Nonparametric adaptive enrichment designs using categorical surrogate data

Adaptive survival trials are particularly important for enrichment designs in oncology and other life-threatening diseases. Current statistical methodology for adaptive survival trials provide type I error rate control only under restrictions. For instance, if we use stage-wise P values based on increments of the log-rank test, then the information used for the interim decisions need to be restricted to the primary survival endpoint. However, it is often desirable to base interim decisions also on correlated short-term endpoints like tumor response. Alternative statistical approaches based on a patient-wise splitting of the data require unnatural restrictions on the follow-up times and do not permit to efficiently account for an early rejection of the primary null hypothesis. We therefore suggest new approaches that enable us to use discrete surrogate endpoints (like tumor response status) and also to incorporate interim rejection boundaries. The new approaches are based on weighted Kaplan-Meier estimates and thereby have additional advantages. They permit us to account for nonproportional hazards and are robust against informative censoring based on the surrogate endpoint. We will show that nonproportionality is an intrinsic and relevant issue in enrichment designs. Moreover, informative censoring based on the surrogate endpoint is likely because of withdrawals and treatment switches after insufficient treatment response. It is shown and illustrated how nonparametric tests based on weighted Kaplan-Meier estimates can be used in closed combination tests for adaptive enrichment designs, such that type I error rate control is achieved and justified asymptotically.