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