A Simulation Based Evaluation of the Asymptotic Power Formulae for Cox Models in Small Sample Cases

Cox proportional hazards (PH) models are commonly used in medical research to investigate the associations between covariates and time to event outcomes. It is frequently noted that with less than ten events per covariate, these models produce spurious results, and therefore, should not be used. Statistical literature contains asymptotic power formulae for the Cox model which can be used to determine the number of events needed to detect an association. Here we investigate via simulations the performance of these formulae in small sample settings for Cox models with 1- or 2-covariates. Our simulations indicate that, when the number of events is small, the power estimate based on the asymptotic formulae is often inflated. The discrepancy between the asymptotic and empirical power is larger for the dichotomous covariate especially in cases where allocation of sample size to its levels is unequal. When more than one covariate is included in the same model, the discrepancy between the asymptotic power and the empirical power is even larger, especially when a high positive correlation exists between the two covariates.