A Critical Review of Multistate Bayesian Models Modelling Approaches in Monitoring Disease Progression: Use of Kolmogorov-Chapman Forward Equations with in WinBUGS

Abstract

There are numerous fields of science in which multistate models are used, including biomedical researched and health economics. In biomedical studies, these stochastic continuous-time models are used to describe the time to event life history of an individual through a flexible framework for longitudinal data which can describe more than one possible time to event outcomes for a single individual. The standard estimation quantities in multistate models are transition probabilities and transition rates which can be mapped through the Kolmogorov-Chapman forward equations. Most multistate models assume the Markov property and time homogeneity; however, if these assumptions are violated an extension to non-Markovian and time-varying transition rates is possible. This manuscript extends reviews in various types of multistate models, assumptions, methods of estimations, data types and emerging software for fitting multistate models. We highlight strengths and limitations in multistate models for different software and emphasis is made on Multistate Bayesian models in Bayes X and Win BUGS software which are underutilized. A partially observed and aggregated dataset from the Zimbabwe national ART program is used to illustrate the use of Kolmogorov-Chapman forward equations in estimating transition rates from a three-state reversible multistate model based on viral load measurements in Win BUGS.