A note on variance estimation in the Cox proportional hazards model

The Cox proportional hazards model is widely used in clinical trials with time-to-event outcomes to compare an experimental treatment with the standard of care. At the design stage of a trial the number of events required to achieve a desired power needs to be determined, which is frequently based on estimating the variance of the maximum partial likelihood estimate of the regression parameter with a function of the number of events. Underestimating the variance at the design stage will lead to insufficiently powered studies, and overestimating the variance will lead to unnecessarily large trials. A simple approach to estimating the variance is introduced, which is compared with two widely adopted approaches in practice. Simulation results show that the proposed approach outperforms the standard ones and gives nearly unbiased estimates of the variance.