An application of a two-level non-Gaussian state-space model in the analysis of longitudinal papilloma count data

Abstract

In this study, a dynamic Bayesian two-level non-Gaussian state-space model is applied in the statistical analysis of longitudinal detectable papilloma count data. This two-level model is established on the basis of the state and hyper-state parameters that depend on the model parameters of biological significance, namely, the initiation rate of normal cells and the birth- and death-rates of initiated cells. As the time-dependent model parameters fluctuate dynamically and stochastically over time, so will the state and hyper-state parameters; thus, smoothness priors that allow a wide range of shapes with no specific forms required on the state/hyper-state parameters can be employed in this model. Gibbs sampler, a Markov chain Monte Carlo approach, is used to implement the Bayesian inferences on the state as well as the hyper-state parameters; and the estimates of the model parameters can be obtained thereon. Illustrations of the Bayesian inference procedure are given by using the datasets from a simulation study as well as a laboratory experiment by Brook et al. [E.A. Brooks, C.M. Kohn, P.J.M. van Birgelen, G.W. Lucier, C.J. Portier, Stochastic models for papilloma formation following exposure to TCDD, Organohalogen Compd. 41 (1999) 521]. Comparing to the parametric approach that assigns specific forms on the time-dependent model parameters, different conclusions are drawn by the two-level state-space modeling approach considered in this study.