Testing for dependence between failure time and visit compliance with interval-censored data

Interval-censored failure-time data arise when subjects miss prescheduled visits at which the failure is to be assessed. The resulting intervals in which the failure is known to have occurred are overlapping. Most approaches to the analysis of these data assume that the visit-compliance process is ignorable with respect to likelihood analysis of the failure-time distribution. While this assumption offers considerable simplification, it is not always plausible. Here we test for dependence between the failure- and visit-compliance processes, applicable to studies in which data collection continues after the occurrence of the failure. We do not make any of the assumptions made by previous authors about the joint distribution of the visit-compliance process, a covariate process, and the failure time. Instead, we consider conditional models of the true failure history given the current visit compliance at each visit time, allowing for correlation across visit times. Because failure status is not known at some visit times due to missed visits, only models of the observed failure history given current visit compliance are estimable. We describe how the parameters from these models can be used to test for a negative association and how bounds on unestimable parameters provided by the observed data are needed additionally to infer a positive association. We illustrate the method with data from an AIDS study and we investigate the power of the test through a simulation study.