Fitting a Semi-Parametric Mixture Model for Competing Risks in Survival Data

Analysis of a semiparametric mixture model for competing risks

“…Specifically, we provide a rigorous large-sample treatment of the resulting estimators. By following the approach and techniques developed by Murphy (1994Murphy ( , 1995 and Parner (1998) for the frailty model (and thereafter extended to various other settings by Fang et al (2005), Dupuy et al (2006), Kosorok and Song (2007), Lu (2008), among others), we prove the consistency and asymptotic normality of the estimators in Escarela and Bowater (2008). We also show that the proposed estimator for the regression parameter of interest, which is the regression parameter in the conditional distribution of the failure time given the failure cause and covariates, is semiparametric efficient.…”

“…In the present paper, we focus-in a detailed fashion-on the properties of the maximum likelihood-based estimators in the semiparametric generalization of Larson and Dinse's model developed by Escarela and Bowater (2008). Specifically, we provide a rigorous large-sample treatment of the resulting estimators.…”

“…, J } denote the cause of failure. For example, in a recent analysis of a prostate cancer dataset (Escarela and Bowater 2008), the failure time T 0 corresponds either to the time to death from prostate cancer, or to death from cardiovascular disease, or to death from other causes, whichever occurs first. The goal of the study was to compare the levels of a drug used to treat prostate cancer, with respect to the survival of the patients.…”

“…To the best of our knowledge, only a few papers have contributed to the large-sample properties of the estimators proposed in these contributions. Dupuy and Escarela (2007) outline a consistency proof for the maximum likelihood-based estimators proposed by Escarela and Bowater (2008). Lu and Peng (2008) construct martingale-based estimating equations for the parameters of a semiparametric version of Larson and Dinse's model, and establish the consistency and asymptotic normality of the resulting estimators.…”

“…For example, Ng and McLachlan (2003) and Escarela and Bowater (2008) consider a semiparametric mixture model with covariates, where the marginal distribution of H conditional on the covariates has a multinomial logistic form, and the conditional distribution of T 0 , given the covariates and the failure cause is specified through a proportional hazards model (Cox 1972). Ng and McLachlan (2003) and Escarela and Bowater (2008) propose and implement EM-type algorithms in this class of models. Naskar et al (2005) consider a similar model in the case of clustered failure time data, and develop a Monte Carlo EM algorithm.…”