Integrated log-rank test

Abstract

The log-rank test can be viewed as nonparametric from the standpoint of a series of tables, as semi-parametric from the standpoint of the proportional hazards model and as parametric from the viewpoint of a constructed empirical process. Under non-proportional hazards the optimality afforded by this test is lost. Some of this lost power can be recovered by more carefully structured tests. We focus on the integrated log-rank test. Under certain alternatives, we show this test to be unbiased, and consistent. It will also be seen to correlate well with the uniformly most powerful test, a test that, in practice, is not available. The integrated log-rank test is a useful addition to the clinical researcher's toolbox. For the purposes of illustration we revisit 3 recently published large scale clinical trials.