Maximum likelihood estimation of semiparametric mixture component models for competing risks data

Sangbum Choi, Xuelin Huang

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)588-598
Number of pages11
Issue number3
Publication statusPublished - 2014 Sept 1
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014, The International Biometric Society.


  • Cumulative incidence
  • Cure model
  • Joint model
  • Martingale
  • Nonparametric likelihood
  • Transformation model

ASJC Scopus subject areas

  • Statistics and Probability
  • General Biochemistry,Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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