Advanced Models for Longitudinal and Spatial Data in Health Research

Intensive longitudinal data are increasingly encountered in many research areas. For example, ecological momentary assessment (EMA) and/or mobile health (mHealth) methods are often used to study subjective experiences within changing environmental contexts. In these studies, up to 30 or 40 observations are usually obtained for each subject over a period of a week or so, allowing one to characterize a subject's mean and variance and specify models for both. In this presentation, we focus on a smoking study of dual users (i.e., both combustible and electronic cigarette users) using EMA where interest is on characterizing changes in mood variation associated with these nicotine products, and whether subjects' mood response can predict future nicotine product use. At the first stage, the MELS model includes random subject effects for the mean (i.e., location), which characterize subjects' differential mood response to combustible and electronic cigarettes. A random effect for subjects' variability (i.e., scale) in mood responses is included to characterize subjects' mood consistency/erraticism. These random location and scale effects are used in a second stage regression, both linear and multinomial, model to predict future nicotine product use. Since the random effects are estimates, repeated draws from the posterior distribution of the random effects for each subject are utilized in the second stage model (i.e., plausible value replications), with results averaged across these repeated draws. A software program, MixWILD, which facilitates this two stage modeling approach, is described. 

Joint modeling of longitudinal and survival data is commonly used to study their association, and to make dynamic risk prediction of the event based on the longitudinal data. Typically, a multivariate linear mixed effect mode is used for the longitudinal submodel, and the Cox proportional hazard model is used for the survival submodel, and shared random effects are used to account for their association. Challenges arise when the number of longitudinal variables increases. We develop a longitudinal variable selection method for the joint modeling of multivariate longitudinal measurements and survival time. The longitudinal variables in the survival submodel are selected by penalized likelihood method, where a Group Lasso is imposed on the coefficients of random intercept and random slope in the survival submodel. Numerical studies are conducted to validate and illustrate the proposed procedure. 

Cardiometabolic risk factors (CRFs) during pregnancy are early indicators of maternal diseases, such as stroke and type 2 diabetes. The total number of CRFs typically takes the form of binomial counts that exhibit overdispersion and zero inflation due to correlations among the underlying CRFs. Motivated by an examination of spatiotemporal trends in five CRFs among pregnant women in the US state of South Carolina during the COVID-19 pandemic, we develop a Bayesian zero-inflated beta-binomial model within a spatiotemporal framework. This model combines a point mass at zero to account for zero inflation and a beta-binomial distribution to model the remaining CRF counts. Given the notable racial disparities in CRFs that vary across the state over time, we incorporate a spatially varying coefficients model to explore the complex relationships between CRFs and geographic and temporal disparities among non-Hispanic White and non-Hispanic Black women. For posterior inference, we develop an efficient hybrid Markov Chain Monte Carlo algorithm that relies on easily sampled Gibbs and Metropolis-Hastings steps. In simulation studies, the model effectively captures trends between the two racial groups and accurately predicts mean CRF scores in each region over time. Our analysis of CRFs in South Carolina reveals that certain counties, such as Chesterfield and Clarendon, exhibit particularly wide gaps in racial health disparities, making them prime candidates for community-level interventions aimed at reducing these disparities.  

Observational cohort data is an important source of information for understanding the causal effects of treatments on survival and the degree to which these effects are mediated through changes in disease-related risk factors. However, these analyses are often complicated by irregular data collection intervals and the presence of longitudinal confounders and mediators. We propose a causal mediation framework that jointly models longitudinal exposures, confounders, mediators, and time-to-event outcomes as continuous functions of age. This framework for longitudinal covariate trajectories enables statistical inference even at ages where the subject's covariate measurements are unavailable. The observed data distribution in our framework is modeled using an enriched Dirichlet process mixture (EDPM) model. Using data from the Atherosclerosis Risk in Communities cohort study, we apply our methods to assess how medication—prescribed to target cardiovascular disease (CVD) risk factors—affects the time-to-CVD death. 

We discuss an application of group-based trajectory modeling where the inference target is the effect of trajectory shape on an outcome variable that is measured at irregular timepoints and possibly more than once per subject. Unlike many applications of group-based trajectory modeling, where measurements of both the trajectory variable and the outcome are taken at the same time points or ages across subjects, our setting requires careful consideration of the temporal dependencies among the variables. We describe techniques for accounting for such dependencies and illustrate them in an application involving longitudinal blood pressure measurements and a neuroimaging outcome.