A consistent NPMLE of the joint distribution function with competing risks data under the dependent masking and right-censoring model

Abstract

Dinse (Biometrics, 38:417-431, 1982) provides a special type of right-censored and masked competing risks data and proposes a non-parametric maximum likelihood estimator (NPMLE) and a pseudo MLE of the joint distribution function [Formula: see text] with such data. However, their asymptotic properties have not been studied so far. Under the extention of either the conditional masking probability (CMP) model or the random partition masking (RPM) model (Yu and Li, J Nonparametr Stat 24:753-764, 2012), we show that (1) Dinse's estimators are consistent if [Formula: see text] takes on finitely many values and each point in the support set of [Formula: see text] can be observed; (2) if the failure time is continuous, the NPMLE is not uniquely determined, and the standard approach (which puts weights only on one element in each observed set) leads to an inconsistent NPMLE; (3) in general, Dinse's estimators are not consistent even under the discrete assumption; (4) we construct a consistent NPMLE. The consistency is given under a new model called dependent masking and right-censoring model. The CMP model and the RPM model are indeed special cases of the new model. We compare our estimator to Dinse's estimators through simulation and real data. Simulation study indicates that the consistent NPMLE is a good approximation to the underlying distribution for moderate sample sizes.

LOESS smoothed density estimates for multivariate survival data subject to censoring and masking

“…Thus, for the sake of model simplification, an independence assumption has traditionally been invoked between the various competing risks. Some recent research has focussed on developing dependent competing risks models (see Escarela & Carriere, 2003; Craiu & Reiser, 2006; Wang et al , 2012; Li & Yu, 2014). The complication of mutually dependent failure modes will not be considered in the ensuing theory.…”

“…Wang et al (2012) proposed a new model for the NPMLE of intervalcensored and masked competing risks data, the random partition masking model, which does not rely on the assumption that masked failure causes are independent of failure time. Yu & Li (2012, 2014 examined the NPMLE proposed by Dinse (1982); they concluded that the NPMLE was inconsistent and not unique and they introduced a consistent NPMLE of the joint distribution function with right-censored and masked competing risks data under another new model (the dependent masking and right-censoring model).…”