Choi Sangbum, Zhu Liang, Huang Xuelin
Department of Statistics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, South Korea.
Department of Internal Medicine, The University of Texas Health Science Center at Houston, Houston, 77230, TX, U.S.A.
Stat Med. 2018 Jan 15;37(1):48-59. doi: 10.1002/sim.7508. Epub 2017 Oct 6.
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.
现代医学治疗方法显著提高了许多慢性病的生存率，并引发了人们对开发具有不可忽视治愈比例的生存数据治愈比例模型的浓厚兴趣。涉及多种类型终点的竞争风险可能会使此类数据的统计分析进一步复杂化。竞争风险的回归分析通常通过基于特定病因风险或子分布风险的比例风险模型进行。在本文中，我们提出了一种替代方法，将竞争事件视为混合中的不同结果。我们考虑针对病因条件生存函数的半参数加速失效时间模型，这些模型在治愈混合建模框架内通过多项逻辑模型进行组合。竞争风险的治愈混合方法提供了一种确定治疗总体效果的方法，并深入了解在存在治愈比例的情况下该治疗如何改变混合成分。回归和非参数参数通过基于非参数核的最大似然估计方法进行估计。方差估计通过对核平滑似然函数的重采样方法实现。模拟研究表明，这些程序在实际环境中运行良好。对肉瘤研究的应用展示了所提出方法在具有治愈比例的竞争风险数据中的应用。
