Title: Revisiting Non-Parametric Maximum Likelihood Estimation of Current Status Data with Competing Risks

Author(s): Anup Dewanji and Tamalika Koley
Issue: Volume 81 Series B Part 1 Year 2019
Pages: 39 -- 59
Re-parametrization is often done to make a constrained optimization problem an unconstrained one. This paper focuses on the non-parametric maximum likelihood estimation of the sub-distribution functions for current status data with competing risks. Our main aim is to propose a method using re-parametrization, which is simpler and easier to handle with compared to the constrained maximization methods discussed in Jewell and Kalbfleisch (Biostatistics. 5, 291–306, 2004) and Maathuis (2006), when both the monitoring times and the number of individuals observed at these times are fixed. Then the Expectation-Maximization (EM) algorithm is used for estimating the unknown parameters. We have also established some asymptotic results of these maximum likelihood estimators. Finite sample properties of these estimators are investigated through an extensive simulation study. Some generalizations have been discussed.
Primary 62N01, 62N02; Secondary 62P10
Keywords and phrases: Monitoring time, Isotonic constraints, Re-parametrization, Cover percentage, Observed Mahalanobis distance, Interval hazards, EM algorithm, Complete data likelihood