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Great diversity in the utilization and reporting of latent growth modeling approaches in type 2 diabetes: A literature review

Introduction The progression of complications of type 2 diabetes (T2D) is unique to each patient and can be depicted through individual temporal trajectories. Latent growth modeling approaches (latent growth mixture models [LGMM] or latent class growth analysis [LCGA]) can be used to classify similar individual trajectories in a priori non-observed groups (latent groups), sharing common characteristics. Although increasingly used in the field of T2D, many questions remain regarding the utilization of these methods. Objective To review the literature of longitudinal studies using latent growth modeling approaches to study T2D. Methods MEDLINE (Ovid), EMBASE, CINAHL and Wb of Science were searched through August 25th, 2021. Data was collected on the type of latent growth modeling approaches (LGMM or LCGA), characteristics of studies and quality of reporting using the GRoLTS-Checklist and presented as frequencies. Results From the 4,694 citations screened, a total of 38 studies were included. The studies were published beetween 2011 and 2021 and the length of follow-up ranged from 8 weeks to 14 years. Six studies used LGMM, while 32 studies used LCGA. The fields of research varied from clinical research, psychological science, healthcare utilization research and drug usage/pharmaco-epidemiology. Data sources included primary data (clinical trials, prospective/retrospective cohorts, surveys), or secondary data (health records/registries, medico-administrative). Fifty percent of studies evaluated trajectory groups as exposures for a subsequent clinical outcome, while 24% used predictive models of group membership and 5% used both. Regarding the quality of reporting, trajectory groups were adequately presented, however many studies failed to report important decisions made for the trajectory group identification. Conclusion Although LCGA were preferred, the contexts of utilization were diverse and unrelated to the type of methods. We recommend future authors to clearly report the decisions made regarding trajectory groups identification.

Introduction: The progression of complications of type 2 diabetes (T2D) is unique to each patient and can be depicted through individual temporal trajectories. Latent growth modeling approaches (latent growth mixture models [LGMM] or latent class growth analysis [LCGA]) can be used to classify similar individual trajectories in a priori non-observed groups (latent groups), sharing common characteristics. Although increasingly used in the field of T2D, many questions remain regarding the utilization of these methods. Objective: To review the literature of longitudinal studies using latent growth modeling approaches to study T2D. Methods: MEDLINE (Ovid), EMBASE, CINAHL and Wb of Science were searched through August 25 th , 2021. Data was collected on the type of latent growth modeling approaches (LGMM or LCGA), characteristics of studies and quality of reporting using the GRoLTS-Checklist and presented as frequencies.
Results: From the 4,694 citations screened, a total of 38 studies were included. The studies were published beetween 2011 and 2021 and the length of follow-up ranged from 8 weeks to 14 years. Six studies used LGMM, while 32 studies used LCGA. The fields of research varied from clinical research, psychological science, healthcare utilization research and drug usage/pharmaco-epidemiology. Data sources included primary data (clinical trials, prospective/retrospective cohorts, surveys), or secondary data (health records/registries, medico-administrative). Fifty percent of studies evaluated trajectory groups as exposures for a subsequent clinical outcome, while 24% used predictive models of group membership and 5% used both. Regarding the quality of reporting, trajectory groups were adequately presented, however many studies failed to report important decisions made for the trajectory group identification. Conclusion: Although LCGA were preferred, the contexts of utilization were diverse and unrelated to the type of methods. We recommend future authors to clearly report the decisions made regarding trajectory groups identification.

