This paper considers statistical inference for the receiver operating characteristic (ROC) curve in the presence of missing biomarker values by utilizing estimating equations (EEs) together with smoothed empirical likelihood (SEL). Three approaches are developed to estimate ROC curve and construct its SEL-based confidence intervals based on the kernel-assisted EE imputation, multiple imputation, and hybrid imputation combining the inverse probability weighted imputation and multiple imputation. Under some regularity conditions, we show asymptotic properties of the proposed maximum SEL estimators for ROC curve. Simulation studies are conducted to investigate the performance of the proposed SEL approaches. An example is illustrated by the proposed methodologies. Empirical results show that the hybrid imputation method behaves better than the kernel-assisted and multiple imputation methods, and the proposed three SEL methods outperform existing nonparametric method.

中文翻译：

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在缺少生物标志物值的情况下平滑 ROC 曲线的经验似然推断

本文通过利用估计方程 (EE) 和平滑经验似然 (SEL) 来考虑在缺少生物标志物值的情况下对受试者工作特征 (ROC) 曲线的统计推断。开发了三种方法来估计 ROC 曲线并基于核辅助 EE 插补、多重插补和结合逆概率加权插补和多重插补的混合插补构建其基于 SEL 的置信区间。在某些规律性条件下，我们展示了所提出的 ROC 曲线最大 SEL 估计量的渐近特性。进行模拟研究以调查所提出的 SEL 方法的性能。所提出的方法说明了一个例子。