Using a Bayesian latent growth curve model to identify trajectories of positive affect and negative events following myocardial infarction

Joint clustering multiple longitudinal features: A comparison of methods and software packages with practical guidance

Clustering longitudinal features is a common goal in medical studies to identify distinct disease developmental trajectories. Compared to clustering a single longitudinal feature, integrating multiple longitudinal features allows additional information to be incorporated into the clustering process, which may reveal co-existing longitudinal patterns and generate deeper biological insight. Despite its increasing importance and popularity, there is limited practical guidance for implementing cluster analysis approaches for multiple longitudinal features and evaluating their comparative performance in medical datasets. In this paper, we provide an overview of several commonly used approaches to clustering multiple longitudinal features, with an emphasis on application and implementation through R software. These methods can be broadly categorized into two categories, namely model-based (including frequentist and Bayesian) approaches and algorithm-based approaches. To evaluate their performance, we compare these approaches using real-life and simulated datasets. These results provide practical guidance to applied researchers who are interested in applying these approaches for clustering multiple longitudinal features. Recommendations for applied researchers and suggestions for future research in this area are also discussed.

Uncovering circadian rhythms in metabolic longitudinal data: A Bayesian latent class modeling approach

Researchers in biology and medicine have increasingly focused on characterizing circadian rhythms and their potential impact on disease. Understanding circadian variation in metabolomics, the study of chemical processes involving metabolites may provide insight into important aspects of biological mechanism. Of scientific importance is developing a statistical rigorous approach for characterizing different types of 24-hour patterns among high dimensional longitudinal metabolites. We develop a latent class approach to incorporate variation in 24-hour patterns across metabolites where profiles are modeled with finite mixtures of distinct shape-invariant circadian curves that themselves incorporate variation in amplitude and phase across metabolites. An efficient Markov chain Monte Carlo sampling is used to carry out Bayesian posterior computation. When the model was fit separately by individual to the data from a small group of participants, two distinct 24-hour rhythms were identified, with one being sinusoidal and the other being more complex with multiple peaks. Interestingly, the latent pattern associated with circadian variation (simple sinusoidal curve) had a similar phase across the three participants, while the more complex latent pattern reflecting diurnal variation differed across individual. The results suggested that this modeling framework can be used to separate 24-hour rhythms into an endogenous circadian and one or more exogenous diurnal patterns in describing human metabolism.

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.

Bayesian consensus clustering for multivariate longitudinal data

In clinical and epidemiological studies, there is a growing interest in studying the heterogeneity among patients based on longitudinal characteristics to identify subtypes of the study population. Compared to clustering a single longitudinal marker, simultaneously clustering multiple longitudinal markers allow additional information to be incorporated into the clustering process, which reveals co-existing longitudinal patterns and generates deeper biological insight. In the current study, we propose a Bayesian consensus clustering (BCC) model for multivariate longitudinal data. Instead of arriving at a single overall clustering, the proposed model allows each marker to follow marker-specific local clustering and these local clusterings are aggregated to find a global (consensus) clustering. To estimate the posterior distribution of model parameters, a Gibbs sampling algorithm is proposed. We apply our proposed model to the primary biliary cirrhosis study to identify patient subtypes that may be associated with their prognosis. We also perform simulation studies to compare the clustering performance between the proposed model and existing models under several scenarios. The results demonstrate that the proposed BCC model serves as a useful tool for clustering multivariate longitudinal data.

AAAPT: Assessment of the Acute Pain Trajectory

OBJECTIVE

Define and contrast acute pain trajectories vs. the aggregate pain measurements, summarize appropriate linear and nonlinear statistical analyses for pain trajectories at the patient level, and present methods to classify individual pain trajectories. Clinical applications of acute pain trajectories are also discussed.

SETTING

In 2016, an expert panel involving the Analgesic, Anesthetic, and Addiction Clinical Trial Translations, Innovations, Opportunities, and Networks (ACTTION), American Pain Society (APS), and American Academy of Pain Medicine (AAPM) established an initiative to create a pain taxonomy, named the ACTTION-APS-AAPM Pain Taxonomy (AAAPT), for the multidimensional classification of acute pain. The AAAPT panel commissioned the present report to provide further details on analysis of the individual acute pain trajectory as an important component of comprehensive pain assessment.

METHODS

Linear mixed models and nonlinear models (e.g., regression splines and polynomial models) can be applied to analyze the acute pain trajectory. Alternatively, methods for classifying individual pain trajectories (e.g., using the 50% confidence interval of the random slope approach or using latent class analyses) can be applied in the clinical context to identify different trajectories of resolving pain (e.g., rapid reduction or slow reduction) or persisting pain. Each approach has advantages and disadvantages that may guide selection. Assessment of the acute pain trajectory may guide treatment and tailoring to anticipated symptom recovery. The acute pain trajectory can also serve as a treatment outcome measure, informing further management.

CONCLUSIONS

Application of trajectory approaches to acute pain assessments enables more comprehensive measurement of acute pain, which forms the cornerstone of accurate classification and treatment of pain.