Introduction
Type 2 diabetes (T2D) is a major public health threat worldwide, with approximately 1 person out of 11 living with the disease in 2019 [1]. To prevent complications, the management of T2D requires a long-term control of glycemia, healthy lifestyle behaviors, adequate medication usage as well as regular medical examinations [1]. However, in a real-life context, the management of T2D can differ between patients due to individual and environmental factors, but may also change in time (e.g. changes in treatment guidelines, preferences, physicians, living contexts, etc.). This heterogeneity may be reflected through different longitudinal trajectories in adherence patterns, glycemic control, lifestyle behaviors or healthcare utilization, unique to each patient.
Latent growth modeling approaches are statistical methods that consider individuals being part of a heterogeneous population, composed of unobserved groups of individual trajectories sharing similar characteristics [2,3]. The goal of latent growth modeling approaches is to estimate a given number of a priori unobserved latent groups within a population, based on the probability of membership of individuals to a specific trajectory group [2]. Two distinct methods of latent growth modeling approaches can be identified, namely Latent Growth Mixture Modeling (LGMM) and Latent Class Growth Analysis (LCGA) [LCGA is also known as Latent Class Growth Modeling (LCGM) or Group-Based Trajectory Modeling (GBTM)] [4].
LGMM allows the modelization of within-class heterogeneity [5]. In contrast, LCGA assumes that no within-group heterogeneity remains within the trajectory groups [2]. Latent growth modeling approaches, which have been initially developed in the fields of social sciences, psychopathology or criminology [3] are now increasingly used in the field of T2D. These approaches are well suited for the study of T2D given the repeated follow-ups in time, and also encourage the consideration of the overall temporal trajectories of care for clinical decisions [6,7]. The latent groups may help identifying subgroups of the population with different needs and developing adapted care strategies [7]. The possibility of using these approaches with multiple types of data, long follow-up lengths and unstructured datasets makes these methods highly appealing in the study of T2D [3]. However, latent growth modeling approaches are complex to use; many decisions must be made and should be reported correctly in order to ensure comparability between studies [4]. Accordingly, the Guidelines for Reporting on Latent Trajectory Studies (GRoLTS) checklist was build up for maximised transparency and to improve comparison between studies [4].
Although there is a growing number of studies using latent growth modeling approaches in the field of T2D, the variety of methods used, their context of utilization and quality of reporting remain unknown. Hence, by identifying longitudinal studies using latent growth modeling approaches among individuals with T2D, we sought (1) to identify the latent growth modeling approaches used, (2) to describe the context of utilization of the different methods, and (3) to assess the quality of reporting, using the GRoLTS checklist framework [4]. Of note, this review did not seek to describe the methods per se, which have been done previously [2,5,8]. To our knowledge, this review is the first to comprehensively describe the latent growth modeling approaches used in the field of T2D as of December 2021.

Eligibility criteria
This study is a review of longitudinal studies using latent growth modeling approaches among human cases with T2D, as defined by the authors. Studies needed to have at least 50% of participants with T2D to be included. Eligible studies must have used a method for discriminating latent groups of individual trajectories, no matter the duration of the follow-up. Studies determining groups using standard/arbitrary thresholds (e.g. body mass index categories, age groups, etc.) or sample stratifications (quartiles, percentiles, medians, interquartile ranges) were excluded. Only published peer-reviewed studies written in English or French were included. Case-control, cross-sectional and qualitative studies as well as reviews, grey literature and conference abstracts were excluded.          COPD: Chronic obstructive pulmonary disease, eGFR: Estimated glomerular filtration rate, EURODIAB: European Community funded Concerted Action Programme into the epidemiology and prevention of diabetes; HbA1c: Glycated hemoglobin A1c, ICD ¼ International classification of diseases; T2D: Type 2 diabetes. * as mentioned and cited in text.

Search of the studies
MEDLINE (Ovid), EMBASE, CINAHL and Web of Science were systematically searched through August 25 th , 2021, using a prespecified search strategy available in the Supplemental material. Citations were combined and duplicates were removed in Endnote 20 software (Clarivate, London, United Kingdom). Selection and full-text eligibility were performed by one reviewer (SO) in Covidence software (Melbourne, Australia). Since some published articles shared the same population/ data sources but had different primary outcomes and methods, they were considered as two separated studies. However, any article using the same data source with duplicate methods and identical objectives were considered as only one study.

Data extraction
Data extraction was performed by one reviewer (SO) using a prepiloted form in Excel software (Microsoft, Redmond, Washington, USA). Extracted data included: (1) Type of method: Method as identified in the studies and associated references, (2) Context of utilization: Study design, year of publication, data source(s), objective(s), field of research, population (incident or prevalent cases of T2D), number of subjects, exposure(s)/outcome(s) of interest, time-points, follow-up periods, other statistical method(s) (descriptive analysis, trends, predictive models, explanatory models, trajectory groups as exposure or outcomes) and, (3) Quality of reporting using the GRoLTS checklist [4]. The GRoLTS checklist is composed of 16 items, covered by 21 questions [4]. In addition, we collected information about actions taken for preventing indication bias and immortal time bias. We tabulated the results in summary tables inspired by Jandoc et al. [9].

