title: Maximum likelihood estimation of semiparametric mixture component models for competing risks data.
abstract: In the analysis of competing risks data, the cumulative incidence function is a useful quantity to characterize the crude risk of failure from a specific event type. In this article, we consider an efficient semiparametric analysis of mixture component models on cumulative incidence functions. Under the proposed mixture model, latency survival regressions given the event type are performed through a class of semiparametric models that encompasses the proportional hazards model and the proportional odds model, allowing for time-dependent covariates. The marginal proportions of the occurrences of cause-specific events are assessed by a multinomial logistic model. Our mixture modeling approach is advantageous in that it makes a joint estimation of model parameters associated with all competing risks under consideration, satisfying the constraint that the cumulative probability of failing from any cause adds up to one given any covariates. We develop a novel maximum likelihood scheme based on semiparametric regression analysis that facilitates efficient and reliable estimation. Statistical inferences can be conveniently made from the inverse of the observed information matrix. We establish the consistency and asymptotic normality of the proposed estimators. We validate small sample properties with simulations and demonstrate the methodology with a data set from a study of follicular lymphoma.
authors.affiliation: Division of Clinical and Translational Sciences, Department of Internal Medicine, The University of Texas, Health Science Center at Houston, Houston, Texas 77030, U.S.A.
authors.forename: Sangbum
authors.initials: S
authors.lastname: Choi
authors.affiliation: Department of Biostatistics, The University of Texas, MD Anderson Cancer Center, 1515 Holcombe Boulevard, Unit 1411, Houston, Texas 77030, U.S.A.
authors.forename: Xuelin
authors.initials: X
authors.lastname: Huang
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D015994:Incidence; D016013:Likelihood Functions; D008223:Lymphoma / Q000401:mortality* / Q000628:therapy*; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000379:methods*; D011379:Prognosis; D012044:Regression Analysis; D015203:Reproducibility of Results; D018570:Risk Assessment / Q000379:methods; D012680:Sensitivity and Specificity; D015996:Survival Rate
keywords: Cumulative incidence; Cure model; Joint model; Martingale; Nonparametric likelihood; Transformation model