Challenges in modelling the random structure correctly in growth mixture models and the impact this has on model mixtures

The relationship between HbA1c control pattern and atherosclerosis progression of diabetes: a prospective study of Chinese population

BACKGROUND

This study aims to comprehensively explain of glycosylated Hemoglobin (HbA1c) control patterns and help determine the causal relationship between glycemic control patterns and atherosclerosis progression, thereby contributing to the effective management of diabetes complications.

METHOD

All participants registered at the National Metabolic Management Center (MMC) of Beijing Luhe Hospital. The HbA1c pattern was described by HbA1c variability and trajectory groups of HbA1c. Then we examined the associations between the HbA1c pattern and the changes of intima-media thickness (ΔIMT) using covariate-adjusted means (SE) of ΔIMT, which were calculated by multiple linear regression analyses adjusted for the covariates. Finally, a cross-lagged panel model (CLPM) was performed to further verify the bidirectional relationship between IMT and HbA1c.

RESULTS

After data cleaning, a total of 1041 type 2 diabetes patients aged 20-80 years were included in this study. Except for average real variability (ARV), the other variation variables of HbA1c were associated with ΔIMT% (P < 0.05). Four discrete trajectories of HbA1c were identified in trajectory analysis. Comparing with the low-stable trajectory group of HbA1c, the covariate-adjusted means (SE) of ΔIMT% were significantly higher in Moderate-increase, U-shape and relative high trajectory groups, the mean (SE) were 7.03 (0.031), 15.49 (0.185), 14.15 (0.029), respectively. Meanwhile, there were significant bidirectional cross-lagged associations between HbA1c and IMT after adjusting for covariates.

CONCLUSION

We found four discrete trajectory groups of HbA1c during the long-term follow-up of diabetes. There was a positive association between HbA1c variability and the progression of atherosclerosis. Our study suggested that patients with diabetes should avoid roller coaster changes in glucose over a long period when controlling blood glucose.

Life-course social disparities in body mass index trajectories across adulthood: cohort study evidence from China health and nutrition survey

BACKGROUND

The social disparities in obesity may originate in early life or in adulthood, and the associations of socioeconomic position (SEP) with obesity could alter over time. It is unclear how lifetime-specific and life-course SEP influence adult obesity development in China.

METHODS

Based on the China Health and Nutrition Survey (CHNS), three SEP-related indicators, including the father's occupational position and the participant's education and occupational position, were obtained. The life-course socioeconomic changes and a cumulative SEP score were established to represent the life-course SEP of the participants in the study. The growth mixture modeling was used to identify BMI trajectories in adulthood. Multinomial logistic regression was adopted to assess the associations between SEP and adult BMI trajectories.

RESULTS

A total of 3,138 participants were included in the study. A positive correlation was found between the paternal occupational position, the participants' occupational position, education, and obesity in males, whereas an inverse correlation was observed among females. Males who experienced social upward mobility or remained stable high SEP during the follow-up had 2.31 and 2.52-fold risks of progressive obesity compared to those with a stable-low SEP. Among females, stable high SEP in both childhood and adulthood was associated with lower risks of progressive obesity (OR = 0.63, 95% CI: 0.43-0.94). Higher risks of obesity were associated with the life-course cumulative SEP score among males, while the opposite relationship was observed among females.

CONCLUSIONS

The associations between life-course SEP and BMI development trajectories differed significantly by gender. Special emphasis should be placed on males experiencing upward and stable high socioeconomic change.