Bayesian estimation and model selection in group-based trajectory models

We develop a Bayesian group-based trajectory model (GBTM) and extend it to incorporate dual trajectories and Bayesian model averaging for model selection. Our framework lends itself to many of the standard distributions used in GBTMs, including normal, censored normal, binary, and ordered outcomes. On the model selection front, GBTMs require the researcher to specify a functional relationship between time and the outcome within each latent group. These relationships are generally polynomials with varying degrees in each group, but can also include additional covariates or other functions of time. When the number of groups is large, the model space can grow prohibitively complex, requiring a time-consuming brute-force search over potentially thousands of models. The approach developed in this article requires just one model fit and has the additional advantage of accounting for uncertainty in model selection. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Will the Questions Ever End? Person-Level Increases in Careless Responding During Questionnaire Completion

Is there a point within a self-report questionnaire where participants will start responding carelessly? If so, then after how many items do participants reach that point? And what can researchers do to encourage participants to remain careful throughout the entirety of a questionnaire? We conducted two studies (Study 1 N = 358; Study 2 N = 129) to address these questions. Our results found (a) consistent evidence that participants responded more carelessly as they progressed further into a questionnaire, (b) mixed evidence that participants who were warned that carelessness would be punished displayed smaller increases in carelessness, and (c) mixed evidence that increases in carelessness were greater within an unproctored online study (Study 1) than within a proctored laboratory study (Study 2). These findings help address when and why careless responding is likely to occur, and they suggest effective preventive strategies.

A Bayesian multi-dimensional couple-based latent risk model with an application to infertility

Motivated by the Longitudinal Investigation of Fertility and the Environment (LIFE) Study that investigated the association between exposure to a large number of environmental pollutants and human reproductive outcomes, we propose a joint latent risk class modeling framework with an interaction between female and male partners of a couple. This formulation introduces a dependence structure between the chemical patterns within a couple and between the chemical patterns and the risk of infertility. The specification of an interaction enables the interplay between the female and male's chemical patterns on the risk of infertility in a parsimonious way. We took a Bayesian perspective to inference and used Markov chain Monte Carlo algorithms to obtain posterior estimates of model parameters. We conducted simulations to examine the performance of the estimation approach. Using the LIFE Study dataset, we found that in addition to the effect of PCB exposures on females, the male partners' PCB exposures play an important role in determining risk of infertility. Further, this risk is subadditive in the sense that there is likely a ceiling effect which limits the probability of infertility when both partners of the couple are at high risk.

Latent Class Dynamic Mediation Model with Application to Smoking Cessation Data

Traditional mediation analysis assumes that a study population is homogeneous and the mediation effect is constant over time, which may not hold in some applications. Motivated by smoking cessation data, we propose a latent class dynamic mediation model that explicitly accounts for the fact that the study population may consist of different subgroups and the mediation effect may vary over time. We use a proportional odds model to accommodate the subject heterogeneities and identify latent subgroups. Conditional on the subgroups, we employ a Bayesian hierarchical nonparametric time-varying coefficient model to capture the time-varying mediation process, while allowing each subgroup to have its individual dynamic mediation process. A simulation study shows that the proposed method has good performance in estimating the mediation effect. We illustrate the proposed methodology by applying it to analyze smoking cessation data.

Shape invariant mixture model for clustering non-linear longitudinal growth trajectories

In longitudinal studies, it is often of great interest to cluster individual trajectories based on repeated measurements taken over time. Non-linear growth trajectories are often seen in practice, and the individual data can also be measured sparsely, and at irregular time points, which may complicate the modeling process. Motivated by a study of pregnant women hormone profiles, we proposed a shape invariant growth mixture model for clustering non-linear growth trajectories. Bayesian inference via Monte Carlo Markov Chain was employed to estimate the parameters of interest. We compared our model to the commonly used growth mixture model and functional clustering approach by simulation studies. Results from analyzing the real data and simulated data were presented and discussed.

Bayesian Latent Class Analysis Tutorial

This article is a how-to guide on Bayesian computation using Gibbs sampling, demonstrated in the context of Latent Class Analysis (LCA). It is written for students in quantitative psychology or related fields who have a working knowledge of Bayes Theorem and conditional probability and have experience in writing computer programs in the statistical language R . The overall goals are to provide an accessible and self-contained tutorial, along with a practical computation tool. We begin with how Bayesian computation is typically described in academic articles. Technical difficulties are addressed by a hypothetical, worked-out example. We show how Bayesian computation can be broken down into a series of simpler calculations, which can then be assembled together to complete a computationally more complex model. The details are described much more explicitly than what is typically available in elementary introductions to Bayesian modeling so that readers are not overwhelmed by the mathematics. Moreover, the provided computer program shows how Bayesian LCA can be implemented with relative ease. The computer program is then applied in a large, real-world data set and explained line-by-line. We outline the general steps in how to extend these considerations to other methodological applications. We conclude with suggestions for further readings.

