Statistical Analysis of Doubly Interval-Censored Failure Time Data

Doubly interval-censored failure time data refer to the failure time data where the survival time of interest is defined as the elapsed time between two related events. Furthermore, observations on the occurrences of both events could be rightor interval-censored. One field in which such data often occur is epidemiological studies where the two events may represent infection and subsequent onset of certain disease, respectively. If the occurrence of the first event can be exactly observed, we then have usual rightor interval-censored failure time data (Kalbfleisch and Prentice, 1980; Sun, 1998). This article reviews statistical methods that have been proposed in the literature for analyzing doubly interval-censored data and discusses their merits. In particular, we will consider nonparametric estimation of a distribution function and regression analysis of the data. Directions for future research are also discussed.