Spatial and mixture models for recurrent event processes

Abstract

SUMMARYStudies 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.

Semiparametric regression during 2003–2007

“…Dean, Nathoo & Nielsen [68] use penalized splines as a component of multi-state models for longitudinal panel count data, where the processes corresponding to different subjects may be spatially correlated. Application is made to weevil infestation in white spruce trees.…”

Canadian contributions to environmetrics

“…This reflection of contributions focused on wildland fire science and management; however, there are many other fields where statisticians have had an impact. Of note, we mention the important field of forest ecology, with leadership in research provided by Marie‐Josée Fortin and important contributions by Ainsworth & Dean (2008) and Feng & Dean (2012) in zero‐heavy spatial modelling, and Dean, Nathoo & Nielsen (2007) in mixture models for pine weevil studies. With such a large field of research in forestry and much work to be done, there is a need for continued training and talent to engage in these areas.…”

Modeling the duration and size of wildfires using joint mixture models

“…Vink et al (2016) uses a bivariate Gaussian mixture model for estimating vaccine‐type seroprevalence from correlated antibody responses, hence incorporating mixtures in correlated outcomes. In forestry study, Dean et al (2007) developed a multistate model for tree disease status using a two‐component mixture. In the component of affected trees, the forward and backward transition probabilities of the disease status are linked with a tree‐specific spatial random effect.…”