Quantifying the impact of non-adherence to drug therapy: a technical note concerning an application of a branch and bound algorithm

Pharmacokinetic models typically rely on a key assumption that patients take their medication as prescribed, whereas this is often not the case. We present a branch and bound algorithm that can be used to estimate the time–varying probability that, given a specified pattern of non–adherence to a prescribed regimen, a patient receives no therapeutic benefit from treatment. Use of this algorithm is a much faster method for obtaining this probability than exhaustive computation of the relevant probability distribution. The use of this algorithm to assess, in quantitative terms, the impact of non–adherence on the effectiveness of treatment provides a rational basis for evaluating the potential harm to patients.