The impact of patient compliance on drug concentration profile in multiple doses

Physicians commonly prescribe drugs in a multiple dosage regimen for prolonged therapeutic activity. To study the effect of multiple dosing on drug concentration in blood, researchers often use deterministic models with the assumption that drugs are administered at a fixed dosage, with equal or unequal (fixed) dosing intervals. In practice, many patients do not comply with such a rigid schedule. Hence, two possible scenarios might occur: patients might not take the prescribed dosing amount, resulting in erratic dosing sizes; they might not adhere to the dosing schedule, resulting in erratic dosing times. We propose separate statistical models for these two scenarios and study their impact on blood serum/plasma concentration. With non-compliance, some basic concepts such as steady state need new definition. We provide a rigorous formulation for the principle of superposition which enables us to generalize the concept of steady state. Applying the proposed models, we demonstrate that non-compliance causes the drug concentration time curve to exhibit an increase in fluctuation. The increase in fluctuation due to non-compliance cannot be explained with use of the classical deterministic multiple dose model.