Spatial and mixture models for recurrent event processes

Abstract

AbstractStudies of recurring infection or chronic disease often collect longitudinal data on the disease status of subjects. Two types of models may be envisioned for the analysis of such data: counting process models or multi‐state transitional models. We consider both scenarios in the specific case where the population consists of mixtures. A flexible semi‐parametric model for analyzing longitudinal panel count data is presented. Discrete mixtures of smooth counting process intensity forms are considered, including mixtures of splines, which permit time‐varying covariate effects, with the so‐called proportional intensity model as a limiting case. For recurrent events handled in a multi‐state transitional model framework, individuals may be said to occupy one of a discrete set of states and interest centers on the transition process between states. We examine the use of mixed Markov models for the analysis of such longitudinal data where the processes corresponding to different subjects may be correlated spatially over a region. Both discrete and continuous‐time models incorporating spatially correlated random effects are discussed. Examples illustrate the methods discussed including a study of recurrent weevil infestation, and one to assess the effectiveness of a pheromone treatment in disturbing the mating habits of the cherry bark tortrix moth. Copyright © 2007 John Wiley & Sons, Ltd.