Exploration of model misspecification in latent class methods for longitudinal data: Correlation structure matters

Modeling longitudinal trajectories and identifying latent classes of trajectories is of great interest in biomedical research, and software to identify latent classes of such is readily available for latent class trajectory analysis (LCTA), growth mixture modeling (GMM) and covariance pattern mixture models (CPMM). In biomedical applications, the level of within-person correlation is often non-negligible, which can impact the model choice and interpretation. LCTA does not incorporate this correlation. GMM does so through random effects, while CPMM specifies a model for within-class marginal covariance matrix. Previous work has investigated the impact of constraining covariance structures, both within and across classes, in GMMs-an approach often used to solve convergence problems. Using simulation, we focused specifically on how misspecification of the temporal correlation structure and strength, but correct variances, impacts class enumeration and parameter estimation under LCTA and CPMM. We found (1) even in the presence of weak correlation, LCTA often does not reproduce original classes, (2) CPMM performs well in class enumeration when the correct correlation structure is selected, and (3) regardless of misspecification of the correlation structure, both LCTA and CPMM give unbiased estimates of the class trajectory parameters when the within-individual correlation is weak and the number of classes is correctly specified. However, the bias increases markedly when the correlation is moderate for LCTA and when the incorrect correlation structure is used for CPMM. This work highlights the importance of correlation alone in obtaining appropriate model interpretations and provides insight into model choice.

Trajectories of glycated hemoglobin of T2DM and progress of arterial stiffness: a prospective study

AIM

This study aimed to describe the different trajectories groups of HbA1c during the long-term treatment of diabetes and explore the effect of glycemic control on the progression of arterial stiffness.

METHOD

The study participants registered at the National Metabolic Management Center (MMC) of Beijing Luhe hospital. The latent class mixture model (LCMM) was used to identify distinct trajectories of HbA1c. We calculated the change value of baPWV (ΔbaPWV) of each participant between the whole follow-up time as the primary outcome. Then we examined the associations between each HbA1c trajectory pattern and ΔbaPWV using covariate-adjusted means (SE) of ΔbaPWV, which were calculated by multiple linear regression analyses adjusted for the covariates.

RESULTS

After data cleaning, a total of 940 type 2 diabetes patients aged 20-80 years were included in this study. According to the BIC, we identified four discrete trajectories of HbA1c: Low-stable, U-shape, Moderate-decrease, High-increase, respectively. Compared with the low-stable group of HbA1c, the adjusted mean values of baPWV were significantly higher in U-shape, Moderate-decrease, and High-increase groups (all P < 0.05, and P for trend < 0.001), the mean values (SE) were 82.73 (0.08), 91.19 (0.96), 116.00 (0.81) and 223.19 (11.54), respectively.

CONCLUSION

We found four different trajectories groups of HbA1c during the long-term treatment of diabetes. In addition, the result proves the causal relationship between long-term glycemic control and arterial stiffness on a time scale.

Facilitating Growth Mixture Model Convergence in Preventive Interventions

Growth mixture models (GMMs) are applied to intervention studies with repeated measures to explore heterogeneity in the intervention effect. However, traditional GMMs are known to be difficult to estimate, especially at sample sizes common in single-center interventions. Common strategies to coerce GMMs to converge involve post hoc adjustments to the model, particularly constraining covariance parameters to equality across classes. Methodological studies have shown that although convergence is improved with post hoc adjustments, they embed additional tenuous assumptions into the model that can adversely impact key aspects of the model such as number of classes extracted and the estimated growth trajectories in each class. To facilitate convergence without post hoc adjustments, this paper reviews the recent literature on covariance pattern mixture models, which approach GMMs from a marginal modeling tradition rather than the random effect modeling tradition used by traditional GMMs. We discuss how the marginal modeling tradition can avoid complexities in estimation encountered by GMMs that feature random effects, and we use data from a lifestyle intervention for increasing insulin sensitivity (a risk factor for type 2 diabetes) among 90 Latino adolescents with obesity to demonstrate our point. Specifically, GMMs featuring random effects-even with post hoc adjustments-fail to converge due to estimation errors, whereas covariance pattern mixture models following the marginal model tradition encounter no issues with estimation while maintaining the ability to answer all the research questions.

The associations of maternal and paternal obesity with latent patterns of offspring BMI development between 7 and 17 years of age: pooled analyses of cohorts born in 1958 and 2001 in the United Kingdom

OBJECTIVE

We aimed to 1) describe how the UK obesity epidemic reflects a change over time in the proportion of the population demonstrating adverse latent patterns of BMI development and 2) investigate the potential roles of maternal and paternal BMI in this secular process.

