Non-parametric estimation of relative r...

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.