Adjusting Power Calculations and Trial Sample Size for Treatment Resistance

Statistical calculations for clinical trials traditionally assume that if a treatment fails, it fails for mechanistic reasons - the drug itself is ineffective. However, patients may be treatment-resistant, rendering them unable to benefit from an otherwise effective treatment. This creates an identifiability problem: a null hypothesis that we fail to reject can indicate either an ineffective treatment, or an effective treatment tested in a population dominated by treatment-resistant subjects. However, the strategy to administer the drug should be different for these cases. Here we present a simple way to adjust the sample size of a randomized controlled trial to account for the anticipated level of treatment resistance to reach a certain statistical power. We show that the resistant-adjusted population size exponentially increases with the anticipated resistance prevalence, whereas power decreases almost linearly for a given population size as the resistance prevalence increases.