METHODS

We used serial BMI data between 7 and 17 years of age from 13220 boys and 12711 girls. Half the sample was born in 1958 and half in 2001. Sex-specific growth mixture models were developed. The relationships of maternal and paternal BMI and weight status with class membership were estimated using the 3-step BCH approach, with covariate adjustment.

RESULTS

The selected models had five classes. For each sex, in addition to the two largest normal weight classes, there were "normal weight increasing to overweight" (17% of boys and 20% of girls), "overweight increasing to obesity" (8% and 6%), and "overweight decreasing to normal weight" (3% and 6%) classes. More than 1-in-10 children from the 2001 birth cohort were in the "overweight increasing to obesity" class, compared to less than 1-in-30 from the 1958 birth cohort. Approximately 75% of the mothers and fathers of this class had overweight or obesity. When considered together, both maternal and paternal BMI were associated with latent class membership, with evidence of negative departure from additivity (i.e., the combined effect of maternal and paternal BMI was smaller than the sum of the individual effects). The odds of a girl belonging to the "overweight increasing to obesity" class (compared to the largest normal weight class) was 13.11 (8.74, 19.66) times higher if both parents had overweight or obesity (compared to both parents having normal weight); the equivalent estimate for boys was 9.01 (6.37, 12.75).

CONCLUSIONS

The increase in obesity rates in the UK over more than 40 years has been partly driven by the growth of a sub-population demonstrating excess BMI gain during adolescence. Our results implicate both maternal and paternal BMI as correlates of this secular process.

Evidence for machine learning guided early prediction of acute outcomes in the treatment of depressed children and adolescents with antidepressants

BACKGROUND

The treatment of depression in children and adolescents is a substantial public health challenge. This study examined artificial intelligence tools for the prediction of early outcomes in depressed children and adolescents treated with fluoxetine, duloxetine, or placebo.

METHODS

The study samples included training datasets (N = 271) from patients with major depressive disorder (MDD) treated with fluoxetine and testing datasets from patients with MDD treated with duloxetine (N = 255) or placebo (N = 265). Treatment trajectories were generated using probabilistic graphical models (PGMs). Unsupervised machine learning identified specific depressive symptom profiles and related thresholds of improvement during acute treatment.

RESULTS

Variation in six depressive symptoms (difficulty having fun, social withdrawal, excessive fatigue, irritability, low self-esteem, and depressed feelings) assessed with the Children's Depression Rating Scale-Revised at 4-6 weeks predicted treatment outcomes with fluoxetine at 10-12 weeks with an average accuracy of 73% in the training dataset. The same six symptoms predicted 10-12 week outcomes at 4-6 weeks in (a) duloxetine testing datasets with an average accuracy of 76% and (b) placebo-treated patients with accuracies of 67%. In placebo-treated patients, the accuracies of predicting response and remission were similar to antidepressants. Accuracies for predicting nonresponse to placebo treatment were significantly lower than antidepressants.

CONCLUSIONS

PGMs provided clinically meaningful predictions in samples of depressed children and adolescents treated with fluoxetine or duloxetine. Future work should augment PGMs with biological data for refined predictions to guide the selection of pharmacological and psychotherapeutic treatment in children and adolescents with depression.

Sleep behaviour and cardiorespiratory fitness in patients after percutaneous coronary intervention during cardiac rehabilitation: protocol for a longitudinal study

INTRODUCTION

Most patients with coronary heart disease experience sleep disturbances and low cardiorespiratory fitness (CRF), but their relationship during cardiac rehabilitation (CR) is still unclear. This article details a protocol for the study of sleep trajectory in patients with coronary heart disease during CR and the relationship between sleep and CRF. A better understanding of the relationship between sleep and CRF on patient outcomes can improve sleep management strategies.

