Continuous time Markov chain approaches for analysing transtheoretical models of health behavioural change: a case study and comparison of model estimations - Ma, Junsheng (Stat Methods Med Res, 2016)
Continuous time Markov chain (CTMC) models are frequently employed in medical research to study disease progression, but are rarely applied to the transtheoretical model (TTM), a psychosocial model widely used in studies of health-related outcomes. The TTM often includes more than three states and conceptually allows for all possible instantaneous transitions (referred to as general CTMC). This complicates the likelihood function because it involves calculating a matrix exponential that may not be simplified for general CTMC models. We undertook a Bayesian approach wherein we numerically evaluated the likelihood using ordinary differential equation solvers available from the GNU scientific library. We compared our Bayesian approach with the maximum likelihood (ML) method implemented with the R package MSM. Our simulation study showed that the Bayesian approach provided more accurate point and interval estimates than the ML method, especially in complex CTMC models with five states. When applied to data from a four-state TTM collected from a nutrition intervention study in the Next Step Trial, we observed results consistent with the results of the simulation study. Specifically, the two approaches provided comparable point estimates and standard errors for most parameters, but the ML offered substantially smaller standard errors for some parameters. Comparable estimates of the standard errors are obtainable from package MSM, which works only when the model estimation algorithm converges.