Assessment of Markov-dependent stochastic models for drug administration compliance

There are few analytical results that describe patient compliance with drug administration regimens. The purpose of this paper is to develop and assess stochastic approaches for mathematical modelling of patient compliance with administration regimens.

Two stochastic models based on Markov-dependent random variables and on the Ising model were assessed for their ability to describe the variable nature of drug compliance.

Both models use only experimentally accessible data, and their predictions were tested against published clinical compliance data obtained from electronic monitoring devices. The models satisfactorily fitted administration interval distribution data from several patients treated with diltiazem, a calcium channel antagonist, or zidovudine, an antiretroviral agent. The Ising model provides additional analytical expressions for the distribution of success runs and 'drug holidays' in administration regimens. These distribution predictions were tested with success run data for diltiazem and drug holiday data for two nonsteroidal anti-inflammatory drugs, piroxicam and tenoxicam.

Stochastic models can provide useful insights into drug compliance, and can be used to identify the administration patterns that are more likely to occur during drug self-administration in populations.