterized postdiagnosis trajectories of physical and mental Health-Related Quality of Life (HRQoL) in prostate cancer survivors and identified a group of patients with lower and declining HRQoL for potential interventions.[24] Another study characterized trajectories of physical activity and physical function in cancer survivors enrolled in a randomized trial of home-based lifestyle counseling and identified characteristics of survivors who benefited from the assigned interventions.[25]

Cautions and challenges

While the trajectory analysis provides a powerful tool to address some questions that are difficult to answer using traditional longitudinal approach, careful considerations are needed to avoid potential misuse and inappropriate inference. The first issue relates to decision making in the model building process. Although BIC is a commonly used statistical criterion for model selection, just as in other modeling process, it is important to be aware of the risk of mechanical and rigid application of any formal statistical criteria. Subjective judgement is still essential to ensure the interpretability of any selected model. In the end, the objective of model selection is not to maximize some statistic of model fit; but rather to summarize the distinctive features of the data in a manner that is as parsimonious and useful as possible.[15] Second, it remains to be determined whether random effects should be included in GBTM. Although some extension method and software have been developed to include random effects,[26] others have argued that the addition of random effects to allow for more within-group variability and thus reduce the number of identified groups is at odds with the goal of GBTM to capture as much population variability as possible by using groups as a device for approximation.[15] Third, when trajectories are further studied as a potential risk factor for subsequent outcomes, how to control for confounding is a challenging question, because of our typically limited knowledge about the determinants of the trajectories. Conceivably, many of the trajectory determinants that are also predictors for the outcome are likely to be early-life characteristics that may not be characterized in most cohort studies of adults. Fourth, because GBTM remains relatively new in epidemiologic research, few guidelines exist to assist users in reporting model results for trajectory analysis.[15, 27] This clearly warrants further work to ensure adequate information is presented for critical appraisal of results and comparison between studies.