METHODS AND ANALYSIS

This is a longitudinal study with a recruitment target of 101 patients after percutaneous cardiac intervention from the Seventh People's Hospital of Shanghai, China. Data collection will include demographic characteristics, medical history, physical examination, blood sampling, echocardiography and the results of cardiopulmonary exercise tests. The information provided by a 6-min walk test will be used to supplement the CPET. The Pittsburgh Sleep Quality Index will be used to understand the sleep conditions of the participants in the past month. The Patient Health Questionnaire and General Anxiety Disorder Scale will be used to assess depression and anxiety, respectively. All participants will be required to wear an actigraphy on their wrists for 72 hours to monitor objective sleep conditions. This information will be collected four times within 6 months of CR, and patients will be followed up for 1 year. The growth mixture model will be used to analyse the longitudinal sleep data. The generalised estimating equation will be used to examine the associations between sleep and CRF during CR.

ETHICS AND DISSEMINATION

Ethical approval for this observational longitudinal study was granted by the Shanghai Seventh People's Hospital Ethics Committee on 23 April 2021 (2021-7th-HIRB-012). Study results will be disseminated in peer-reviewed journal articles.

Early childhood weight gain: Latent patterns and body composition outcomes

BACKGROUND

Despite early childhood weight gain being a key indicator of obesity risk, we do not have a good understanding of the different patterns that exist.

OBJECTIVES

To identify and characterise distinct groups of children displaying similar early-life weight trajectories.

METHODS

A growth mixture model captured heterogeneity in weight trajectories between 0 and 60 months in 1390 children in the Avon Longitudinal Study of Parents and Children. Differences between the classes in characteristics and body size/composition at 9 years were investigated.

RESULTS

The best model had five classes. The "Normal" (45%) and "Normal after initial catch-down" (24%) classes were close to the 50th centile of a growth standard between 24 and 60 months. The "High-decreasing" (21%) and "Stable-high" (7%) classes peaked at the ~91st centile at 12-18 months, but while the former declined to the ~75th centile and comprised constitutionally big children, the latter did not. The "Rapidly increasing" (3%) class gained weight from below the 50th centile at 4 months to above the 91st centile at 60 months. By 9 years, their mean body mass index (BMI) placed them at the 98th centile. This class was characterised by the highest maternal BMI; highest parity; highest levels of gestational hypertension and diabetes; and the lowest socio-economic position. At 9 years, the "Rapidly increasing" class was estimated to have 68.2% (95% confidence interval [CI] 48.3, 88.1) more fat mass than the "Normal" class, but only 14.0% (95% CI 9.1, 18.9) more lean mass.

CONCLUSIONS

Criteria used in growth monitoring practice are unlikely to consistently distinguish between the different patterns of weight gain reported here.

Prediction of short-term antidepressant response using probabilistic graphical models with replication across multiple drugs and treatment settings

Heterogeneity in the clinical presentation of major depressive disorder and response to antidepressants limits clinicians' ability to accurately predict a specific patient's eventual response to therapy. Validated depressive symptom profiles may be an important tool for identifying poor outcomes early in the course of treatment. To derive these symptom profiles, we first examined data from 947 depressed subjects treated with selective serotonin reuptake inhibitors (SSRIs) to delineate the heterogeneity of antidepressant response using probabilistic graphical models (PGMs). We then used unsupervised machine learning to identify specific depressive symptoms and thresholds of improvement that were predictive of antidepressant response by 4 weeks for a patient to achieve remission, response, or nonresponse by 8 weeks. Four depressive symptoms (depressed mood, guilt feelings and delusion, work and activities and psychic anxiety) and specific thresholds of change in each at 4 weeks predicted eventual outcome at 8 weeks to SSRI therapy with an average accuracy of 77% (p = 5.5E-08). The same four symptoms and prognostic thresholds derived from patients treated with SSRIs correctly predicted outcomes in 72% (p = 1.25E-05) of 1996 patients treated with other antidepressants in both inpatient and outpatient settings in independent publicly-available datasets. These predictive accuracies were higher than the accuracy of 53% for predicting SSRI response achieved using approaches that (i) incorporated only baseline clinical and sociodemographic factors, or (ii) used 4-week nonresponse status to predict likely outcomes at 8 weeks. The present findings suggest that PGMs providing interpretable predictions have the potential to enhance clinical treatment of depression and reduce the time burden associated with trials of ineffective antidepressants. Prospective trials examining this approach are forthcoming.