LATENT CLASS MODELING USING MATRIX COVARIATES WITH APPLICATION TO IDENTIFYING EARLY PLACEBO RESPONDERS BASED ON EEG SIGNALS

Latent class models are widely used to identify unobserved subgroups (i.e., latent classes) based upon one or more manifest variables. The probability of belonging to each subgroup is typically modeled as a function of a set of measured covariates. In this paper, we extend existing latent class models to incorporate matrix covariates. This research is motivated by a randomized placebo-controlled depression clinical trial. One study goal is to identify a subgroup of subjects who experience symptoms improvement early on during antidepressant treatment, which is considered to be an indication of a placebo rather than a true pharmacological response. We want to relate the likelihood of belonging to this subgroup of early responders to baseline electroencephalography (EEG) measurement that takes the form of a matrix. The proposed method is built upon a low rank Candecomp/Parafac (CP) decomposition of the target coefficient matrix through low-dimensional latent variables, which effectively reduces the model dimensionality. We adopt a Bayesian hierarchical modeling approach to estimate the latent variables, which allows a flexible way to incorporate prior knowledge about covariate effect heterogeneity and offers a data-driven method of regularization. Simulation studies suggest that the proposed method is robust against potentially misspecified rank in the CP decomposition. With the motivating example we show how the proposed method can be applied to extract valuable information from baseline EEG measurements that explains the likelihood of belonging to the early responder subgroup, helping to identify placebo responders and suggesting new targets for the study of placebo response.

Methods for analyzing observational longitudinal prognosis studies for rheumatic diseases: a review & worked example using a clinic-based cohort of juvenile dermatomyositis patients

Most outcome studies of rheumatic diseases report outcomes ascertained on a single occasion. While single assessments are sufficient for terminal or irreversible outcomes, they may not be sufficiently informative if outcomes change or fluctuate over time. Consequently, longitudinal studies that measure non-terminal outcomes repeatedly afford a better understanding of disease evolution.Longitudinal studies require special analytic methods. Newer longitudinal analytic methods have evolved tremendously to deal with common challenges in longitudinal observational studies. In recent years, an increasing number of studies have used longitudinal design. This review aims to help readers understand and apply the findings from longitudinal studies. Using a cohort of children with juvenile dermatomyositis (JDM), we illustrate how to study evolution of disease activity in JDM using longitudinal methods.

Bayesian analysis of piecewise growth mixture models with skew-t distributions: Application to AIDS studies

A major problem in HIV/AIDS studies is the development of drug resistance to antiretroviral (ARV) drug or therapy. Estimating the time at which such drug resistance would develop is usually sought. The goal of this article is to perform this estimation by developing growth mixture models with change-points and skew-t distributions based on longitudinal data. For such data, following ARV treatment, the profile of each subject's viral load tends to follow a 'broken stick' like growth trajectory, indicating multiple phases of decline and increase in viral loads. These multiple phases with multiple change-points are captured by subject-specific random parameters of growth curve models. To account for heterogeneity of drug resistance among subjects, the change-points are also allowed to differ by subgroups (subpopulations) of patients classified into latent classes on the basis of trajectories of observed viral loads. The proposed methods are illustrated using real data from an AIDS clinical study.

A prospective, longitudinal, observational cohort study examining how glaucoma affects quality of life and visually-related function over 4 years: design and methodology

Background

The aim of this study is to summarize the design and methodology of a prospective, longitudinal, observational cohort study to investigate how glaucoma affects patients’ quality of life and visually-related function over a 4-year period.

Methods/Design

One hundred sixty-one (161) subjects were enrolled in this ongoing study. Patients between the ages of 21–85 years with a minimum 2-year diagnosis of primary open-angle glaucoma, chronic primary angle-closure glaucoma or pseudoexfoliation glaucoma were included. Each patient visited Wills Eye Hospital for a baseline visit. Follow-up is planned for a minimum of 4 years, with annual visits. Each visit includes (1) Clinical evaluation: a slit lamp examination, fundoscopy, intraocular pressure measurement, visual field examination, spectral domain optical coherence tomography, Pelli-Robson Contrast Sensitivity test and the Spaeth-Richman Contrast Sensitivity test; (2) a performance based measure: the Compressed Assessment of Ability Related to Vision; and (3) Subjective measures of vision-related quality of life (the National Eye Institute Visual Functioning Questionnaire 25 and the Modified Glaucoma Symptom Scale).

Discussion

The results of this ongoing, prospective, longitudinal study are expected to shed light on the relationships between clinical measures, performance-based measures and subjective measures of well-being, in order to assess changes in the quality of life and the ability to function of patients with glaucoma over time.

Neighborhood social environment and patterns of adherence to oral hypoglycemic agents among patients with type 2 diabetes mellitus

This study examined whether neighborhood social environment was related to patterns of adherence to oral hypoglycemic agents among primary care patients with type 2 diabetes mellitus. Residents in neighborhoods with high social affluence, high residential stability, and high neighborhood advantage, compared to residents in neighborhoods with one or no high features present, were significantly more likely to have an adherent pattern compared to a nonadherent pattern. Neighborhood social environment may influence patterns of adherence. Reliance on a multilevel contextual framework, extending beyond the individual, to promote diabetic self-management activities may be essential for notable public health improvements.

