  Medication adherence is a well-known problem for pharmaceutical treatment of
chronic diseases. Understanding how nonadherence affects treatment efficacy is
made difficult by the ethics of clinical trials that force patients to skip
doses of the medication being tested, the unpredictable timing of missed doses
by actual patients, and the many competing variables that can either mitigate
or magnify the deleterious effects of nonadherence, such as pharmacokinetic
absorption and elimination rates, dosing intervals, dose sizes, adherence
rates, etc. In this paper, we formulate and analyze a mathematical model of the
drug concentration in an imperfectly adherent patient. Our model takes the form
of the standard single compartment pharmacokinetic model with first order
absorption and elimination, except that the patient takes medication only at a
given proportion of the prescribed dosing times. Doses are missed randomly, and
we use stochastic analysis to study the resulting random drug level in the
body. We then use our mathematical results to propose principles for designing
drug regimens that are robust to nonadherence. In particular, we quantify the
resilience of extended release drugs to nonadherence, which is quite
significant in some circumstances, and we show the benefit of taking a double
dose following a missed dose if the drug absorption or elimination rate is slow
compared to the dosing interval. We further use our results to compare some
antiepileptic and antipsychotic drug regimens.
