Department of Biostatistics, Indiana University Fairbanks School of Public Health and School of Medicine, 410 West 10th Street, Suite 3000, Indianapolis, IN, 46202, USA.
Department of Biostatistics, University of Nebraska Medical Center, Omaha, USA.
Lifetime Data Anal. 2020 Oct;26(4):659-684. doi: 10.1007/s10985-020-09494-1. Epub 2020 Jan 25.
The cause of failure in cohort studies that involve competing risks is frequently incompletely observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariate-specific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a unified framework for inference about both the regression coefficients of the proportional cause-specific hazards model and the covariate-specific cumulative incidence functions under missing at random cause of failure. Our approach is based on a novel computationally efficient maximum pseudo-partial-likelihood estimation method for the semiparametric proportional cause-specific hazards model. Using modern empirical process theory we derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing cause of failures, and that the regression coefficient estimator can be substantially more efficient compared to the previously proposed augmented inverse probability weighting estimator. The method is applied using data from an HIV cohort study and a bladder cancer clinical trial.
在涉及竞争风险的队列研究中，失败的原因常常未被完全观察到。为了解决这个问题，已经提出了几种方法用于随机缺失假设下的半参数比例病因特异性风险模型。然而，这些建议仅提供了回归系数的推断，而没有考虑无限维参数，例如协变量特异性累积发生率函数。然而，后者对于现代医学中的风险预测至关重要。在本文中，我们提出了一种统一的框架，用于在随机缺失失败原因下对比例病因特异性风险模型的回归系数和协变量特异性累积发生率函数进行推断。我们的方法基于一种新颖的计算有效的半参数比例病因特异性风险模型的最大拟似然估计方法。我们使用现代经验过程理论推导了所提出的回归系数和协变量特异性累积发生率函数的估计量的渐近性质，并提供了构建后者的同时置信带的方法。模拟研究表明，即使在存在大量缺失失败原因的情况下，我们的估计量也能很好地工作，并且与之前提出的增强逆概率加权估计量相比，回归系数估计量可以显著提高效率。该方法应用于 HIV 队列研究和膀胱癌临床试验的数据。