Joint modeling of cross-sectional health outcomes and longitudinal predictors via mixtures of means and variances

Joint modeling methods have become popular tools to link important features extracted from longitudinal data to a primary event. While most modeling strategies have focused on the association between the longitudinal mean trajectories and risk of an event, we consider joint models that incorporate information from both long-term trends and short-term variability in a longitudinal submodel. We also consider both shared random effect and latent class (LC) approaches in the primary-outcome model to predict a binary outcome of interest. We develop simulation studies to compare and contrast these two modeling strategies; in particular, we study in detail the effects of the primary-outcome model misspecification. Among other findings, we note that when we analyze data from a shared random-effect using a LC model while the information from the longitudinal data is weak, the LC approach is more sensitive to such a model misspecification. Under this setting, the LC model has a superior performance in within-sample prediction that cannot be duplicated when predicting new samples. This is a unique feature of the LC approach that is new as far as we know to the existing literature. Finally, we use the proposed models to study how follicle stimulating hormone (FSH) trajectories are related to the risk of developing severe hot flashes for participating women in the Penn Ovarian Aging Study.

A brief adherence intervention that improved glycemic control: mediation by patterns of adherence

This study examined whether longitudinal adherence profiles mediated the relationship between a brief adherence intervention and glycemic control among patients with type 2 diabetes. Adherence was assessed using the Medication Event Monitoring System. Longitudinal analysis via growth curve mixture modeling was carried out to classify patients according to patterns of adherence to oral hypoglycemic agents. Hemoglobin A1c assays were used to measure glycemic control as the clinical outcome. Across the whole sample, longitudinal adherence profiles mediated 35.2% (13.2, 81.0%) of the effect of a brief adherence intervention on glycemic control [from odds ratio (OR) = 8.48, 95% confidence interval (CI) (3.24, 22.2) to 4.00, 95% CI (1.34, 11.93)]. Our results suggest that patients in the intervention had better glycemic control largely due to their greater likelihood of adherence to oral hypoglycemic agents.

Identifying the Zheng in psoriatic patients based on latent class analysis of traditional Chinese medicine symptoms and signs

Background

There are approximately five Zhengs reported in psoriatic patients. Systematic data collection and proper analysis for the classification of psoriasis have been lacking. This study aims to cluster the Zhengs in psoriatic patients based on the application of a checklist of traditional Chinese medicine (TCM) symptoms and signs followed by latent class analysis (LCA).

Methods

A cross-sectional study of 507 psoriatic patients aged above 10 years was performed in Yunnan Provincial Hospital of TCM and the First Affiliated Hospital of Kunming Medicine University from October 2010 to September 2011 using a TCM symptoms and signs checklist obtained from 16 TCM experts by the Delphi technique. LCA was applied to obtain the best fitted model for clustering of symptoms and signs that can be interpreted as underlying Zhengs of psoriasis.

Results

The LCA identified three Zhengs: dampness-heat Zheng (35.1%); blood heat Zheng (34.7%); and yin deficiency and blood dryness Zheng (30.2%). The first Zheng was associated with winter, the second with male sex, old age, smoking, and drinking alcohol, and the third with outpatient status, which reflected a mild disease course.

Conclusions

In this study, 507 psoriasis patients were clustered into three Zhengs, which had different associated factors.

Internet-based early intervention to prevent posttraumatic stress disorder in injury patients: randomized controlled trial

BACKGROUND

Posttraumatic stress disorder (PTSD) develops in 10-20% of injury patients. We developed a novel, self-guided Internet-based intervention (called Trauma TIPS) based on techniques from cognitive behavioral therapy (CBT) to prevent the onset of PTSD symptoms.

OBJECTIVE

To determine whether Trauma TIPS is effective in preventing the onset of PTSD symptoms in injury patients.

METHODS

Adult, level 1 trauma center patients were randomly assigned to receive the fully automated Trauma TIPS Internet intervention (n=151) or to receive no early intervention (n=149). Trauma TIPS consisted of psychoeducation, in vivo exposure, and stress management techniques. Both groups were free to use care as usual (nonprotocolized talks with hospital staff). PTSD symptom severity was assessed at 1, 3, 6, and 12 months post injury with a clinical interview (Clinician-Administered PTSD Scale) by blinded trained interviewers and self-report instrument (Impact of Event Scale-Revised). Secondary outcomes were acute anxiety and arousal (assessed online), self-reported depressive and anxiety symptoms (Hospital Anxiety and Depression Scale), and mental health care utilization. Intervention usage was documented.

RESULTS

The mean number of intervention logins was 1.7, SD 2.5, median 1, interquartile range (IQR) 1-2. Thirty-four patients in the intervention group did not log in (22.5%), 63 (41.7%) logged in once, and 54 (35.8%) logged in multiple times (mean 3.6, SD 3.5, median 3, IQR 2-4). On clinician-assessed and self-reported PTSD symptoms, both the intervention and control group showed a significant decrease over time (P<.001) without significant differences in trend. PTSD at 12 months was diagnosed in 4.7% of controls and 4.4% of intervention group patients. There were no group differences on anxiety or depressive symptoms over time. Post hoc analyses using latent growth mixture modeling showed a significant decrease in PTSD symptoms in a subgroup of patients with severe initial symptoms (n=20) (P<.001).

CONCLUSIONS

Our results do not support the efficacy of the Trauma TIPS Internet-based early intervention in the prevention of PTSD symptoms for an unselected population of injury patients. Moreover, uptake was relatively low since one-fifth of individuals did not log in to the intervention. Future research should therefore focus on innovative strategies to increase intervention usage, for example, adding gameplay, embedding it in a blended care context, and targeting high-risk individuals who are more likely to benefit from the intervention.

