发表机构
University of Waterloo（滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对不完美参考标准下的ROC分析，提出基于Box-Cox密度比模型的半参数方法，自动估计变换参数，结合经验似然和EM算法，实现准确稳定的估计与推断。
AI 中文摘要
接收者操作特征（ROC）分析常用于评估连续生物标志物的诊断准确性。在实际中，真实的疾病状态可能无法获得，只能观察到由不完美参考标准提供的名义疾病状态。现有非参数方法已被开发用于此设置下的ROC分析，但可能面临估计效率降低、数值不稳定性或对生物标志物尺度选择敏感的问题。我们提出一种基于Box-Cox密度比模型的半参数方法，该模型将真正健康与患病群体的生物标志物分布联系起来，同时保持基线分布未指定。所提方法的一个关键特征是变换参数从数据中估计而非预先指定，使得密度比结构能够适应不同的变换尺度。我们开发了用于估计的经验似然方法和用于计算的期望最大化算法。我们建立了ROC曲线、曲线下面积、约登指数以及约登最优截断点处灵敏度和特异度估计量的渐近分布，并开发了自助置信区间和拟合优度检验。模拟研究表明，所提方法在无需预先指定变换尺度的情况下，在各种分布设置中提供准确且数值稳定的估计和推断。所提方法通过一项疟疾研究的数据进行了说明。
英文摘要
Receiver operating characteristic (ROC) analysis is commonly used to evaluate the diagnostic accuracy of continuous biomarkers. In practice, the true disease status may be unavailable and only a nominal disease status provided by an imperfect reference standard is observed. Existing nonparametric methods have been developed for ROC analysis in this setting, but may suffer from reduced estimation efficiency, numerical instability, or sensitivity to the choice of biomarker scale. We propose a semiparametric method based on a Box-Cox density ratio model, which links the biomarker distributions of the truly healthy and diseased populations while leaving the baseline distribution unspecified. A key feature of the proposed method is that the transformation parameter is estimated from the data rather than specified in advance, allowing the density-ratio structure to adapt to different transformation scales. We develop an empirical likelihood approach for estimation and an expectation-maximization algorithm for computation. We establish the asymptotic distributions of estimators of the ROC curve, area under the curve, Youden's index, and the sensitivity and specificity at the Youden-optimal cutoff, and develop bootstrap confidence intervals and a goodness-of-fit test. Simulation studies demonstrate that the proposed method provides accurate and numerically stable estimation and inference across a range of distributional settings without requiring the transformation scale to be specified in advance. The proposed method is illustrated using data from a malaria study.
