Power and sample size for dose-finding studies with survival endpoints under model uncertainty

Multiple comparison procedures combined with modeling techniques (MCP-Mod) (Bretz et al., 2005) is an efficient and robust statistical methodology for the model-based design and analysis of dose-finding studies with an unknown dose-response model. With this approach, multiple comparison methods are used to identify statistically significant contrasts corresponding to a set of candidate dose-response models, and the best model is then used to estimate the target dose. Power and sample size calculations for this methodology require knowledge of the covariance matrix for the estimators of the (placebo-adjusted) mean responses among the dose groups. In this article, we consider survival endpoints and derive an analytic form of the covariance matrix for the estimators of the log hazard ratios as a function of the total number of events in the study. We then use this closed-form expression of the covariance matrix to derive the power and sample size formulas. We discuss practical considerations in the application of these formulas. In addition, we provide an illustration with a motivating example on chronic obstructive pulmonary disease. Finally, we demonstrate through simulation studies that the proposed formulas are accurate enough for practical use.