Semiparametric Stochastic Modeling of the Rate Function in Longitudinal Studies

• Activity Number: 340
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Bin Zhu*+ and Peter Song and Jeremy Michael George Taylor
• Companies: Duke University and University of Michigan and University of Michigan
• Keywords: Euler approximation ; Functional data analysis ; Gaussian process ; Rate function ; Stochastic differential equations ; Semiparametric stochastic velocity model

Abstract

In longitudinal biomedical studies, there is often interest in the rate functions, which describe the functional rates of change of biomarker profiles. This paper proposes a semiparametric approach to model those functions as the realizations of stochastic processes, using the stochastic differential equations. These processes are dependent on the covariates of interest, and are expected to be centered on some parametric forms while allowing significant deviations from these functional expectations. An efficient Markov chain Monte Carlo algorithm is developed for the inference. The proposed method is compared with several existing methods in aspects of goodness-of-fit and more importantly the ability of forecasting via validation functional data in a simulation study and an application to prostate-specific antigen profiles.