On Algorithms for the Nonparametric Maximum Likelihood Estimator of the Failure Function With Censored Data

In this article, we study algorithms for computing the nonparametric maximum likelihood estimator (NPMLE) of the failure function with two types of censored data: doubly censored data and (type 2) interval-censored data. We consider two projection methods, namely the iterative convex minorant algorithm (ICM) and a generalization of the Rosen algorithm (GR) and compare these methods to the well-known EM algorithm. The comparison conducted via simulation studies shows that the hybrid algorithms that alternately use the EM and GR for doubly censored data or, alternately, use the EM and ICM for (type 2) interval-censored data appear to be much more efficient than the EM, especially in large sample situation.