Markov transition models for binary repeated measures with ignorable and nonignorable missing values

Motivated by problems encountered in studying treatments for drug dependence, where repeated binary outcomes arise from monitoring biomarkers for recent drug use, this article discusses a statistical strategy using Markov transition model for analyzing incomplete binary longitudinal data. When the mechanism giving rise to missing data can be assumed to be `ignorable', standard Markov transition models can be applied to observed data to draw likelihood-based inference on transition probabilities between outcome events. Illustration of this approach is provided using binary results from urine drug screening in a clinical trial of baclofen for cocaine dependence. When longitudinal data have `nonignorable' missingness mechanisms, random-effects Markov transition models can be used to model the joint distribution of the binary data matrix and the matrix of missingness indicators. Categorizing missingness patterns into those for occasional or `intermittent' missingness and those for monotonic missingness or `missingness due to dropout', the random-effects Markov transition model was applied to a data set containing repeated breath samples analyzed for expired carbon monoxide levels among opioid-dependent, methadone-maintained cigarette smokers in a smoking cessation trial. Markov transition models provide a novel reconceptualization of treatment outcomes, offering both intuitive statistical values and relevant clinical insights.