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Department of Statistics, UCLA

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A Random-effects Markov Transition Model for Poisson-distributed Repeated Measures with Nonignorable Missing Values

Abstract

In biomedical research with longitudinal designs, missing values due to intermittent nonresponse or premature withdrawal are usually ’nonignorable’ in the sense that un- observed values are related to the patterns of missingness. When missing values are simply ignored, analyses based on observed-data likelihood may yield biased estimates or invalid inferences. By drawing the framework of a shared-parameter mechanism, the process yielding the repeated count measures and the process yielding missing val- ues can be modelled separately, conditionally on a group of shared parameters. For chronic diseases, Markov transition models can be used to study the transitional fea- tures of the pathologic processes. In this paper, Markov chain Monte Carlo (MCMC) algorithms are developed to fit a random-effects Markov transition model (REMTM) for incomplete count repeated measures, within which random effects are shared by the counting process and the missing-data mechanism. Assuming a Poisson distribu- tion for the count measures, the transition probabilities are estimated using a Poisson linear regression model. The missingness mechanism is modeled 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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