Latent class regression improves the predictive acuity and clinical utility of survival prognostication amongst chronic heart failure patients

The present study aimed to compare the predictive acuity of latent class regression (LCR) modelling with: standard generalised linear modelling (GLM); and GLMs that include the membership of subgroups/classes (identified through prior latent class analysis; LCA) as alternative or additional candidate predictors. Using real world demographic and clinical data from 1,802 heart failure patients enrolled in the UK-HEART2 cohort, the study found that univariable GLMs using LCA-generated subgroup/class membership as the sole candidate predictor of survival were inferior to standard multivariable GLMs using the same four covariates as those used in the LCA. The inclusion of the LCA subgroup/class membership together with these four covariates as candidate predictors in a multivariable GLM showed no improvement in predictive acuity. In contrast, LCR modelling resulted in a 18-22% improvement in predictive acuity and provided a range of alternative models from which it would be possible to balance predictive acuity against entropy to select models that were optimally suited to improve the efficient allocation of clinical resources to address the differential risk of the outcome (in this instance, survival). These findings provide proof-of-principle that LCR modelling can improve the predictive acuity of GLMs and enhance the clinical utility of their predictions. These improvements warrant further attention and exploration, including the use of alternative techniques (including machine learning algorithms) that are also capable of generating latent class structure while determining outcome predictions, particularly for use with large and routinely collected clinical datasets, and with binary, count and continuous variables.

Growth mixture models: a case example of the longitudinal analysis of patient-reported outcomes data captured by a clinical registry

Background

An assumption in many analyses of longitudinal patient-reported outcome (PRO) data is that there is a single population following a single health trajectory. One approach that may help researchers move beyond this traditional assumption, with its inherent limitations, is growth mixture modelling (GMM), which can identify and assess multiple unobserved trajectories of patients’ health outcomes. We describe the process that was undertaken for a GMM analysis of longitudinal PRO data captured by a clinical registry for outpatients with atrial fibrillation (AF).

Methods

This expository paper describes the modelling approach and some methodological issues that require particular attention, including (a) determining the metric of time, (b) specifying the GMMs, and (c) including predictors of membership in the identified latent classes (groups or subtypes of patients with distinct trajectories). An example is provided of a longitudinal analysis of PRO data (patients’ responses to the Atrial Fibrillation Effect on QualiTy-of-Life (AFEQT) Questionnaire) collected between 2008 and 2016 for a population-based cardiac registry and deterministically linked with administrative health data.

Results

In determining the metric of time, multiple processes were required to ensure that “time” accounted for both the frequency and timing of the measurement occurrences in light of the variability in both the number of measures taken and the intervals between those measures. In specifying the GMM, convergence issues, a common problem that results in unreliable model estimates, required constrained parameter exploration techniques. For the identification of predictors of the latent classes, the 3-step (stepwise) approach was selected such that the addition of predictor variables did not change class membership itself.

Conclusions

GMM can be a valuable tool for classifying multiple unique PRO trajectories that have previously been unobserved in real-world applications; however, their use requires substantial transparency regarding the processes underlying model building as they can directly affect the results and therefore their interpretation.

Changes over time in latent patterns of childhood-to-adulthood BMI development in Great Britain: evidence from three cohorts born in 1946, 1958, and 1970

BACKGROUND

Most studies on secular trends in body mass index (BMI) are cross-sectional and the few longitudinal studies have typically only investigated changes over time in mean BMI trajectories. We aimed to describe how the evolution of the obesity epidemic in Great Britain reflects shifts in the proportion of the population demonstrating different latent patterns of childhood-to-adulthood BMI development.

