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J Am Stat Assoc. 2011 Dec 1;106(496):1485-1495.

Semiparametric Stochastic Modeling of the Rate Function in Longitudinal Studies.

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1
Department of Statistical Science and Center for Human Genetics, Duke University, Durham, NC 27708, ( bin.zhu@duke.edu ).

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.

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