Characteristics of included studies
From the 4,694 citations screened, a total of 38 publications were included in this review (Figure 1). The characteristics of studies are summarized in Table 1   of variables (step counts, utilization of cellphone application, hypoglycemic episodes). Eight studies included only incident cases of T2D, while 2 studies recruited participants with a diagnosis of T2D in the last 2 years. The other studies included participants with various lengths of T2D duration (prevalent cases). The objectives of the studies evaluating trajectory groups could be separated in three main categories. (1) The description/comparison of trajectory groups: Twenty-nine (76%) of studies compared baseline characteristics of groups using comparison tests, such as t-tests, chisquare, ANOVA, Wilcoxon or Kruskal-Wallis tests. Three studies evaluated the trends of a specific outcome according to the trajectory groups, either descriptive analyses, Cochrane Armitage test or binomial mixed models. One study depicted trajectory groups in graphs, without further analysis.
(2) Predictive model of group membership: Eleven studies used a predictive model (multivariate, bivariate, polytomous or cumulative logistic regression models) to identify predictors of belonging to the different trajectory groups. (3) Trajectory groups as exposition to an outcome of interest: Twenty-one studies used a latent growth modeling approach as a first step to identify exposure groups, then used regression models to test the association between trajectory groups and outcome(s) of interest (univariate and/or multivariate linear or logistic regression models, Kaplan-Meier, Cox proportional hazard model, joint survival analysis). From these studies, two evaluated the exposition trajectory groups and outcomes simultaneously [6,11], while the rest (n ¼ 19) identified trajectory groups during a given period, then evaluated outcomes during a subsequent period following the end of the trajectory assessment.
A total of 6 studies considered within-class heterogeneity by using LGMM [12,13,14,15,16] or a General Growth Class Mixture Modeling (GGCMM) for randomized intervention [17,18]. Most studies (n ¼ 32) used LCGA. Although citing the same references, the terminology used by the investigators varied between LCGM, GBTM, LCGA, "Latent class trajectory analyses", "group-based trajectory", "group-based semi-parametric mixture modeling approach", "semi-parametric group-based modeling strategy" or "multinomial modeling strategy". One study used a dual trajectory modeling, which consisted of identifying trajectory groups for two distinct variables (body mass index and disability trajectories) [19]. One study used a joint LCGA to assess the association between HbA1c trajectories and mortality, in which survival analysis and trajectory group identification was performed simultaneously [20].

Quality of reporting using the GRoLTS checklist
The summary of the GRoLTS checklist items across studies is presented in Table 3. Well-reported items included the metric of time used, the statistical software used, the characteristics and graphical depiction of the final model and confirmation of group membership of the final solution using average posterior probability and/or entropy. Ninety-two percent of studies reported the tools used for trajectory identification, from which 94% used the Bayesian information criterion (BIC). The number of latent groups identified varied between 2 and 7, where most studies identified either 3 (n ¼ 12), 4 (n ¼ 15) or 5 trajectory groups (n ¼ 7). Items partially reported included missing data mechanisms and management, the total number of fitted models tested or the distribution of observed data and the functional forms of trajectories in the final model. The items poorly reported included the consideration of mean and variance of time as well as within-class heterogeneity, the alternative across-class variance-covariance matrices considered, the number of random start values, the number of cases or graphical depiction of other models tested and availability of syntax files. From the 21 questions covered by the GRoLST checklist, the total of elements reported ranged from 3 to 17 within studies while most studies adequately reported 7 to 10 elements. The details of the items for individual studies are available in Supplemental Material.

Major findings
This review depicted the utilization of latent growth modeling approaches in longitudinal studies conducted among individuals with T2D. The heterogeneity in environmental, genetic, socio-economic factors influencing the outcomes of patients with T2D throughout time justifies the relevance of using latent growth modeling approaches [1,2]. Our results brought evidence on the wide diversity of contexts of utilization, follow-up periods, type of data sources and research questions considered using these methods. In this first literature review on the topic to our knowledge, we observed an overall preference in the choice of LCGA over LGMM. In contrast, we did not observe any context of utilization specific to a method or another. Finally, this review identified some recurrent issues in reporting, notably on consideration of within-group heterogeneity, how the decisions were made or the management of missing data, as examples.

