Marginalized random effects models for multivariate longitudinal binary data

Generalized linear models with random effects are often used to explain the serial dependence of longitudinal categorical data. Marginalized random effects models (MREMs) permit likelihood‐based estimations of marginal mean parameters and also explain the serial dependence of longitudinal data. In this paper, we extend the MREM to accommodate multivariate longitudinal binary data using a new covariance matrix with a Kronecker decomposition, which easily explains both the serial dependence and time‐specific response correlation. A maximum marginal likelihood estimation is proposed utilizing a quasi‐Newton algorithm with quasi‐Monte Carlo integration of the random effects. Our approach is applied to analyze metabolic syndrome data from the Korean Genomic Epidemiology Study for Korean adults. Copyright © 2009 John Wiley & Sons, Ltd.     

A Dirichlet process mixture model for clustering longitudinal gene expression data

Subgroup identification (clustering) is an important problem in biomedical research. Gene expression profiles are commonly utilized to define subgroups. Longitudinal gene expression profiles might provide additional information on disease progression than what is captured by baseline profiles alone. Therefore, subgroup identification could be more accurate and effective with the aid of longitudinal gene expression data. However, existing statistical methods are unable to fully utilize these data for patient clustering. In this article, we introduce a novel clustering method in the Bayesian setting based on longitudinal gene expression profiles. This method, called BClustLonG, adopts a linear mixed‐effects framework to model the trajectory of genes over time, while clustering is jointly conducted based on the regression coefficients obtained from all genes. In order to account for the correlations among genes and alleviate the high dimensionality challenges, we adopt a factor analysis model for the regression coefficients. The Dirichlet process prior distribution is utilized for the means of the regression coefficients to induce clustering. Through extensive simulation studies, we show that BClustLonG has improved performance over other clustering methods. When applied to a dataset of severely injured (burn or trauma) patients, our model is able to identify interesting subgroups. Copyright © 2017 John Wiley & Sons, Ltd.     

Common predictor effects for multivariate longitudinal data

Multivariate outcomes measured longitudinally over time are common in medicine, public health, psychology and sociology. The typical (saturated) longitudinal multivariate regression model has a separate set of regression coefficients for each outcome. However, multivariate outcomes are often quite similar and many outcomes can be expected to respond similarly to changes in covariate values. Given a set of outcomes likely to share common covariate effects, we propose the clustered outcome common predictor effect model and offer a two step iterative algorithm to fit the model using available software for univariate longitudinal data. Outcomes that share predictor effects need not be chosen a priori; we propose model selection tools to let the data select outcome clusters. We apply the proposed methods to psychometric data from adolescent children of HIV+ parents. Copyright © 2009 John Wiley & Sons, Ltd.     

A joint modeling and estimation method for multivariate longitudinal data with mixed types of responses to analyze physical activity data generated by accelerometers

A mixed effect model is proposed to jointly analyze multivariate longitudinal data with continuous, proportion, count, and binary responses. The association of the variables is modeled through the correlation of random effects. We use a quasi‐likelihood type approximation for nonlinear variables and transform the proposed model into a multivariate linear mixed model framework for estimation and inference. Via an extension to the EM approach, an efficient algorithm is developed to fit the model. The method is applied to physical activity data, which uses a wearable accelerometer device to measure daily movement and energy expenditure information. Our approach is also evaluated by a simulation study.     

Unsupervised clustering of multivariate circular data

In this paper, we study an unsupervised clustering problem. The originality of this problem lies in the data, which consist of the positions of five separate X‐ray beams on a circle. Radiation therapists positioned the five X‐ray beam ‘projectors’ around each patient on a predefined circle. However, similarities exist in positioning for certain groups of patients, and we aim to describe these similarities with the goal of creating pre‐adjustment settings that could help save time during X‐ray positioning. We therefore performed unsupervised clustering of observed X‐ray positions. Because the data for each patient consist of five angle measurements, Euclidean distances are not appropriated. Furthermore, we cannot perform k‐means algorithm, usually used for minimizing corresponding distortion because we cannot calculate centers of clusters. We present here solutions to these problems. First, we define a suitable distance on the circle. Then, we adapt an algorithm based on simulated annealing to minimize distortion. This algorithm is shown to be theoretically convergent. Finally, we present simulations on simulated and real data. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of treatment efficacy using a Bayesian mixture piecewise linear model of longitudinal biomarkers

