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Time-varying Markov regression random-effect model with Bayesian estimation procedures: Application to dynamics of functional recovery in patients with stroke. (English) Zbl 1194.92043

Summary: The rates of functional recovery after stroke tend to decrease with time. Time-varying Markov processes (TVMP) may be more biologically plausible than time-invariant Markov process for modeling such data. However, analysis of such stochastic processes, particularly tackling reversible transitions and the incorporation of random effects into models, can be analytically intractable. We make use of ordinary differential equations to solve continuous-time TVMP with reversible transitions. The proportional hazard form was used to assess the effects of an individual’s covariates on multi-state transitions with the incorporation of random effects that capture the residual variation after being explained by measured covariates under the concept of generalized linear models. We further built up a Bayesian directed acyclic graphic model to obtain full joint posterior distributions. Markov chain Monte Carlo (MCMC) with Gibbs sampling was applied to estimate parameters based on posterior marginal distributions with multiple integrands. The proposed method was illustrated with empirical data from a study on the functional recovery after stroke.

MSC:

92C50 Medical applications (general)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
62F15 Bayesian inference
05C90 Applications of graph theory
62P10 Applications of statistics to biology and medical sciences; meta analysis
65C40 Numerical analysis or methods applied to Markov chains
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