A Bayesian Semiparametric Model for Bivariate Sparse Longitudinal Data
*Kiranmoy Das, Penn State University, Statistics department 

Keywords: Bivariate response, penalized spline, truncated dirichlet process mixture, MCMC

Mixed effects models have become popular recently to analyze sparse longitudinal data which arise naturally in biological, agricultural and bio-medical studies. The traditional approaches assume independence for the residuals and explain the longitudinal dependence by random effects. However, when bivariate or multivariate traits are measured longitudinally, this fundamental assumption is likely to be violated because of inter-trait dependence over time. We provide a more general framework where the dependence of the observations from the same subject over different time points is not assumed to be explained completely by the random effect of the model. We propose a novel mixed model based approach and estimate the error covariance matrix non-parametrically under a generalized linear model framework. Penalized splines are used to model the general mean effect of time on the observed trait and we consider a truncated Dirichlet Process Mixture (DPM) prior on the random effect. We analyze blood pressure data from Framingham Heart Study (FHS) where body mass index (BMI), gender and time are treated as covariates. We compare our method with the traditional methods including the parametric modeling of the random effects and independent errors. Extensive simulation studies have been performed to investigate the practical usefulness of the proposed method. The current approach will be very helpful for the analysis of bivariate irregular longitudinal traits.