Premium
A random‐effects Markov transition model for Poisson‐distributed repeated measures with non‐ignorable missing values
Author(s) -
Li Jinhui,
Yang Xiaowei,
Wu Yingnian,
Shoptaw Steven
Publication year - 2007
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2717
Subject(s) - missing data , statistics , markov chain , poisson distribution , multinomial logistic regression , poisson regression , multinomial distribution , econometrics , markov chain monte carlo , count data , mathematics , random effects model , computer science , monte carlo method , population , medicine , meta analysis , environmental health
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. Copyright © 2006 John Wiley & Sons, Ltd.