Current applications and limits of latent growth modeling approaches
The research questions covered in the included studies were diverse. Indeed, only a handful of studies limited their analysis to simply identify trajectory groups; most studies used the identified groups to answer subsequent questions. The utilization of trajectory groups as exposures to a clinical outcome was used in half of included studies. However, some issues can be documented with the utilization of trajectory groups as exposures.
First, most authors used a two-step approach, by identifying trajectory groups during an initial follow-up period, then using a regression model during a subsequent follow-up period for outcome assessment [6]. This design imposes individuals to survive up to the beginning of the second period in order to be considered in the analysis. Depending on the length of the follow-up, this 2-step approach may introduce an immortal time bias, notably because individuals must be exempt from the outcome of interest (and above all: survive) during the initial period of group identification [6]. Unfortunately, no study presented the potential impact of this immortal time bias on their results. Furthermore, given the broken temporality between group trajectory identification and outcome assessment, the clinical applicability of results is likely reduced [6]. In alternative, two studies evaluated trajectories and clinical outcomes simultaneously. This approach tackles the issue of immortal time bias yet might bring other issues about whether the temporality between the exposure and the outcome is adequately respected. Another issue of using latent classes in regression models is that the statistical uncertainty associated with finding the latent classes is not taken into account in the subsequent analysis. [80] While this may be expected to lead to underestimating the uncertainty of the regression parameters, it has been argued that this process leads to adequate large sample inferences if the data on the outcome are not used for the latent growth modeling step [80]. However, in case of poor classification (i.e.: low average posterior probabilities and/or low entropy), the interpretation of regression parameters using uncertain classes should be done with caution.
Second, another issue with the utilization of trajectory groups as exposures is the adjustment of covariates. Given the long follow-up expected in T2D progression, the advent of concurrent events or life changes might affect the occurrence of the outcome of interest [3]. In the context of a long-term follow-up, as the trajectories can vary in time, some covariates may be time-dependent and thus, may act as confounding and/or intermediate factors [80]. In other words, covariates may have an impact on both the exposure and the outcome of interest at some point in time; yet these might be influenced by the trajectory itself and become a mediator in the association. Both ignoring or adjusting for these changing covariates using standard approaches could lead to invalid estimates, especially when trajectory groups are modelized as exposures [80]. Only a few studies clearly reported having considered Table 3. Assessing the quality of reporting of latent growth modeling approaches using the GRoLTS checklist. covariates to identify trajectory groups, from which a minority integrated time-varying covariates in the models. Third, many studies included prevalent cases of T2D with differences in the duration of the disease. The non-consideration of T2D duration, for instance, might create some systematic distortions in the association between trajectory groups and a given outcome. Many strategies can be used for tackling this confounder, notably by restricting to incident cases, which was done by some researchers [16,58,65,70]. Even though improving internal validity, restricting the selection of cases could affect generalizability of results. One study used propensity score matching [15], while other studies adjusted explanatory models with T2D duration or severity of T2D [37,58,58,59,63,67].
In sum, although using trajectory groups as exposure to an outcome was the most preferred approach in the included studies, one should recognize its complexity and should be aware of the limits inherent to its utilization.

