A review of multistate modelling approaches in monitoring disease progression: Bayesian estimation using the Kolmogorov-Chapman forward equations
Open Access
- 7 April 2021
- journal article
- review article
- Published by SAGE Publications in Statistical Methods in Medical Research
- Vol. 30 (5), 1373-1392
- https://doi.org/10.1177/0962280221997507
Abstract
There are numerous fields of science in which multistate models are used, including biomedical research 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. The multistate framework can describe more than one possible time-to-event outcome 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 from the Bayesian estimation perspective. 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 estimation and data features compatible with fitting multistate models. We highlight the contrast between the frequentist (maximum likelihood estimation) and the Bayesian estimation approaches in the multistate modeling framework and point out where the latter is advantageous. A partially observed and aggregated dataset from the Zimbabwe national ART program was used to illustrate the use of Kolmogorov-Chapman forward equations. The transition rates from a three-stage reversible multistate model based on viral load measurements in WinBUGS were reported.Funding Information
- Developing Excellence in Leadership, Training and Science (DELTAS) Consortium (107754/Z/15/Z)
This publication has 46 references indexed in Scilit:
- Interval censoringStatistical Methods in Medical Research, 2009
- Bayesian statisticsScholarpedia, 2009
- Bayesian semi parametric multi-state modelsStatistical Modelling, 2008
- Multi-state models for the analysis of time-to-event dataStatistical Methods in Medical Research, 2008
- Treatment interruptions predict resistance in HIV-positive individuals purchasing fixed-dose combination antiretroviral therapy in Kampala, UgandaAIDS, 2007
- Tutorial in biostatistics: competing risks and multi‐state modelsStatistics in Medicine, 2006
- Calibrated BayesThe American Statistician, 2006
- Bayesian Measures of Model Complexity and FitJournal of the Royal Statistical Society Series B: Statistical Methodology, 2002
- A Proportional Hazards Model for the Subdistribution of a Competing RiskJournal of the American Statistical Association, 1999
- An Actuarial Survey of Statistical Models for Decrement and Transition Data - I: Multiple State, Poisson and Binomial ModelsBritish Actuarial Journal, 1996