How to choose a time zero for patients in external control arms.

When a sponsor carries out a single-arm trial of a novel oncology compound, it may wish to assess the efficacy of the compound via comparison of overall survival to an external control arm, constructed using patients included in some retrospective registry. If efficacy of the novel compound is compared to efficacy of physician's choice of chemotherapy, patients in the retrospective registry might qualify for inclusion in the external control arm at multiple different points in time, when they receive different chemotherapy treatments. For example, a patient might qualify at the start of their second, third and fourth lines of therapy. From the start of which line of therapy should this patient's survival be compared to survival of participants in the single-arm trial? Some sponsors have elected to include patients in the external control arm from the last available line of therapy in the retrospective database. Another possibility is to randomly select a line of therapy for each external control arm patient from among those available. In this paper, we show, via probabilistic arguments and also via simulation based on real data, that both of these methods give rise to a bias in favor of the single-arm trial. We further show that this bias can be avoided by instead including external control arm patients multiple times in the external control arm, once for each time they receive qualifying treatment.