The generalized MLE with the interval centered and masked competing risks data

We consider the estimation problem of the joint cumulative distribution function of the failure time T and the failure cause C of a J-component series system. The study is motivated by a cancer research data (from the Memorial Sloan-Kettering Cancer Center) with interval-censored T and masked C but without second stage data. This type of data is called the interval-censored and masked competing risks data. We propose to study the generalized maximum likelihood estimator (GMLE) under the new random partition masking (RPM) model, which does not rely on the commonly used symmetry assumption (see Flehinger et al. (1996)). The RPM model is more realistic and general than the existing models, and is easy to implement in simulation studies. We discuss the algorithms for computing the GMLE and study its asymptotic properties. Our simulation and data analysis indicates that the GMLE is feasible for moderate sample sizes. Strong consistency in the L 1(mu)-topology is established for some finite measure mu derived from the characteristic of the censoring and masking mechanism. Under additional assumptions this consistency result is shown to lead to strong consistency for the topologies of weak convergence, point-wise convergence and uniform convergence. Furthermore, its asymptotical normality is established under the discrete inspection times.