BAYESIAN APPROACHES TO ADDRESS MISSING DATA AND ANALYSIS CHALLENGES IN LONGITUDINAL STUDIES WITH FREQUENT MEASUREMENTS

Patient-reported outcome data collected at a large number of time points using an electronic diary or other questionnaire technology is a common feature of modern longitudinal research studies. Patient-report outcomes are frequently comprised of individual items combined to derive a construct of interest (e.g., a summary score). Data from these studies often exhibit missingness at the item and construct level (e.g., insufficient item responses to apply a scoring formula). In this work, we propose a Bayesian approach that addresses missingness in time-varying covariates and response variables using lagged-transition models tailored for these types of longitudinal studies. Traditional multiple imputation approaches may perform poorly in these settings where there is often a small number of participants, a large number of observations, and where some participants have a high degree of missingness. In the analysis of longitudinal diary data, multilevel models are frequently used to account for the nested structure of diary data where repeated entries (e.g., from multiple days) are nested within participants. These approaches allow for the examination of both within- and between-participant effects. Group-mean centering is a commonly used approach for multilevel modeling in this setting to characterize how a participant varies from their typical value as well as how participants vary compared to one another. In this work, we propose a Bayesian model that utilizes the stationary distribution of the time-varying covariate in place of a participant’s sample average value, which is typically used in a standard multilevel model. The proposed approach allows for the imputation of the time-varying covariate and outcome variables, computation of the stationary distribution, and inclusion of the stationary distribution in a regression model for the outcome to understand how a participant’s “typical state” impacts their outcome distribution. We extend our work to allow for multiple time-varying covariates in a Bayesian Multivariate Markov Model. Due to the number of parameter constraints required by commonly used Multivariate Markov models, maximum likelihood estimation for these models is challenging. Here, we propose the use of a Markov Chain Monte Carlo (MCMC) model fitting algorithm that naturally avoids the complications associated with the constraints, resulting in an efficient conditionally conjugate sampler. Analysis methods are applied to data from an Adolescent Medicine Trials Network for HIV/AIDS study as well as assessed through simulation studies.