A Markov mixed effect regression model for drug compliance

Patient compliance (adherence) with prescribed medication is often erratic, while clinical outcomes are causally linked to actual, rather than nominal medication dosage. We propose here a hierarchical Markov model for patient compliance. At the first stage, conditional upon individual random effects and a set of individual-specific nominal daily dose times, we assume that (i) the subject-specific probability of taking zero, one, or more than one dose associated with a given nominal dose time depends on the value of certain covariates, and on the number of doses associated with the immediate previous time, but is independent of any other previous or future dosing events (the Markov hypothesis); and (ii) the set of 'errors' between actual dose times associated with each nominal time is multivariate normally distributed, conditional on covariates and the number of such actual dose times, as in (i). At the second stage, a multivariate normal distribution is assumed for the individual random effects. We fit this model by maximum likelihood to data collected over three months using an electronic system for recording actual dose times in HIV-positive patients assigned to a regimen of zidovudine thrice daily. Beyond its value for describing and quantifying compliance behaviour, as illustrated here, the model may prove useful for explanatory analyses of clinical trials.