METHODS

We used pooled serial BMI data from 25,655 participants in three British cohorts: the 1946 National Survey of Health and Development (NSHD), 1958 National Child Development Study (NCDS), and 1970 British Cohort Study (BCS). Sex-specific growth mixture models captured latent patterns of BMI development between 11 and 42 years. The classes were characterised in terms of their birth cohort composition.

RESULTS

The best models had four classes, broadly similar for both sexes. The 'lowest' class (57% of males; 47% of females) represents the normal weight sub-population, the 'middle' class (16%; 15%) represents the sub-population who likely develop overweight in early/mid-adulthood, and the 'highest' class (6%; 9%) represents those who likely develop obesity in early/mid-adulthood. The remaining class (21%; 29%) reflects a sub-population with rapidly 'increasing' BMI between 11 and 42 years. Both sexes in the 1958 NCDS had greater odds of being in the 'highest' class compared to their peers in the 1946 NSHD but did not have greater odds of being in the 'increasing' class. Conversely, males and females in the 1970 BCS had 2.78 (2.15, 3.60) and 1.87 (1.53, 2.28), respectively, times higher odds of being in the 'increasing' class.

CONCLUSIONS

Our results suggest that the obesity epidemic in Great Britain reflects not only an upward shift in BMI trajectories but also a more recent increase in the number of individuals demonstrating more rapid weight gain, from normal weight to overweight, across the second, third, and fourth decades of life.

Distinct Body Mass Index Trajectories to Young-Adulthood Obesity and Their Different Cardiometabolic Consequences

[Figure: see text].

Patient-reported outcomes and the identification of subgroups of atrial fibrillation patients: a retrospective cohort study of linked clinical registry and administrative data

PURPOSE

Previous research about the health and quality of life of people with atrial fibrillation has typically identified a single health trajectory. Our study aimed to examine variability in health trajectories and patient characteristics associated with such variability.

METHODS

We conducted a retrospective analysis of data collected between 2008 and 2016 for a cardiac registry in British Columbia (Canada) linked with administrative health data. The Atrial Fibrillation Effect on Quality of Life Questionnaire was used to measure health status at up to 10 clinic visits. Growth mixture models were used and a three-step multinomial logistic regression was conducted to identify predictors of subgroups with different trajectories.

RESULTS

The patients (N = 7439) were primarily men (61.1%) over 60 years of age (72.9%). Three subgroups of health status trajectories were identified: "poor but improving", "good and stable", and "excellent and stable" health. Compared with the other two groups, patients in the "poor but improving group" were more likely to (1) be less than 60 years of age; (2) be women; (3) have greater risk of stroke; (4) have had ablation therapy within 6 months to 1 year or more than 2 years after their initial consultation; and (5) have had anticoagulation therapy within 6 months.

CONCLUSION

Using growth mixture models, we found that not all health trajectories are the same. These models can help to understand variability in trajectories with different patient characteristics that could inform tailored interventions and patient education strategies.

Improving convergence in growth mixture models without covariance structure constraints

Growth mixture models are a popular method to uncover heterogeneity in growth trajectories. Harnessing the power of growth mixture models in applications is difficult given the prevalence of nonconvergence when fitting growth mixture models to empirical data. Growth mixture models are rooted in the random effect tradition, and nonconvergence often leads researchers to modify their intended model with constraints in the random effect covariance structure to facilitate estimation. While practical, doing so has been shown to adversely affect parameter estimates, class assignment, and class enumeration. Instead, we advocate specifying the models with a marginal approach to prevent the widespread practice of sacrificing class-specific covariance structures to appease nonconvergence. A simulation is provided to show the importance of modeling class-specific covariance structures and builds off existing literature showing that applying constraints to the covariance leads to poor performance. These results suggest that retaining class-specific covariance structures should be a top priority and that marginal models like covariance pattern growth mixture models that model the covariance structure without random effects are well-suited for such a purpose, particularly with modest sample sizes and attrition commonly found in applications. An application to PTSD data with such characteristics is provided to demonstrate (a) convergence difficulties with random effect models, (b) how covariance structure constraints improve convergence but to the detriment of performance, and (c) how covariance pattern growth mixture models may provide a path forward that improves convergence without forfeiting class-specific covariance structures.

