Confidence bands for the difference of two survival functions under the additive risk model

Abstract

In many clinical studies, a commonly encountered problem is to compare the survival probabilities of two treatments for a given patient with a certain set of covariates, and there is often a need to make adjustments for other covariates that may affect outcomes. One approach is to plot the difference between the two subject-specific predicted survival estimates with a simultaneous confidence band. Such a band will provide useful information about when these two treatments differ and which treatment has a better survival probability. In this paper, we show how to construct such a band based on the additive risk model and we use the martingale central limit theorem to derive its asymptotic distribution. The proposed method is evaluated from a simulation study and is illustrated with two real examples.

Keywords:

• simultaneous confidence band
• survival function
• additive hazards model
• Cox model
• martingales

Acknowledgements

The authors would like to thank the editor and the referees for helpful comments that led to great improvement of the paper.