Models for interval censoring and simulation-based inference for lifetime distributions

Abstract

Interval-censored lifetime data arise when individuals in a study are inspected intermittently so that a lifetime is observed to lie between two successive times. In settings where only these two times are available, methods exist for nonparametric or parametric estimation of lifetime distributions. However, there has been virtually no discussion of how inspection processes may be estimated or identified. Such estimates are needed if one is to generate interval-censored data by simulation. This paper identifies which aspects of an independent inspection process are estimable from interval-censored data, and shows how to obtain nonparametric estimates. The results allow interval-censored data from any specified distribution to be generated, and give new simulation procedures for estimation or testing. A new omnibus goodness-of-fit test is introduced.