TRIAL REGISTRATION

International Standard Randomized Controlled Trial Number (ISRCTN): 57754429; http://www.controlled-trials.com/ISRCTN57754429 (Archived by WebCite at http://webcitation.org/6FeJtJJyD).

Latent class analysis of early developmental trajectory in baby siblings of children with autism

BACKGROUND

Siblings of children with autism (sibs-A) are at increased genetic risk for autism spectrum disorders (ASD) and milder impairments. To elucidate diversity and contour of early developmental trajectories exhibited by sibs-A, regardless of diagnostic classification, latent class modeling was used.

METHODS

Sibs-A (N = 204) were assessed with the Mullen Scales of Early Learning from age 6 to 36 months. Mullen T scores served as dependent variables. Outcome classifications at age 36 months included: ASD (N = 52); non-ASD social/communication delay (broader autism phenotype; BAP; N = 31); and unaffected (N = 121). Child-specific patterns of performance were studied using latent class growth analysis. Latent class membership was then related to diagnostic outcome through estimation of within-class proportions of children assigned to each diagnostic classification.

RESULTS

A 4-class model was favored. Class 1 represented accelerated development and consisted of 25.7% of the sample, primarily unaffected children. Class 2 (40.0% of the sample), was characterized by normative development with above-average nonverbal cognitive outcome. Class 3 (22.3% of the sample) was characterized by receptive language, and gross and fine motor delay. Class 4 (12.0% of the sample), was characterized by widespread delayed skill acquisition, reflected by declining trajectories. Children with an outcome diagnosis of ASD were spread across Classes 2, 3, and 4.

CONCLUSIONS

Results support a category of ASD that involves slowing in early non-social development. Receptive language and motor development is vulnerable to early delay in sibs-A with and without ASD outcomes. Non-ASD sibs-A are largely distributed across classes depicting average or accelerated development. Developmental trajectories of motor, language, and cognition appear independent of communication and social delays in non-ASD sibs-A.

Health span approximates life span among many supercentenarians: compression of morbidity at the approximate limit of life span

We analyze the relationship between age of survival, morbidity, and disability among centenarians (age 100-104 years), semisupercentenarians (age 105-109 years), and supercentenarians (age 110-119 years). One hundred and four supercentenarians, 430 semisupercentenarians, 884 centenarians, 343 nonagenarians, and 436 controls were prospectively followed for an average of 3 years (range 0-13 years). The older the age group, generally, the later the onset of diseases, such as cancer, cardiovascular disease, dementia, and stroke, as well as of cognitive and functional decline. The hazard ratios for these individual diseases became progressively less with older and older age, and the relative period of time spent with disease was lower with increasing age group. We observed a progressive delay in the age of onset of physical and cognitive function impairment, age-related diseases, and overall morbidity with increasing age. As the limit of human life span was effectively approached with supercentenarians, compression of morbidity was generally observed.

Optimal Partitioning for Linear Mixed Effects Models: Applications to Identifying Placebo Responders

A long-standing problem in clinical research is distinguishing drug treated subjects that respond due to specific effects of the drug from those that respond to non-specific (or placebo) effects of the treatment. Linear mixed effect models are commonly used to model longitudinal clinical trial data. In this paper we present a solution to the problem of identifying placebo responders using an optimal partitioning methodology for linear mixed effects models. Since individual outcomes in a longitudinal study correspond to curves, the optimal partitioning methodology produces a set of prototypical outcome profiles. The optimal partitioning methodology can accommodate both continuous and discrete covariates. The proposed partitioning strategy is compared and contrasted with the growth mixture modelling approach. The methodology is applied to a two-phase depression clinical trial where subjects in a first phase were treated openly for 12 weeks with fluoxetine followed by a double blind discontinuation phase where responders to treatment in the first phase were randomized to either stay on fluoxetine or switched to a placebo. The optimal partitioning methodology is applied to the first phase to identify prototypical outcome profiles. Using time to relapse in the second phase of the study, a survival analysis is performed on the partitioned data. The optimal partitioning results identify prototypical profiles that distinguish whether subjects relapse depending on whether or not they stay on the drug or are randomized to a placebo.

Bayesian variable selection for latent class models

In this article, we develop a latent class model with class probabilities that depend on subject-specific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model-averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.

Growth modeling with nonignorable dropout: alternative analyses of the STAR*D antidepressant trial

This article uses a general latent variable framework to study a series of models for nonignorable missingness due to dropout. Nonignorable missing data modeling acknowledges that missingness may depend not only on covariates and observed outcomes at previous time points as with the standard missing at random assumption, but also on latent variables such as values that would have been observed (missing outcomes), developmental trends (growth factors), and qualitatively different types of development (latent trajectory classes). These alternative predictors of missing data can be explored in a general latent variable framework with the Mplus program. A flexible new model uses an extended pattern-mixture approach where missingness is a function of latent dropout classes in combination with growth mixture modeling. A new selection model not only allows an influence of the outcomes on missingness but allows this influence to vary across classes. Model selection is discussed. The missing data models are applied to longitudinal data from the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study, the largest antidepressant clinical trial in the United States to date. Despite the importance of this trial, STAR*D growth model analyses using nonignorable missing data techniques have not been explored until now. The STAR*D data are shown to feature distinct trajectory classes, including a low class corresponding to substantial improvement in depression, a minority class with a U-shaped curve corresponding to transient improvement, and a high class corresponding to no improvement. The analyses provide a new way to assess drug efficiency in the presence of dropout.

