A testing procedure for survival data with few responders

In the course of designing a clinical trial, investigators are often faced with the possibility that only a fraction of the patients will benefit from the experimental treatment. A proper clinical trial design requires prospective specification of the testing procedures to be used in the analysis. In the absence of reliable prognostic factors capable of identifying the appropriate subset of patients, there is a need for a test procedure that will be sensitive to a range of possible fractions of responders. Focusing on survival data, we propose guidelines for selecting a proper test procedure based on the anticipated proportion of responding patients. These guidelines suggest that the logrank test should be used when the fraction of responders is expected to be greater than 0.5, otherwise procedures based on weighted linear rank tests are preferable. Overall this approach provides good power properties when the treatment affects only a small proportion of patients while protecting against Substantial loss of power when all patients are affected. Use of the procedure is illustrated with data from two published randomized studies.