title: Semiparametric Stochastic Modeling of the Rate Function in Longitudinal Studies.
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 these functions as the realizations of stochastic processes defined by stochastic differential equations. These processes are dependent on the covariates of interest and vary around a specified parametric function. An efficient Markov chain Monte Carlo algorithm is developed for inference. The proposed method is compared with several existing methods in terms of goodness-of-fit and more importantly the ability to forecast future functional data in a simulation study. The proposed methodology is applied to prostate-specific antigen profiles for illustration. Supplementary materials for this paper are available online.
authors.affiliation: Department of Statistical Science and Center for Human Genetics, Duke University, Durham, NC 27708, ( bin.zhu@duke.edu ).
authors.forename: Bin
authors.initials: B
authors.lastname: Zhu
authors.forename: Jeremy M G
authors.initials: JM
authors.lastname: Taylor
authors.forename: Peter X-K
authors.initials: PX
authors.lastname: Song