A Bayesian growth mixture model to examine maternal hypertension and birth outcomes

Maternal hypertension is a major contributor to adverse pregnancy outcomes, including preterm birth (PTB) and low birth weight (LBW). Although several studies have explored the relationship between maternal hypertension and fetal health, few have examined how the longitudinal trajectory of blood pressure, considered over the course of pregnancy, affects birth outcomes. In this paper, we propose a Bayesian growth mixture model to jointly examine the associations between longitudinal blood pressure measurements, PTB, and LBW. The model partitions women into distinct classes characterized by a mean arterial pressure (MAP) curve and joint probabilities of PTB and LBW. Each class contains a unique mixed effects model for MAP with class-specific regression coefficients and random effect covariances. To account for the strong correlation between PTB and LBW, we introduce a bivariate probit model within each class to capture residual within-class dependence between PTB and LBW. The model permits the association between PTB and LBW to vary by class, so that for some classes, PTB and LBW may be positively correlated, whereas for others, they may be uncorrelated or negatively correlated. We also allow maternal covariates to influence the class probabilities via a multinomial logit model. For posterior computation, we propose an efficient MCMC algorithm that combines full-conditional Gibbs and Metropolis steps. We apply our model to a sample of 1027 women enrolled in the Healthy Pregnancy, Healthy Baby Study, a prospective cohort study of host, social, and environmental contributors to disparities in pregnancy outcomes.

A bayesian two-part latent class model for longitudinal medical expenditure data: assessing the impact of mental health and substance abuse parity

In 2001, the U.S. Office of Personnel Management required all health plans participating in the Federal Employees Health Benefits Program to offer mental health and substance abuse benefits on par with general medical benefits. The initial evaluation found that, on average, parity did not result in either large spending increases or increased service use over the four-year observational period. However, some groups of enrollees may have benefited from parity more than others. To address this question, we propose a Bayesian two-part latent class model to characterize the effect of parity on mental health use and expenditures. Within each class, we fit a two-part random effects model to separately model the probability of mental health or substance abuse use and mean spending trajectories among those having used services. The regression coefficients and random effect covariances vary across classes, thus permitting class-varying correlation structures between the two components of the model. Our analysis identified three classes of subjects: a group of low spenders that tended to be male, had relatively rare use of services, and decreased their spending pattern over time; a group of moderate spenders, primarily female, that had an increase in both use and mean spending after the introduction of parity; and a group of high spenders that tended to have chronic service use and constant spending patterns. By examining the joint 95% highest probability density regions of expected changes in use and spending for each class, we confirmed that parity had an impact only on the moderate spender class.

Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data

Growth mixture models (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class probabilities depend on some observed explanatory variables and data missingness depends on both the explanatory variables and a latent class variable. A full Bayesian method is then proposed to estimate the model. Through the data augmentation method, conditional posterior distributions for all model parameters and missing data are obtained. A Gibbs sampling procedure is then used to generate Markov chains of model parameters for statistical inference. The application of the model and the method is first demonstrated through the analysis of mathematical ability growth data from the National Longitudinal Survey of Youth 1997 (Bureau of Labor Statistics, U.S. Department of Labor, 1997). A simulation study considering 3 main factors (the sample size, the class probability, and the missing data mechanism) is then conducted and the results show that the proposed Bayesian estimation approach performs very well under the studied conditions. Finally, some implications of this study, including the misspecified missingness mechanism, the sample size, the sensitivity of the model, the number of latent classes, the model comparison, and the future directions of the approach, are discussed.

A Bayesian analysis of mixture structural equation models with non-ignorable missing responses and covariates

In behavioral, biomedical, and social-psychological sciences, it is common to encounter latent variables and heterogeneous data. Mixture structural equation models (SEMs) are very useful methods to analyze these kinds of data. Moreover, the presence of missing data, including both missing responses and missing covariates, is an important issue in practical research. However, limited work has been done on the analysis of mixture SEMs with non-ignorable missing responses and covariates. The main objective of this paper is to develop a Bayesian approach for analyzing mixture SEMs with an unknown number of components, in which a multinomial logit model is introduced to assess the influence of some covariates on the component probability. Results of our simulation study show that the Bayesian estimates obtained by the proposed method are accurate, and the model selection procedure via a modified DIC is useful in identifying the correct number of components and in selecting an appropriate missing mechanism in the proposed mixture SEMs. A real data set related to a longitudinal study of polydrug use is employed to illustrate the methodology.

A Bayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service use

In applications involving count data, it is common to encounter an excess number of zeros. In the study of outpatient service utilization, for example, the number of utilization days will take on integer values, with many subjects having no utilization (zero values). Mixed-distribution models, such as the zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB), are often used to fit such data. A more general class of mixture models, called hurdle models, can be used to model zero-deflation as well as zero-inflation. Several authors have proposed frequentist approaches to fitting zero-inflated models for repeated measures. We describe a practical Bayesian approach which incorporates prior information, has optimal small-sample properties, and allows for tractable inference. The approach can be easily implemented using standard Bayesian software. A study of psychiatric outpatient service use illustrates the methods.

