Using Markov Chain Models as a Longitudinal Outcome or a Covariate Process in Statistical Analysis with Applications to Medical Research

Abstract

Stochastic processes are traditionally used to analytically describe natural phenomena or to examine their mathematical properties. This presentation will focus on methods for using continuous-time Markov chains (CTMC) as (1) a longitudinal outcome or (2) a covariate process in a statistical model for data analysis. The former is extended to cover potentially misclassified outcomes (a hidden Markov model) and joint models of two binary CTMC outcome processes. The latter will focus on the joint modeling of a logistic regression and its CTMC covariate process and will be applied to the prediction of a cross-sectional outcome from a longitudinal covariate. Identifiability and estimability of parameters in each model will be discussed. A practical method for examining the Markov and stationarity property on a sequence of observed discrete outcomes will also be presented. Each model will be illustrated with a real data example from medical research.