Nonparametric estimation of the cumulative incidence function for doubly-truncated and interval-censored competing risks data

Interval sampling is widely used for collection of disease registry data, which typically report incident cases during a certain time period. Such sampling scheme induces doubly truncated data if the failure time can be observed exactly and doubly truncated and interval censored (DTIC) data if the failure time is known only to lie within an interval. In this article, we consider nonparametric estimation of the cumulative incidence functions (CIF) using doubly-truncated and interval-censored competing risks (DTIC-C) data obtained from interval sampling scheme. Using the approach of Shen (Stat Methods Med Res 31:1157–1170, 2022b), we first obtain the nonparametric maximum likelihood estimator (NPMLE) of the distribution function of failure time ignoring failure types. Using the NPMLE, we proposed nonparametric estimators of the CIF with DTIC-C data and establish consistency of the proposed estimators. Simulation studies show that the proposed estimator performs well for finite sample size.