Sample size considerations for historical control studies with survival outcomes

Historical control trials (HCTs) are frequently conducted to compare an experimental treatment with a control treatment from a previous study, when they are applicable and favored over a randomized clinical trial (RCT) due to feasibility, ethics and cost concerns. Makuch and Simon developed a sample size formula for historical control (HC) studies with binary outcomes, assuming that the observed response rate in the HC group is the true response rate. This method was extended by Dixon and Simon to specify sample size for HC studies comparing survival outcomes. For HC studies with binary and continuous outcomes, many researchers have shown that the popular Makuch and Simon method does not preserve the nominal power and type I error, and suggested alternative approaches. For HC studies with survival outcomes, we reveal through simulation that the conditional power and type I error over all the random realizations of the HC data have highly skewed distributions. Therefore, the sampling variability of the HC data needs to be appropriately accounted for in determining sample size. A flexible sample size formula that controls arbitrary percentiles, instead of means, of the conditional power and type I error, is derived. Although an explicit sample size formula with survival outcomes is not available, the computation is straightforward. Simulations demonstrate that the proposed method preserves the operational characteristics in a more realistic scenario where the true hazard rate of the HC group is unknown. A real data application of an advanced non-small cell lung cancer (NSCLC) clinical trial is presented to illustrate sample size considerations for HC studies in comparison of survival outcomes.