Sample size calculations for nonproportional hazards utilizing the concept of Weighted Relative Time

Music City Center 

Sample size calculations (SSC) for fixed two-arm randomized control trials (RCTs) with a survival endpoint have traditionally relied on the proportional hazards (PH) assumption or on the assumption of exponentially distributed survival times. When the PH assumption is not met, popular choices of SSC deploy the piecewise linear survival (Lakatos) approach or newer methods based on accelerated failure time (AFT) models that allow NPH. Recent advances in literature have shown how the concept of Relative Time (RT) using two different Weibull distributions can be used to handle the non-AFT and NPH scenarios. The main limitation of this method is that SSC is based on survival differences in the two arms at prespecified time points of interest. Here, we extend this method to conduct SSC comparing full survival curves using the concept of Weighted Relative Time (WRT). We consider two scenarios – early treatment effect, and delayed treatment effect and compare results to the Lakatos method and the logrank test with Fleming-Harrington weights. Simulations are conducted to assess the operation characteristics of the proposed method, and a real-life example is discussed.

nonproportional hazards

randomized control trial

sample size

survival endpoint

relative time

weighted approach 

Biometrics Section