An independence test for doubly censored failure time data

The analysis of doubly censored failure time data has recently attracted a great deal of attention and for this, a number of methods have been proposed (De Gruttola and Lagakos, 1989; Kim et al., 1993; Pan, 2001; Sun, 2004). To simplify the analysis, most of these methods make an independence assumption: the distribution of the survival time of interest is independent of the occurrence of the initial event that defines the survival time. Although it is well-known that the assumption may not be true, there does not seem to be any existing research discussing the checking of the assumption. In this article, a Wald test is developed for testing this assumption and the method is applied to an AIDS cohort study.