6533b7dafe1ef96bd126ee03

RESEARCH PRODUCT

A Log-Rank Test for Equivalence of Two Survivor Functions

Stefan Wellek

subject

Statistics and ProbabilityBiometryGaussianGeneral Biochemistry Genetics and Molecular BiologyCombinatoricssymbols.namesakeNeoplasmsLinear regressionStatisticsChi-square testHumansComputer SimulationCerebellar NeoplasmsChildEquivalence (measure theory)Proportional Hazards ModelsStatistical hypothesis testingMathematicsClinical Trials as TopicGeneral Immunology and MicrobiologyApplied MathematicsEstimatorGeneral MedicineSurvival AnalysisLog-rank testLinear ModelssymbolsGeneral Agricultural and Biological SciencesMedulloblastomaQuantile

description

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 delta0. Under the assumption of proportional hazards, this hypothesis is shown to be (logically) equivalent to the statement [beta[log(1 + epsilon), where beta denotes the regression coefficient associated with the treatment group indicator, and epsilon is a simple strictly increasing function of delta. The testing procedure proposed consists of carrying out in terms of beta (i.e., the standard Cox likelihood estimator of beta) the uniformly most powerful level alpha 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 alpha th quantile of a noncentral chi-square distribution with a single degree of freedom.

yearjournalcountryeditionlanguage
1993-09-01Biometrics
https://doi.org/10.2307/2532208