Asymptic Properties Of Parametric Model's Mle For Competing Risks With Current Status Data

The analysis of competing risks data goes to the heart of modern preoccupations in survival analysis, touching as it does on many of the major areas of importance in the subject. The classification of death or failure by " type " or " cause " is a natural extension of (single-cause) survival analysis, once we consider alternative or " competing " causes of death or failure.The effort expended in fitting and interpreting competing risks models of some sort, evident from a glance at the current literature, recommends them as a worthwhile object of study. See, for example, Larson and Dinse (1985), David and Moeschberger (1978), Kalbfleisch and Prentice (1980), Gaynor et al. (1993), Escarela, Francis and Soothill (2000), Tai, Machin, White and Gebski (2001), and their references.While there have been many investigations, often from the point of view of counting process theory (e.g., Andersen, Borgan, Gill and Keiding (1993), Fleming and Harrington (1991), Kalbfleisch and Prentice (1980)), of properties of various formulations of competing risks models, a comprehensive large-sample analysis of certain interesting aspects has been given so far. A class of " mixture models ", used for example in a paper by Larson and Dinse (1985) (see also Elandt-Johnson and Johnson (1980, p.288), which plays a prominent role in the analysis of competing risks and directly addresses the data-analytic questions of interest. To fill this need we provide a rigorous analysis of the parametric mixture models and derive useful large-sample properties of maximum likelihood estimators. Some of the parameters of interest in the model, namely the mixing probabilities, are constrained to a J-dimensional simplex, and one of the interesting hypotheses requires those parameters to lie on the face of the simplex.Under right censor model, Mailer and Xian Zhou provide a rigorous analysis of the parametric mixture models and derive useful large-sample properties of maximum likelihood estimators and test statistics, which cover both interior and boundary cases.This study proposes a method of computing the maximum likelihood estimator (MLE) of parameters under the non-negative restriction. A similar method is also proposed for the case where the parameters are restricted by a simple order.Under an i.i.d. current status data model,when the parameters are in the interior of the parameter space, we show that the mixture model approach produces strong consistent estimates which are asymptotically normally distributed. Firstly,we survey the identifiability od the model,then provide the large-sampleanalysis.