In the analysis of time-to-event data, e.g. from cancer studies, the group effect
\nof main interest such as treatment effect of a chemo-therapy often needs to be
\nadjusted by confounding factors (possibly continuous) such as hormonal receptor
\nstatus, age at diagnosis, and pathological tumor size, when the study outcome
\nis affected by their imbalanced distributions across the comparison groups. The
\nmedian, or quantile, is a popular summary measure for censored survival data
\ndue to its robustness. In this paper, \ffirst the logistic regression is extended to
\nfractional responses transformed from censored survival data, which can directly
\npredict conditional survival probabilities beyond a \ffixed time point given covariates. As a special case, we construct a median test for censored survival data
\nthat can be used to assess a group effect adjusting for the potentially multiple
\nconfounding factors. A quasi-likelihood-based inference procedure is adopted to
\nconstruct the test statistic. Simulation studies show empirical type I error prob-
\nabilities and powers for the adjusted two-sample median test are reasonable. The
\nmethod is illustrated with a breast cancer dataset.<\/p>\n