The lay abstract featured today (for Exact test and exact confidence interval for the Cox model by Yongwu Shao, Zhishen Ye, Zhiwei Zhang) is from Statistics in Medicine with the full article now available to read here.

Abstract

The Cox proportional hazards model is commonly used to analyze time-to-event data in clinical trials. Standard inference procedures for the Cox model are based on asymptotic approximations and may perform poorly when there are few events in one or both treatment groups, as may be the case when the event of interest is rare or when the experimental treatment is highly efficacious.  For example, the Wald test does not work when the treatment has zero events, and it may give a smaller one-sided p-value when events are added to the active arm, where events are considered harmful.  For the score test and the likelihood ratio test, the type I error rates can be quite inflated when the number of events is small.  Type I error control is important in regulatory settings as an inflated type I error rate means that there is a more than expected chance that an ineffective drug meets the efficacy boundary and gets approved.

In this article, we propose an exact test of equivalence and efficacy under a proportional hazard model with treatment effect as the only fixed effect, together with an exact confidence interval that is obtained by inverting the exact test.  The proposed test always strictly controls the type I error, is computationally efficient, and is easy to implement.  The procedures are evaluated in simulation studies and illustrated using real data from an HIV prevention trial.  A companion R package ‘ExactTest’ is available for download on CRAN.  Just like the Fisher’s exact test for binary outcomes, the proposed methods can be a useful alternative for time-to-event data when type I error control is important.