A primer of quasi-exact tests for randomized clinical trials with binary endpoints

Abstract

For planned clinical trials with a binary endpoint, standard statistical tests can be very inaccurate in their error control, especially when the trial is unbalanced. Specifically, type 1 error can greatly exceed a nominal target like 5%, even for quite large sample sizes, and power can be much less than a nominal target such as 80%. Confidence limits may not have the correct coverage. The purpose of this article is firstly to give clinical trialists an appreciation of this fact. We then describe well-studied alternatives to the standard methods, which are simple in conception but can be quite challenging to implement. These contemporary methods in frequentist statistical theory, known as quasi-exact methods, have been neglected in medical applications. We provide an R-package that can be used to provide accurate inference results based on our recommended quasi-exact test. The package will also calculate the exact size and power of the test, once the control and treatment samples sizes are finalised. All proposals are illustrated with a real-world example on the treatment of prostate cancer. We would recommend practitioners to use quasi-exact methods in the analysis of randomized clinical trials.