Analysis of dependent interval-censored time-to-event data

Background. Left-, right-, and interval-censored time-to-event data arise in a variety of settings. In many cases, the censoring is not independent of the event. For such dependent censored data, the current regression techniques such as the Cox (1972) proportional hazards model for right-censored data or Finkelstein's (1986) proportional hazards model for interval-censored data are inapplicable.;Conditional modeling. We propose a new likelihood-based dependent interval-censored estimator/estimation (DICE) based on a class of innovative conditional hazard models for time-to-event data with a marker for those observation times (visits) that might be correlated with the event time. This generalizes the current analysis methods assuming independent censoring, such as Turnbull's (1976) non-parametric estimator for the survival function using interval-censored data. The proposed model for interval-censored data is conditional on the marker history and accounts for both regularly scheduled visits and visits whose timing is motivated by patient status; thus allowing for dependent censoring.;Marginal inference. Right-censored data can be imputed from the conditional hazard model. Marginal inferences about time-to-event can then be derived using standard right-censored survival data methods and multiple imputation based on the conditional hazard model results. Here we present the approach with non-parametric marginal models. The relationship between this dependent interval-censoring model and coarsening at random (CAR) is examined. A test for dependent interval-censoring is given. Asymptotic results are investigated.;Results. Simulation results reveal that the DICE method has high power for detecting dependent censoring. The DICE estimates are less biased than other estimators that ignore the dependence of censoring, while not sacrificing efficiency. The DICE approach is illustrated through an application to a study of nursing home residents who were followed for two years. Results provide evidence that the interval-censoring is indeed dependent on the outcome. Current analysis methods that assume independent censoring results in coarser and biased estimates for the survival function. The DICE approach is superior compared to these other methods in this case.