The population-wise error rate for clinical trials with overlapping populations.

We introduce a new multiple type I error criterion for clinical trials with multiple, overlapping populations. Such trials are of interest in precision medicine where the goal is to develop treatments that are targeted to specific sub-populations defined by genetic and/or clinical biomarkers. The new criterion is based on the observation that not all type I errors are relevant to all patients in the overall population. If disjoint sub-populations are considered, no multiplicity adjustment appears necessary, since a claim in one sub-population does not affect patients in the other ones. For intersecting sub-populations we suggest to control the average multiple type I error rate, i.e. the probability that a randomly selected patient will be exposed to an inefficient treatment. We call this the population-wise error rate, exemplify it by a number of examples and illustrate how to control it with an adjustment of critical boundaries or adjusted p-values. We furthermore define corresponding simultaneous confidence intervals. We finally illustrate the power gain achieved by passing from family-wise to population-wise error rate control with two simple examples and a recently suggested multiple-testing approach for umbrella trials.