Time-dependent cross ratio estimation for bivariate failure times

In the analysis of bivariate correlated failure time data, it is important to measure the strength of association among the correlated failure times. One commonly used measure is the cross ratio. Motivated by Cox's partial likelihood idea, we propose a novel parametric cross ratio estimator that is a flexible continuous function of both components of the bivariate survival times. We show that the proposed estimator is consistent and asymptotically normal. Its finite sample performance is examined using simulation studies, and it is applied to the Australian twin data.