  We consider a Kendall's tau measure between a binary group indicator and the
continuous variable under investigation to develop a thorough two-sample
comparison procedure. The measure serves as a useful alternative to the hazard
ratio whose applicability depends on the proportional hazards assumption. For
right censored data, we propose a weighted log-rank statistic with weights
adapted to the censoring distributions and develop theoretical properties of
the derived estimators. In absence of censoring, the proposed estimator reduces
to the WMW statistic. The proposed methodology is applied to analyze several
data examples.
