Sample size calculation for the augmented logrank test in randomized clinical trials

In randomized clinical trials, incorporating baseline covariates can improve the power in hypothesis testing for treatment effects. For survival endpoints, the Cox proportional hazards model with baseline covariates as explanatory variables can improve the standard logrank test in power. Although this has long been recognized, this adjustment is not commonly used as the primary analysis and instead the logrank test followed by the estimation of the hazard ratio between treatment groups is often used. By projecting the score function for the Cox proportional hazards model onto a space of covariates, the logrank test can be more powerful. We derive a power formula for this augmented logrank test under the same setting as the widely used power formula for the logrank test and propose a simple strategy for sizing randomized clinical trials utilizing historical data of the control treatment. Through numerical studies, the proposed procedure was found to have the potential to reduce the sample size substantially as compared to the standard logrank test. A concern to utilize historical data is that those might not reflect well the data structure of the study to design and then the sample size calculated might not be accurate. Since our power formula is applicable to datasets pooled across the treatment arms, the validity of the power calculation at the design stage can be checked in blind reviews.