| Abstract: | Abstract In this article, we extend the concept of univariate frailty to a bivariate case to quantify and visualize the loss of efficiency of the log-rank test when a dependence structure between failure and censoring times is being ignored. We assume that an unobservable frailty influences the risk of failure and the other affects the risk of censoring, and those two frailties are correlated. Under the model being compared as a benchmark, the dependence structure between failure and censoring times is assumed to be completely observed. Under the model where the log-rank test is constructed without considering the dependency between failure and censoring times, it is assumed that the unobservable dependence structure has been absorbed into the baseline distributions. We note in our particular example that the loss of efficiency is minimal under the proportional hazards model even when the correlation between potential failure and censoring times is strong unless the dependence censorship induces a severe nonproportionality. |
