The cumulative incidence is the probability of failure from the cause of interest over a certain time period in the presence of other risks. A semiparametric regression model proposed by Fine and Gray (1999) has become the method of choice for formulating the effects of covariates on the cumulative incidence. Its estimation, however, requires modeling of the censoring distribution and is not statistically efficient. In this paper, we present a broad class of semiparametric transformation models which extends the Fine and Gray model, and we allow for unknown causes of failure. We derive the nonparametric maximum likelihood estimators (NPMLEs) and develop simple and fast numerical algorithms using the profile likelihood. We establish the consistency, asymptotic normality, and semiparametric efficiency of the NPMLEs. In addition, we construct graphical and numerical procedures to evaluate and select models. Finally, we demonstrate the advantages of the proposed methods over the existing ones through extensive simulation studies and an application to a major study on bone marrow transplantation.

中文翻译：

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竞争风险累积发生率的半参数转换模型的有效估计。

累积发生率是在存在其他风险的情况下，在特定时间段内因感兴趣的原因而失败的概率。Fine和Gray（1999）提出的半参数回归模型已经成为表达协变量对累积发生率影响的一种选择方法。但是，其估计需要对检查分布进行建模，并且统计上效率不高。在本文中，我们提出了一大类半参数转换模型，这些模型扩展了Fine和Gray模型，并且允许出现未知的故障原因。我们推导非参数最大似然估计器（NPMLE），并使用轮廓似然来开发简单快速的数值算法。我们建立了NPMLE的一致性，渐近正态性和半参数效率。此外，我们构建图形和数字程序来评估和选择模型。最后，我们通过广泛的模拟研究以及在骨髓移植的一项重大研究中的应用，证明了所提出方法相对于现有方法的优势。