Modern medical treatments have substantially improved survival rates for many chronic diseases and have generated considerable interest in developing cure fraction models for survival data with a non-ignorable cured proportion. Statistical analysis of such data may be further complicated by competing risks that involve multiple types of endpoints. Regression analysis of competing risks is typically undertaken via a proportional hazards model adapted on cause-specific hazard or subdistribution hazard. In this article, we propose an alternative approach that treats competing events as distinct outcomes in a mixture. We consider semiparametric accelerated failure time models for the cause-conditional survival function that are combined through a multinomial logistic model within the cure-mixture modeling framework. The cure-mixture approach to competing risks provides a means to determine the overall effect of a treatment and insights into how this treatment modifies the components of the mixture in the presence of a cure fraction. The regression and nonparametric parameters are estimated by a nonparametric kernel-based maximum likelihood estimation method. Variance estimation is achieved through resampling methods for the kernel-smoothed likelihood function. Simulation studies show that the procedures work well in practical settings. Application to a sarcoma study demonstrates the use of the proposed method for competing risk data with a cure fraction.
Bibliographical noteFunding Information:
Dr Choi was supported in part by the Korea University Grant (KU-FRG, K1614571), and Dr Huang was supported by National Science Foundation grant (DMS-1612965).
Copyright © 2017 John Wiley & Sons, Ltd.
- competing risks
- cure fraction
- kernel smoothing
- mixture model
- nonparametric likelihood
ASJC Scopus subject areas
- Statistics and Probability