A Bayesian latent variable mixture model for longitudinal fetal growth

Fetal growth restriction is a leading cause of perinatal morbidity and mortality that could be reduced if high-risk infants are identified early in pregnancy. We propose a Bayesian model for aggregating 18 longitudinal ultrasound measurements of fetal size and blood flow into three underlying, continuous latent factors. Our procedure is more flexible than typical latent variable methods in that we relax the normality assumptions by allowing the latent factors to follow finite mixture distributions. Using mixture distributions also permits us to cluster individuals with similar observed characteristics and identify latent classes of subjects who are more likely to be growth or blood flow restricted during pregnancy. We also use our latent variable mixture distribution model to identify a clinically meaningful latent class of subjects with low birth weight and early gestational age. We then examine the association of latent classes of intrauterine growth restriction with latent classes of birth outcomes as well as observed maternal covariates including fetal gender and maternal race, parity, body mass index, and height. Our methods identified a latent class of subjects who have increased blood flow restriction and below average intrauterine size during pregnancy. These subjects were more likely to be growth restricted at birth than a class of individuals with typical size and blood flow.

Extending conceptual frameworks: life course epidemiology for the study of back pain

BACKGROUND

Epidemiological studies have identified important causal and prognostic factors for back pain, but these frequently only identify a proportion of the variance, and new factors add little to these models. Recently, interest has increased in studying diseases over the life course, stimulated by the 1997 book by Kuh and Ben-Shlomo, a move accompanied by important conceptual and methodological developments. This has resulted in improvements in the understanding of other conditions like cardiovascular and respiratory disease. This paper aims to examine how conceptual frameworks from life course epidemiology could enhance back pain research.

DISCUSSION

Life course concepts can be divided into three categories. Concept 1: patterns over time, risk chains and accumulation. Simple 'chains of risk' have been studied - e.g. depression leading to back pain - but studies involving more risk factors in the chain are infrequent. Also, we have not examined how risk accumulation influences outcome, e.g. whether multiple episodes or duration of depression, throughout the life course, better predicts back pain. One-year back pain trajectories have been described, and show advantages for studying back pain, but there are few descriptions of longer-term patterns with associated transitions and turning points. Concept 2: influences and determinants of pathways. Analyses in back pain studies commonly adjust associations for potential confounders, but specific analysis of factors modifying risk, or related to the resilience or susceptibility to back pain, are rarely studied. Concept 3: timing of risk. Studies of critical or sensitive periods - crucial times of life which influence health later in life - are scarce in back pain research. Such analyses could help identify factors that influence the experience of pain throughout the life course.

SUMMARY

Back pain researchers could usefully develop hypotheses and models of how risks from different stages of life might interact and influence the onset, persistence and prognosis of back pain throughout the life course. Adoption of concepts and methods from life course epidemiology could facilitate this.

Principal Point Classification: Applications to Differentiating Drug and Placebo Responses in Longitudinal Studies

Principal points are cluster means for theoretical distributions. A discriminant methodology based on principal points is introduced. The principal point classification method is useful in clinical trials where the goal is to distinguish and differentiate between different treatment effects. Particularly, in psychiatric studies where placebo response rates can be very high, the principal point classification is illustrated to distinguish specific drug responders from non-specific placebo responders.

Estimating drug effects in the presence of placebo response: causal inference using growth mixture modeling

Placebo-controlled randomized trials for antidepressants and other drugs often show a response for a sizeable percentage of the subjects in the placebo group. Potential placebo responders can be assumed to exist also in the drug treatment group, making it difficult to assess the drug effect. A key drug research focus should be to estimate the percentage of individuals among those who responded to the drug who would not have responded to the placebo ('Drug Only Responders'). This paper investigates a finite mixture model approach to uncover percentages of up to four potential mixture components: Never Responders, Drug Only Responders, Placebo Only Responders, and Always Responders. Two examples are used to illustrate the modeling, a 12-week antidepressant trial with a continuous outcome (Hamilton D score) and a 7-week schizophrenia trial with a binary outcome (illness level). The approach is formulated in causal modeling terms using potential outcomes and principal stratification. Growth mixture modeling (GMM) with maximum-likelihood estimation is used to uncover the different mixture components. The results point to the limitations of the conventional approach of comparing marginal response rates for drug and placebo groups. It is useful to augment such reporting with the GMM-estimated prevalences for the four classes of subjects and the Drug Only Responder drug effect estimate.

Identification of Multivariate Responders/Non-Responders Using Bayesian Growth Curve Latent Class Models

In this paper, we propose a multivariate growth curve mixture model that groups subjects based on multiple symptoms measured repeatedly over time. Our model synthesizes features of two models. First, we follow Roy and Lin (2000) in relating the multiple symptoms at each time point to a single latent variable. Second, we use the growth mixture model of Muthén and Shedden (1999) to group subjects based on distinctive longitudinal profiles of this latent variable. The mean growth curve for the latent variable in each class defines that class's features. For example, a class of "responders" would have a decline in the latent symptom summary variable over time. A Bayesian approach to estimation is employed where the methods of Elliott et al (2005) are extended to simultaneously estimate the posterior distributions of the parameters from the latent variable and growth curve mixture portions of the model. We apply our model to data from a randomized clinical trial evaluating the efficacy of Bacillus Calmette-Guerin (BCG) in treating symptoms of Interstitial Cystitis. In contrast to conventional approaches using a single subjective Global Response Assessment, we use the multivariate symptom data to identify a class of subjects where treatment demonstrates effectiveness. Simulations are used to confirm identifiability results and evaluate the performance of our algorithm. The definitive version of this paper is available at onlinelibrary.wiley.com.