Prostate‐specific antigen (PSA) is a widely used marker in clinical trials for patients with prostate cancer. We develop a mixture model to estimate longitudinal PSA trajectory in response to treatment. The model accommodates subjects responding and not responding to therapy through a mixture of two functions. A responder is described by a piecewise linear function, represented by an intercept, a PSA decline rate, a period of PSA decline, and a PSA rising rate; a nonresponder is described by an increasing linear function with an intercept and a PSA rising rate. Each trajectory is classified as a linear or a piecewise linear function with a certain probability, and the weighted average of these two functions sufficiently characterizes a variety of patterns of PSA trajectories. Furthermore, this mixture structure enables us to derive clinically useful endpoints such as a response rate and time‐to‐progression, as well as biologically meaningful endpoints such as a cancer cell killing fraction and tumor growth delay. We compare our model with the most commonly used dynamic model in the literature and show its advantages. Finally, we illustrate our approach using data from two multicenter prostate cancer trials. The R code used to produce the analyses reported in this paper is available on request. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian analysis of nonlinear mixed‐effects mixture models for longitudinal data with heterogeneity and skewness

It is a common practice to analyze complex longitudinal data using nonlinear mixed‐effects (NLME) models with normality assumption. The NLME models with normal distributions provide the most popular framework for modeling continuous longitudinal outcomes, assuming individuals are from a homogeneous population and relying on random‐effects to accommodate inter‐individual variation. However, the following two issues may standout: (i) normality assumption for model errors may cause lack of robustness and subsequently lead to invalid inference and unreasonable estimates, particularly, if the data exhibit skewness and (ii) a homogeneous population assumption may be unrealistically obscuring important features of between‐subject and within‐subject variations, which may result in unreliable modeling results. There has been relatively few studies concerning longitudinal data with both heterogeneity and skewness features. In the last two decades, the skew distributions have shown beneficial in dealing with asymmetric data in various applications. In this article, our objective is to address the simultaneous impact of both features arisen from longitudinal data by developing a flexible finite mixture of NLME models with skew distributions under Bayesian framework that allows estimates of both model parameters and class membership probabilities for longitudinal data. Simulation studies are conducted to assess the performance of the proposed models and methods, and a real example from an AIDS clinical trial illustrates the methodology by modeling the viral dynamics to compare potential models with different distribution specifications; the analysis results are reported. Copyright © 2014 John Wiley & Sons, Ltd.     

A copula-based model for multivariate non-normal longitudinal data: analysis of a dose titration safety study on a new antidepressant

A new model for multivariate non-normal longitudinal data is proposed. In a first step, each longitudinal series of data corresponding to a given response is modelled separately using a copula to relate the marginal distributions of the response at each time of observation. In a second step, at each observation time, the conditional (on the past) distributions of each response are related using another copula describing the relationship between the corresponding variables. Note that there is no need to consider the same family of distributions for these response variables. The technique is illustrated in a dose titration safety study on a new antidepressant. The haemodynamic effect on diastolic blood pressure, systolic blood pressure and heart rate is studied. These three responses are measured repeatedly over time on ten healthy volunteers during the dose escalation. The available covariates are sex and the concentration of drug in the plasma at time of measurement.     

