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.

中文翻译：

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半参数回归和风险预测与失败原因缺失下的竞争风险数据。

涉及竞争风险的队列研究失败的原因经常被不完整地观察到。为了解决这个问题，在随机缺失假设下，已经为半参数比例特定原因风险模型提出了几种方法。然而，这些建议仅提供回归系数的推断，并没有考虑无限维参数，例如特定于协变量的累积关联函数。然而，后者的数量对于现代医学中的风险预测是​​必不可少的。在本文中，我们提出了一个统一的框架，用于在随机故障原因缺失的情况下，对比例原因特定风险模型的回归系数和协变量特定累积发生率函数进行推断。我们的方法基于一种新的计算有效的最大伪部分似然估计方法，用于半参数比例原因特定危险模型。使用现代经验过程理论，我们推导出回归系数和协变量特定累积关联函数的建议估计量的渐近特性，并提供为后者构建同时置信带的方法。模拟研究表明，我们的估计器即使在存在很大一部分失败原因的情况下也能很好地执行，并且与之前提出的增强逆概率加权估计器相比，回归系数估计器的效率要高得多。该方法使用来自 HIV 队列研究和膀胱癌临床试验的数据进行应用。