Analysis of time-to-event data under a two-stage survival adaptive design in clinical trials

In recent years, the use of a two-stage seamless design in clinical trials has attracted much attention. A two-stage seamless trial design is referred to as a study design that combines two separate clinical studies that are normally conducted to achieve separate objectives, such as a phase II study for treatment selection and a phase III study for efficacy confirmation. Furthermore, it is not uncommon to consider study endpoints with different treatment durations at different stages (see, e.g., Chow and Chang, 2006; Maca et al., 2006). Chow et al. (2007) and Lu et al. (2009) considered the cases where the study endpoints are continuous variables and binary responses, respectively. In this article, our attention is placed on the case where the study endpoints are time-to-event data with different treatment durations. For testing equality, superiority, and noninferiority/equivalence of two treatments, test statistics for the analysis of the combined data collected from the two stages are developed for Weibull distributed data. In addition, formulas for sample size calculation and sample size allocation between the two stages for each of the hypotheses are derived. Corresponding results are also derived under Cox's proportional hazards model.