Needs for improvement in the quality of reporting of latent growth modeling approaches
We identified many recurring issues in the quality of reporting using the GRoLTS checklist. Among the most important issues noted stands the vast utilization of LCGA, without considering potential residual withingroup heterogeneity, which could lead to important consequences on One study reported rerunning the programs with multiple iterations of random start values. One study considered mentioned using a gridsearch function within the method in order to take in account convergence towards local maxima, yet did not mention iterations with random start value. The remaining studies did not report this information.  the interpretability and inference of results. In accordance, we observed a certain confusion of the "within-group heterogeneity" concept; Some investigators mentioned using models such as LGMM without reporting how within-group heterogeneity was estimated, or on the opposite, mentioned information about within-group heterogeneity while using LCGA. In most cases, adequate reporting on the matter was lacking. Another important aspect in LGMM and LCGA is the utilization of tools/ criteria to identify the optimal number of trajectory groups. The BIC was by far the most used tool for model identification, in accordance with what is usually recommended in the literature [4]. Other tools have been proven efficient to support the BIC, such as the Bayes Factor, the Lo-Mendell-Rubin Likelihood ratio test, the bootstrap likelihood ratio test, the Akaike information criterion and other subjective assessments such as clinical relevance, parsimony and interpretability [3,81].
Although the criteria for model selection were globally well reported, we observed some reporting issues regarding how these tools were actually used for group identification. Indeed, information was often missing on the results of the tools between the models tested (statistical or subjective criterion), how inconsistencies were managed and how the final solution was identified. Another element often missing in the included studies is the reporting of the number of different models tested, including the one-class model. The GRoLST-Checklist recommend testing the one-class model, which could fit the data best in comparison with multiple-classes models. Although adequation criteria (e.g. BIC) are usually used to compare models, these criteria could be misleading and favorize more complex models [72]. The final decision should thus combine adequation criteria with clinical plausibility of one-class versus multiple-classes models. Another strategy would be to visualize individual trajectories from raw data and evaluate if these individual patterns are concordant with the average trajectory identified [72]. This issue highlights all the complexity and subjectivity in the selection of the optimal trajectory class model and further supports the importance of rigorous reporting of the decision process within the scientific literature. We observed that two-third of the included studies used the average posterior probability as the favourite tool to assess model adequacy, while only 5 studies reported entropy. Usually, model adequacy is confirmed by ensuring all average posterior probability exceed a minimal threshold which is recommended at 0.7 [3]. In the included studies, however, 14 studies reported a clear threshold (between 0.5 and 0.8), while 13 studies mentioned considering average posterior probability without detailing how the tool was used. Finally, we observed a major issue with the treatment of missing data. Latent growth modeling approaches are renowned for their flexibility with irregular datasets, where it remains possible to identify trajectories even if some data are missing, but only if these data are missing at random or completely at random [3,82]. However, a minority of studies clearly reported the nature of missing data [83].

The non-standardized terminology associated with latent growth modeling approaches
In a global perspective, we felt important to emphasize the great diversity in the terminology related to latent growth modeling approaches. During the process of this review, we also encountered the term "trajectory" in a wide variety of contexts, sometimes as statistical methods, as indicators of processes of care, as a description of a prospective phenomenon or sometimes purely arbitrary. This non-standardized terminology illustrates the importance of consistency in trajectory evaluation, in a way of clarifying and improving their use in future studies. Overall, we observed some issues relating to transparency and quality of report of latent growth modeling approaches, which unfortunately limit the comparability between studies [4]. This lack of information might reflect some confusion in the utilization of these methods, which further justifies the presence of experienced biostatisticians while planning latent growth modeling approaches, no matter the method used.

Strengths and limitations
This review has strengths, notably the utilization of a rigorous and objective methodology inspired by the Cochrane handbook for systematic reviews of interventions [84]. However, the review has limitations, notably the absence of two reviewers for abstracts and studies selections as well as data collection/extraction. Regarding the review process, we restricted to peer-reviewed published studies only. However, given the novelty of latent growth modeling approaches in the field of type 2 diabetes, some studies reported in conference abstracts or grey literature may have been missed. The review may thus be subject to publication bias. The generalizability of the findings is limited to T2D, even though similarities could be expected with other cardiometabolic/chronic diseases such as hypertension or dyslipidemia. Finally, we decided to exclude studies on type 1 diabetes due to the differences of its inherent pathophysiology and clinical management compared to T2D.

Conclusions
In conclusion, this literature review reports the relevance, the application and the issues related to latent growth modeling approaches in the study of T2D. We encourage future investigators interested into latent growth modeling approaches to consider the following suggestions: (1) to use caution when trajectory groups are treated as exposure in explanatory models, (2) to carefully choose the terminology used to characterize trajectory models in light of current literature, (3) to acknowledge the complexity behind latent growth modeling approaches by involving an experienced statistician in the process and finally, (4) to ensure that methods are reported transparently and comprehensively.

Additional information
Supplementary content related to this article has been published online at https://doi.org/10.1016/j.heliyon.2022.e10493.