Parameter clustering in Bayesian functional principal component analysis of neuroscientific data

The extraordinary advancements in neuroscientific technology for brain recordings over the last decades have led to increasingly complex spatiotemporal data sets. To reduce oversimplifications, new models have been developed to be able to identify meaningful patterns and new insights within a highly demanding data environment. To this extent, we propose a new model called parameter clustering functional principal component analysis (PCl‐fPCA) that merges ideas from functional data analysis and Bayesian nonparametrics to obtain a flexible and computationally feasible signal reconstruction and exploration of spatiotemporal neuroscientific data. In particular, we use a Dirichlet process Gaussian mixture model to cluster functional principal component scores within the standard Bayesian functional PCA framework. This approach captures the spatial dependence structure among smoothed time series (curves) and its interaction with the time domain without imposing a prior spatial structure on the data. Moreover, by moving the mixture from data to functional principal component scores, we obtain a more general clustering procedure, thus allowing a higher level of intricate insight and understanding of the data. We present results from a simulation study showing improvements in curve and correlation reconstruction compared with different Bayesian and frequentist fPCA models and we apply our method to functional magnetic resonance imaging and electroencephalogram data analyses providing a rich exploration of the spatiotemporal dependence in brain time series.     

A mixture of transition models for heterogeneous longitudinal ordinal data: with applications to longitudinal bacterial vaginosis data

Markov models used to analyze transition patterns in discrete longitudinal data are based on the limiting assumption that individuals follow the common underlying transition process. However, when one is interested in diseases with different disease or severity subtypes, explicitly modeling subpopulation‐specific transition patterns may be appropriate. We propose a model which captures heterogeneity in the transition process through a finite mixture model formulation and provides a framework for identifying subpopulations at different risks. We apply the procedure to longitudinal bacterial vaginosis study data and demonstrate that the model fits the data well. Further, we show that under the mixture model formulation, we can make the important distinction between how covariates affect transition patterns unique to each of the subpopulations and how they affect which subgroup a participant will belong to. Practically, covariate effects on subpopulation‐specific transition behavior and those on subpopulation membership can be interpreted as effects on short‐term and long‐term transition behavior. We further investigate models with higher‐order subpopulation‐specific transition dependence. Copyright © 2014 John Wiley & Sons, Ltd.     

A multivariate Bayesian model for embryonic growth

Most longitudinal growth curve models evaluate the evolution of each of the anthropometric measurements separately. When applied to a ‘reference population’, this exercise leads to univariate reference curves against which new individuals can be evaluated. However, growth should be evaluated in totality, that is, by evaluating all body characteristics jointly. Recently, Cole et al. suggested the Superimposition by Translation and Rotation (SITAR) model, which expresses individual growth curves by three subject‐specific parameters indicating their deviation from a flexible overall growth curve. This model allows the characterization of normal growth in a flexible though compact manner. In this paper, we generalize the SITAR model in a Bayesian way to multiple dimensions. The multivariate SITAR model allows us to create multivariate reference regions, which is advantageous for prediction. The usefulness of the model is illustrated on longitudinal measurements of embryonic growth obtained in the first semester of pregnancy, collected in the ongoing Rotterdam Predict study. Further, we demonstrate how the model can be used to find determinants of embryonic growth. Copyright © 2015 John Wiley & Sons, Ltd.     

A Bayesian zero-inflated beta-binomial model for longitudinal data with group-specific changepoints

Timeline followback (TLFB) is often used in addiction research to monitor recent substance use, such as the number of abstinent days in the past week. TLFB data usually take the form of binomial counts that exhibit overdispersion and zero inflation. Motivated by a 12-week randomized trial evaluating the efficacy of varenicline tartrate for smoking cessation among adolescents, we propose a Bayesian zero-inflated beta-binomial model for the analysis of longitudinal, bounded TLFB data. The model comprises a mixture of a point mass that accounts for zero inflation and a beta-binomial distribution for the number of days abstinent in the past week. Because treatment effects appear to level off during the study, we introduce random changepoints for each study group to reflect group-specific changes in treatment efficacy over time. The model also includes fixed and random effects that capture group- and subject-level slopes before and after the changepoints. Using the model, we can accurately estimate the mean trend for each study group, test whether the groups experience changepoints simultaneously, and identify critical windows of treatment efficacy. For posterior computation, we propose an efficient Markov chain Monte Carlo algorithm that relies on easily sampled Gibbs and Metropolis–Hastings steps. Our application shows that the varenicline group has a short-term positive effect on abstinence that tapers off after week 9.     

