A random-effects Markov transition model for Poisson-distributed repeated measures with non-ignorable missing values

UCLA-Department of Statistics, PO Box 951554, Los Angeles, CA 90095-1554, USA.
Statistics in Medicine (Impact Factor: 1.83). 05/2007; 26(12):2519-32. DOI: 10.1002/sim.2717
Source: PubMed


In biomedical research with longitudinal designs, missing values due to intermittent non-response or premature withdrawal are usually 'non-ignorable' in the sense that unobserved values are related to the patterns of missingness. By drawing the framework of a shared-parameter mechanism, the process yielding the repeated count measures and the process yielding missing values can be modelled separately, conditionally on a group of shared parameters. For chronic diseases, Markov transition models can be used to study the transitional features of the pathologic processes. In this paper, Markov Chain Monte Carlo algorithms are developed to fit a random-effects Markov transition model for incomplete count repeated measures, within which random effects are shared by the counting process and the missing-data mechanism. Assuming a Poisson distribution for the count measures, the transition probabilities are estimated using a Poisson regression model. The missingness mechanism is modelled with a multinomial-logit regression to calculate the transition probabilities of the missingness indicators. The method is demonstrated using both simulated data sets and a practical data set from a smoking cessation clinical trial.

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Available from: Steve Shoptaw, Aug 04, 2014
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    • "Here, the inverse Wishart prior for Σ unnecessarily incorporates too many parameters. Some customized structures, say the intra-class correlation matrix (ρ 1 [i = j] ) and the Toeplitz matrix (ρ |i− j| ), are difficult for sampling-based inference since they inherently require a restricted domain where ρ is always between 0 and 1. Li et al. [16] applied a first-order Markov transition to repeated measures Poisson model, where the measurement at time point t for subject i, y i,t is only dependent on y i,t−1 , covariate x i,t and a subject-specific random effect ξ i , e.g., y i,t ∼ Poisson(λ i,t ), log(λ i,t ) = x i,t β + (log(max(1, y i,t−1 )) − x i,t−1 β i )c + ξ i . "
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