Discrete stochastic models for compliance analysis based on an AIDS clinical trial group (ACTG) study

Compliance is the extent to which a patient follows the prescribed regimen. Here we investigate the statistical properties of two popular measures of compliance - percentage of compliant days and percentage of doses taken. We use a stationary Markov chain to model the dependence structure of successive data points for each subject. We illustrate our model using discrete compliance data collected from an AIDS Clinical Trial Group study (ACTG 398). We check the model assumptions and evaluate the small sample as well as large sample properties of our estimators. We show that ignoring the within-subject dependence will usually underestimate the standard errors of the estimates of these compliance measures. Our model allows the application of meta-analytic approaches to assess the variation across subjects in these compliance indices and changes in them due to intervention.