A Bayesian approach to joint analysis of longitudinal measurements and competing risks failure time data

In this paper, we develop a Bayesian method for joint analysis of longitudinal measurements and competing risks failure time data. The model allows one to analyze the longitudinal outcome with nonignorable missing data induced by multiple types of events, to analyze survival data with dependent censoring for the key event, and to draw inferences on multiple endpoints simultaneously. Compared with the likelihood approach, the Bayesian method has several advantages. It is computationally more tractable for high‐dimensional random effects. It is also convenient to draw inference. Moreover, it provides a means to incorporate prior information that may help to improve estimation accuracy. An illustration is given using a clinical trial data of scleroderma lung disease. The performance of our method is evaluated by simulation studies. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian transformation cure frailty models with multivariate failure time data

We propose a class of transformation cure frailty models to accommodate a survival fraction in multivariate failure time data. Established through a general power transformation, this family of cure frailty models includes the proportional hazards and the proportional odds modeling structures as two special cases. Within the Bayesian paradigm, we obtain the joint posterior distribution and the corresponding full conditional distributions of the model parameters for the implementation of Gibbs sampling. Model selection is based on the conditional predictive ordinate statistic and deviance information criterion. As an illustration, we apply the proposed method to a real data set from dentistry.     

A Bayesian multivariate meta-analysis of prevalence data

When conducting a meta-analysis involving prevalence data for an outcome with several subtypes, each of them is typically analyzed separately using a univariate meta-analysis model. Recently, multivariate meta-analysis models have been shown to correspond to a decrease in bias and variance for multiple correlated outcomes compared with univariate meta-analysis, when some studies only report a subset of the outcomes. In this article, we propose a novel Bayesian multivariate random effects model to account for the natural constraint that the prevalence of any given subtype cannot be larger than that of the overall prevalence. Extensive simulation studies show that this new model can reduce bias and variance when estimating subtype prevalences in the presence of missing data, compared with standard univariate and multivariate random effects models. The data from a rapid review on occupation and lower urinary tract symptoms by the Prevention of Lower Urinary Tract Symptoms Research Consortium are analyzed as a case study to estimate the prevalence of urinary incontinence and several incontinence subtypes among women in suspected high risk work environments.     

Parameter-expanded data augmentation for analyzing correlated binary data using multivariate probit models

Data augmentation has been commonly utilized to analyze correlated binary data using multivariate probit models in Bayesian analysis. However, the identification issue in the multivariate probit models necessitates a rigorous Metropolis-Hastings algorithm for sampling a correlation matrix, which may cause slow convergence and inefficiency of Markov chains. It is well-known that the parameter-expanded data augmentation, by introducing a working/artificial parameter or parameter vector, makes an identifiable model be non-identifiable and improves the mixing and convergence of data augmentation components. Therefore, we motivate to develop efficient parameter-expanded data augmentations to analyze correlated binary data using multivariate probit models. We investigate both the identifiable and non-identifiable multivariate probit models and develop the corresponding parameter-expanded data augmentation algorithms. We point out that the approaches, based on one non-identifiable model, circumvent a Metropolis-Hastings algorithm for sampling a correlation matrix and improve the convergence and mixing of correlation parameters; the identifiable model may produce the estimated regression parameters with smaller standard errors than the non-identifiable model does. We illustrate our proposed approaches using simulation studies and through the application to a longitudinal dataset from the Six Cities study.     

