Sample Size Calculation Based on the Semiparametric Analysis of Short-term and Long-term Hazard Ratios
We derive sample size formulae for survival data with non-proportional hazard functions under both fixed and contiguous alternatives. Sample size determination has been widely discussed in literature for studies with failure-time endpoints. Many researchers have developed methods with the assumption of proportional hazards under contiguous alternatives. Without covariate adjustment, the logrank test statistic is often used for the sample size and power calculation. With covariate adjustment, the approaches are often based on the score test statistic for the Cox proportional hazards model. Such methods, however, are inappropriate when the proportional hazards assumption is violated. We develop methods to calculate the sample size based on the semiparametric analysis of short-term and long-term hazard ratios. The methods are built on a semiparametric model by Yang and Prentice (2005). The model accommodates a wide range of patterns of hazard ratios, and includes the Cox proportional hazards model and the proportional odds model as its special cases. Therefore, the proposed methods can be used for survival data with proportional or non-proportional hazard functions. In particular, the sample size formula by Schoenfeld (1983) and Hsieh and Lavori (2000) can be obtained as a special case of our methods under contiguous alternatives.
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