Variance constraints strongly influenced model performance in growth mixture modeling: a simulation and empirical study

BACKGROUND

Growth Mixture Modeling (GMM) is commonly used to group individuals on their development over time, but convergence issues and impossible values are common. This can result in unreliable model estimates. Constraining variance parameters across classes or over time can solve these issues, but can also seriously bias estimates if variances differ. We aimed to determine which variance parameters can best be constrained in Growth Mixture Modeling.

METHODS

To identify the variance constraints that lead to the best performance for different sample sizes, we conducted a simulation study and next verified our results with the TRacking Adolescent Individuals' Lives Survey (TRAILS) cohort.

RESULTS

If variance parameters differed across classes and over time, fitting a model without constraints led to the best results. No constrained model consistently performed well. However, the model that constrained the random effect variance and residual variances across classes consistently performed very poorly. For a small sample size (N = 100) all models showed issues. In TRAILS, the same model showed substantially different results from the other models and performed poorly in terms of model fit.

CONCLUSIONS

If possible, a Growth Mixture Model should be fit without any constraints on variance parameters. If not, we recommend to try different variance specifications and to not solely rely on the default model, which constrains random effect variances and residual variances across classes. The variance structure must always be reported Researchers should carefully follow the GRoLTS-Checklist when analyzing and reporting trajectory analyses.

A comparison of longitudinal modelling approaches: Alcohol and cannabis use from adolescence to young adulthood

BACKGROUND

Modelling trajectories of substance use over time is complex and requires judicious choices from a number of modelling approaches. In this study we examine the relative strengths and weakness of latent curve models (LCM), growth mixture modelling (GMM), and latent class growth analysis (LCGA).

DESIGN

Data were drawn from the Australian Temperament Project, a 36-year-old community-based longitudinal study that has followed a sample of young Australians from infancy to adulthood across 16 waves of follow-up since 1983. Models were fitted on past month alcohol use (n = 1468) and cannabis use (n = 549) across six waves of data collected from age 13-14 to 27-28 years.

FINDINGS

Of the three model types, GMMs were the best fit. However, these models were limited given the variance of numerous growth parameters had to be constrained to zero. Additionally, both the GMM and LCGA solutions had low entropy. The negative binomial LCMs provided a relatively well-fitting solution with fewer drawbacks in terms of growth parameter estimation and entropy issues. In all cases, model fit was enhanced when using a negative binomial distribution.

CONCLUSIONS

Substance use researchers would benefit from adopting a complimentary framework by exploring both LCMs and mixture approaches, in light of the relative strengths and weaknesses as identified. Additionally, the distribution of data should inform modelling decisions.

Framework to construct and interpret latent class trajectory modelling

OBJECTIVES

Latent class trajectory modelling (LCTM) is a relatively new methodology in epidemiology to describe life-course exposures, which simplifies heterogeneous populations into homogeneous patterns or classes. However, for a given dataset, it is possible to derive scores of different models based on number of classes, model structure and trajectory property. Here, we rationalise a systematic framework to derive a 'core' favoured model.

METHODS

We developed an eight-step framework: step 1: a scoping model; step 2: refining the number of classes; step 3: refining model structure (from fixed-effects through to a flexible random-effect specification); step 4: model adequacy assessment; step 5: graphical presentations; step 6: use of additional discrimination tools ('degree of separation'; Elsensohn's envelope of residual plots); step 7: clinical characterisation and plausibility; and step 8: sensitivity analysis. We illustrated these steps using data from the NIH-AARP cohort of repeated determinations of body mass index (BMI) at baseline (mean age: 62.5 years), and BMI derived by weight recall at ages 18, 35 and 50 years.

