Evaluation of Sample Size and Power for Multi-arm Survival Trials Allowing for Non-uniform Accrual, Non-proportional Hazards, Loss to Follow-up and Cross-over

We present a general framework for sample size calculation in survival studies based on comparing two or more survival distributions using any one of a class of tests including the logrank test. Incorporated within this framework are the possible presence of non-uniform staggered patient entry, non-proportional hazards, loss to follow-up and treatment changes including cross-over between treatment arms. The framework is very general in nature and is based on using piecewise exponential distributions to model the survival distributions. We illustrate the use of the approach and explore its validity using simulation studies. These studies have shown that not adjusting for loss to follow-up, non-proportional hazards or cross-over can lead to significant alterations in power or equivalently, a marked effect on sample size. The approach has been implemented in the freely available program ART (for Stata). Our investigations suggest that ART is the first software to allow incorporation of all these elements. Further extensions to the methodology such as non-local alternatives for the logrank test are also considered.