Joint analysis of multiple longitudinal outcomes: application of a latent class model

We address the problem of joint analysis of more than one series of longitudinal measurements. The typical way of approaching this problem is as a joint mixed effects model for the two outcomes. Apart from the large number of parameters needed to specify such a model, perhaps the biggest drawback of this approach is the difficulty in interpreting the results of the model, particularly when the main interest is in the relation between the two longitudinal outcomes. Here we propose an alternative approach to this problem. We use a latent class joint model for the longitudinal outcomes in order to reduce the dimensionality of the problem. We then use a two-stage estimation procedure to estimate the parameters in this model. In the first stage, the latent classes, their probabilities and the mean and covariance structure are estimated based on the longitudinal data of the first outcome. In the second stage, we study the relation between the latent classes and patient characteristics and the other outcome(s). We apply the method to data from 195 consecutive lung cancer patients in two outpatient clinics of lung diseases in The Hague, and we study the relation between denial and longitudinal health measures. Our approach clearly revealed an interesting phenomenon: although no difference between classes could be detected for objective measures of health, patients in classes representing higher levels of denial consistently scored significantly higher in subjective measures of health.

Predicting potential placebo effect in drug treated subjects

Non-specific responses to treatment (commonly known as placebo response) are pervasive when treating mental illness. Subjects treated with an active drug may respond in part due to non-specific aspects of the treatment, i.e, those not related to the chemical effect of the drug. To determine the extent a subject responds due to the chemical effect of a drug, one must disentangle the specific drug effect from the non-specific placebo effect. This paper presents a unique statistical model that allows for the separate prediction of a specific effect and non-specific effects in drug treated subjects. Data from a clinical trial comparing fluoxetine to a placebo for treating depression is used to illustrate this methodology.

Longitudinal population-based studies of affective disorders: where to from here?

BACKGROUND

Longitudinal, population-based, research is important if we are to better characterize the lifetime patterns and determinants of affective disorders. While studies of this type are becoming increasingly prevalent, there has been little discussion about the limitations of the methods commonly used.

METHODS

Discussion paper including a brief review of key prospective population-based studies as the basis for a critical appraisal of current approaches.

RESULTS

We identified a number of common methodological weaknesses that restrict the potential of longitudinal research to characterize the diversity, prognosis, and determinants of affective disorders over time. Most studies using comprehensive diagnostic instruments have either been of relatively brief duration, or have suffered from long periods between waves. Most etiologic research has focused on first onset diagnoses, although these may be relatively uncommon after early adulthood and the burden of mental disorders falls more heavily on individuals with recurring disorders. Analysis has tended to be based on changes in diagnostic status rather than anges in symptom levels, limiting study power. Diagnoses have generally been treated as homogeneous entities and few studies have explored whether diagnostic subtypes such as atypical depression vary in their etiology or prognosis. Little research has considered whether there are distinct trajectories of symptoms over time and most has focused on individual disorders such as depression, rather than considering the relationship over time between symptoms of different affective disorders. There has also been limited longitudinal research on factors in the physical or social environment that may influence the onset, recurrence or chronicity of symptoms.

CONCLUSION

Many important, and in some respects quite basic, questions remain about the trajectory of depression and anxiety disorders over the life course and the factors that influence their incidence, recurrence and prognosis. Innovative approaches that consider symptoms of all affective disorders, and how these change over time, has the potential to greatly increase our understanding of the heterogeneity of these important conditions and of the individual and environmental characteristics that influence their life course. Using longitudinal research to define sub classes of affective disorders may also be of great benefit for studies seeking to define the genetic determinants of susceptibility to these conditions.

Latent class models and their application to missing-data patterns in longitudinal studies

Latent class models have been developed as a flexible way of modeling the correlation of multivariate data, as a method for discovering subpopulations with similar response profiles and as a dimension reduction tool. In this manuscript, we provide a review of some of this literature and describe specific developments in several statistical and substantive areas. We then describe latent class models that could be used for characterizing missing-data patterns in longitudinal studies with regularly spaced observation times, where there is a large amount of intermittent missing data. We illustrate by analyzing data from a longitudinal study of depression, where there were 379 unique missing-data patterns.

Identifying latent clusters of variability in longitudinal data

Means or other central tendency measures are by far the most common focus of statistical analyses. However, as Carroll (2003) noted, "systematic dependence of variability on known factors" may be "fundamental to the proper solution of scientific problems" in certain settings. We develop a latent cluster model that relates underlying "clusters" of variability to baseline or outcome measures of interest. Because estimation of variability is inextricably linked to estimation of trend, assumptions about underlying trends are minimized by using nonparametric regression estimates. The resulting residual errors are then clustered into unobserved clusters of variability that are in turn related to subject-level predictors of interest. An application is made to psychological affect data.