Variable selection for joint models of multivariate longitudinal measurements and event time data

Joint modeling of longitudinal and survival data has attracted a great deal of attention. Some research has been undertaken to extend the joint model to incorporate multivariate longitudinal measurements recently. However, there is a lack of variable selection methods in the joint modeling of multivariate longitudinal measurements and survival time. In this article, we develop penalized likelihood methods for the selection of longitudinal features in the survival submodel. A multivariate linear mixed effect model is used to model multiple longitudinal processes where random intercepts and slopes serve as essential features of the trajectories. We introduce L1 penalty functions to select both random effects in the survival submodel and off‐diagonal elements in the covariance matrix of random effects. An estimation procedure is developed based on Laplace approximation. Our simulations demonstrate excellent selection properties of the proposed procedure. We apply our methods to explore the relationship between mortality and multiple longitudinal processes for end stage renal disease patients on hemodialysis. We find that lower levels of albumin, higher levels of neutrophil‐to‐lymphocyte ratio, and higher levels of interdialytic weight gain at the beginning of the follow‐up time, as well as decrease in predialysis systolic blood pressure and increase of neutrophil‐to‐lymphocyte ratio over time are associated with higher mortality hazard rates.     

A Bayesian mixture of semiparametric mixed‐effects joint models for skewed‐longitudinal and time‐to‐event data

In longitudinal studies, it is of interest to investigate how repeatedly measured markers in time are associated with a time to an event of interest, and in the mean time, the repeated measurements are often observed with the features of a heterogeneous population, non‐normality, and covariate measured with error because of longitudinal nature. Statistical analysis may complicate dramatically when one analyzes longitudinal–survival data with these features together. Recently, a mixture of skewed distributions has received increasing attention in the treatment of heterogeneous data involving asymmetric behaviors across subclasses, but there are relatively few studies accommodating heterogeneity, non‐normality, and measurement error in covariate simultaneously arose in longitudinal–survival data setting. Under the umbrella of Bayesian inference, this article explores a finite mixture of semiparametric mixed‐effects joint models with skewed distributions for longitudinal measures with an attempt to mediate homogeneous characteristics, adjust departures from normality, and tailor accuracy from measurement error in covariate as well as overcome shortages of confidence in specifying a time‐to‐event model. The Bayesian mixture of joint modeling offers an appropriate avenue to estimate not only all parameters of mixture joint models but also probabilities of class membership. Simulation studies are conducted to assess the performance of the proposed method, and a real example is analyzed to demonstrate the methodology. The results are reported by comparing potential models with various scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian joint modeling of longitudinal and spatial survival AIDS data

Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for analyzing cancer and AIDS data. As both repeated measurements (longitudinal) and time‐to‐event (survival) outcomes are observed in an individual, a joint modeling is more appropriate because it takes into account the dependence between the two types of responses, which are often analyzed separately. We propose a Bayesian hierarchical model for jointly modeling longitudinal and survival data considering functional time and spatial frailty effects, respectively. That is, the proposed model deals with non‐linear longitudinal effects and spatial survival effects accounting for the unobserved heterogeneity among individuals living in the same region. This joint approach is applied to a cohort study of patients with HIV/AIDS in Brazil during the years 2002–2006. Our Bayesian joint model presents considerable improvements in the estimation of survival times of the Brazilian HIV/AIDS patients when compared with those obtained through a separate survival model and shows that the spatial risk of death is the same across the different Brazilian states. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive Bayesian variable clustering via structural learning of breast cancer data

The clustering of proteins is of interest in cancer cell biology. This article proposes a hierarchical Bayesian model for protein (variable) clustering hinging on correlation structure. Starting from a multivariate normal likelihood, we enforce the clustering through prior modeling using angle-based unconstrained reparameterization of correlations and assume a truncated Poisson distribution (to penalize a large number of clusters) as prior on the number of clusters. The posterior distributions of the parameters are not in explicit form and we use a reversible jump Markov chain Monte Carlo based technique is used to simulate the parameters from the posteriors. The end products of the proposed method are estimated cluster configuration of the proteins (variables) along with the number of clusters. The Bayesian method is flexible enough to cluster the proteins as well as estimate the number of clusters. The performance of the proposed method has been substantiated with extensive simulation studies and one protein expression data with a hereditary disposition in breast cancer where the proteins are coming from different pathways.