Testing drug additivity based on monotherapies

Under the Loewe additivity, constant relative potency between two drugs is a sufficient condition for the two drugs to be additive. Implicit in this condition is that one drug acts like a dilution of the other. Geometrically, it means that the dose-response curve of one drug is a copy of another that is shifted horizontally by a constant over the log-dose axis. Such phenomenon is often referred to as parallelism. Thus, testing drug additivity is equivalent to the demonstration of parallelism between two dose-response curves. Current methods used for testing parallelism are usually based on significance tests for differences between parameters in the dose-response curves of the monotherapies. A p-value of less than 0.05 is indicative of non-parallelism. The p-value-based methods, however, may be fundamentally flawed because an increase in either sample size or precision of the assay used to measure drug effect may result in more frequent rejection of parallel lines for a trivial difference. Moreover, similarity (difference) between model parameters does not necessarily translate into the similarity (difference) between the two response curves. As a result, a test may conclude that the model parameters are similar (different), yet there is little assurance on the similarity between the two dose-response curves. In this paper, we introduce a Bayesian approach to directly test the hypothesis that the two drugs have a constant relative potency. An important utility of our proposed method is in aiding go/no-go decisions concerning two drug combination studies. It is illustrated with both a simulated example and a real-life example.