Testing equality of survival functions of quality-adjusted lifetime

We present a method for comparing the survival functions of quality-adjusted lifetime from two treatments. This test statistic becomes the ordinary log-rank test when quality-adjusted lifetime is the same as the survival time. Simulation experiments are conducted to examine the behavior of our proposed test statistic under both null and alternative hypotheses. In addition, we apply our method to a breast cancer trial for comparing the distribution of quality-adjusted lifetime between two treatment regimes.