A Log-Rank Test for Equivalence of Two Survivor Functions

Journal/Book: Biometrics. 1993; 49: 877-881.

Abstract: We consider a hypothesis testing problem in which the alternative states that the vertical distance between the underlying survivor functions nowhere exceeds some prespecified bound d > 0. Under the assumption of proportional hazards, this hypothesis is shown to be (logically) equivalent to the statement |ß| < log( l + ?), where ß denotes the regression coefficient associated with the treatment group indicator, and c is a simple strictly increasing function of d. The testing procedure proposed consists of carrying out in terms of ß (i.e., the standard Cox likelihood estimator of ß) the uniformly most powerful level a test for a suitable interval hypothesis about the mean of a Gaussian distribution with fixed variance. The computation of the critical constant of this test is very easy in practice since it admits a representation as the root of the a th quantile of a noncentral chi-square distribution with a single degree of freedom.

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