RESULTS

From 288 993 participants, we derived a five-class model for each gender (men: 177 455; women: 111 538). From seven model structures, the favoured model was a proportional random quadratic structure (model F). Favourable properties were also noted for the unrestricted random quadratic structure (model G). However, class proportions varied considerably by model structure-concordance between models F and G were moderate (Cohen κ: men, 0.57; women, 0.65) but poor with other models. Model adequacy assessments, evaluations using discrimination tools, clinical plausibility and sensitivity analyses supported our model selection.

CONCLUSION

We propose a framework to construct and select a 'core' LCTM, which will facilitate generalisability of results in future studies.

Growth mixture modeling of post-combat aggression: Application to soldiers deployed to Iraq

Prior research has found substantial heterogeneity in the course of key post-deployment outcomes, such as PTSD. The current paper employs growth mixture modeling to identify differential trajectories of change in the course of post-combat aggression. A Brigade Combat Team completed surveys within 72h of return from an Iraq deployment, 4 months later, and at 12 months after return. Based on model fit indices, analyses yielded four latent aggression trajectories: "low-stable", "delayed", "recovery", and "chronic". In addition, most individuals aligned with a "low-stable" trajectory indicative of minimal aggression in the first year following return from a combat deployment. A conditional model showed that lower posttraumatic stress and lower combat exposure characterized individuals aligned with the "low-stable" aggression trajectory relative to individuals aligned with "chronic" and "delayed" aggression trajectories. Implications for targeted intervention and future research are discussed.

The impact of covariance misspecification in group-based trajectory models for longitudinal data with non-stationary covariance structure

One purpose of a longitudinal study is to gain a better understanding of how an outcome of interest changes among a given population over time. In what follows, a trajectory will be taken to mean the series of measurements of the outcome variable for an individual. Group-based trajectory modelling methods seek to identify subgroups of trajectories within a population, such that trajectories that are grouped together are more similar to each other than to trajectories in distinct groups. Group-based trajectory models generally assume a certain structure in the covariances between measurements, for example conditional independence, homogeneous variance between groups or stationary variance over time. Violations of these assumptions could be expected to result in poor model performance. We used simulation to investigate the effect of covariance misspecification on misclassification of trajectories in commonly used models under a range of scenarios. To do this we defined a measure of performance relative to the ideal Bayesian correct classification rate. We found that the more complex models generally performed better over a range of scenarios. In particular, incorrectly specified covariance matrices could significantly bias the results but using models with a correct but more complicated than necessary covariance matrix incurred little cost.

Introducing the fit-criteria assessment plot - A visualisation tool to assist class enumeration in group-based trajectory modelling

Background and objective Group-based trajectory modelling is a model-based clustering technique applied for the identification of latent patterns of temporal changes. Despite its manifold applications in clinical and health sciences, potential problems of the model selection procedure are often overlooked. The choice of the number of latent trajectories (class-enumeration), for instance, is to a large degree based on statistical criteria that are not fail-safe. Moreover, the process as a whole is not transparent. To facilitate class enumeration, we introduce a graphical summary display of several fit and model adequacy criteria, the fit-criteria assessment plot. Methods An R-code that accepts universal data input is presented. The programme condenses relevant group-based trajectory modelling output information of model fit indices in automated graphical displays. Examples based on real and simulated data are provided to illustrate, assess and validate fit-criteria assessment plot's utility. Results Fit-criteria assessment plot provides an overview of fit criteria on a single page, placing users in an informed position to make a decision. Fit-criteria assessment plot does not automatically select the most appropriate model but eases the model assessment procedure. Conclusions Fit-criteria assessment plot is an exploratory, visualisation tool that can be employed to assist decisions in the initial and decisive phase of group-based trajectory modelling analysis. Considering group-based trajectory modelling's widespread resonance in medical and epidemiological sciences, a more comprehensive, easily interpretable and transparent display of the iterative process of class enumeration may foster group-based trajectory modelling's adequate use.