Selection designs for pilot studies based on survival.

In cancer clinical trials new regimens are typically tested for antitumor activities in patients with advanced disease. The promising ones are then compared to the standard treatment in a randomized study, sometimes performed on patients with earlier-stage disease. When there are multiple promising regimens, it may not be possible to compare all of them to the control group because of the prohibitive sample size and study length requirements. We propose a design that uses the Cox regression model to select a best treatment based on survival before the randomized comparison. Sample sizes for an asymptotically correct selection probability of .90 are presented for Weibull survival distributions with parameters in a range we consider to be of practical interest. Simulations verify that the asymptotic approximations to the correct selection probabilities are quite satisfactory. Simulations also indicate that the procedure is reasonably robust to the proportional hazards assumption. In contrast to the two-stage screening design recommended by Schaid, Wieand, and Therneau (1990, Biometrika 77, 507-513), our design has the advantage of fitting naturally to a progression of cancer trials where the selection and comparison phases are carried out on different populations of patients. When the population of interest stays the same, our design can be more conservative on the average but offers the opportunity to base the comparative trial on the experience gained during the selection phase.