Power and sample size for survival analysis under the Weibull distribution when the whole lifespan is of interest

Accessible and readily utilized software, tables and approximation formulae have been developed to estimate power and sample size for studies of time to event (survival times) when the survival times are assumed to be exponential. These methods can markedly misestimate power when the distribution is Weibull and not exponential. The Weibull distribution with increasing hazard is common in aging research, especially when the whole life span of the subjects is of interest. This note considers an extension of power and sample size calculations, previously developed under the exponential distributional assumption, to the more general case of the Weibull distribution for a prospective comparative follow-up study. The hypotheses are defined in terms of the ratio of the median survival times between two groups. It is shown that the power and sample sizes are heavily dependent on the shape parameter of the Weibull distribution. Using the extensions developed, investigators can use existing software and tables to calculate power and sample size under the assumption of a Weibull distribution.