title: Non-parametric estimation of relative risk in survival and associated tests.
abstract: We extend the Tarone and Ware scheme of weighted log-rank tests to cover the associated weighted Mantel-Haenszel estimators of relative risk. Weighting functions previously employed are critically reviewed. The notion of an average hazard ratio is defined and its connection to the effect size measure P(Y > X) is emphasized. The connection makes estimation of P(Y > X) possible also under censoring. Two members of the extended Tarone-Ware scheme accomplish the estimation of intuitively interpretable average hazard ratios, also under censoring and time-varying relative risk which is achieved by an inverse probability of censoring weighting. The empirical properties of the members of the extended Tarone-Ware scheme are demonstrated by a Monte Carlo study. The differential role of the weighting functions considered is illustrated by a comparative analysis of four real data sets.
authors.affiliation: Section for Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Vienna, Austria.
authors.forename: Samo
authors.initials: S
authors.lastname: Wakounig
authors.affiliation: Section for Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Vienna, Austria.
authors.forename: Georg
authors.initials: G
authors.lastname: Heinze
authors.affiliation: Section for Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Vienna, Austria. michael.schemper@meduniwien.ac.at.
authors.forename: Michael
authors.initials: M
authors.lastname: Schemper
mesh_terms: D006801:Humans; D015233:Models, Statistical; D016016:Proportional Hazards Models; D012306:Risk; D013223:Statistics as Topic / Q000379:methods*; D016019:Survival Analysis