Non-linear hierarchical models for monitoring compliance

As biomarkers transformable by specific drug agents increasingly become available, so their usefulness also increases for monitoring compliance in clinical and prevention trials, and for subsequent monitoring in the general population if a treatment is found successful. Marker levels measured over the course of a treatment yield a longitudinal trajectory that is typically non-linear, with varying velocities during the phase-in and steady-state periods of treatment, followed by decays back to normal in the presence of non-compliance. There is often considerable between-individual variability both in the mean parameters of the trajectory and the variability over time. An example is the biomarker mean corpuscular volume (MCV), which increases by 20 per cent from the drug zidovudine (AZT), and has been used to monitor compliance to AZT. Using MCV data from a previous AIDS clinical trial as an example, we describe a non-linear hierarchical growth model suitable for biomarkers that exhibit sigmoidal and/or asymptotic growth behaviour and show how such models can be supplemented with a change-point to identify potential times of non-compliance. We perform a fully Bayesian analysis to obtain a variety of posterior summaries for the behaviour of the longitudinal trajectory and the times of non-compliance, and describe how to obtain predictions of non-compliance for new individuals.