Fractional logistic regression for censored survival data

Abstract

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 probabilities and powers for the adjusted two-sample median test are reasonable. The method is illustrated with a breast cancer data set.