基于加权Youden指数的最优诊断界值及其置信区间构建

Optimal Cut-point and its Confidence Interval Construction based on Weighted Youden Index

目的在ROC曲线分析中,Youden指数常被用于最优诊断界值的选择。加权Youden指数考虑了灵敏度和特异度的不同权重,更符合实际应用需求,但基于该新指数用于选择最优诊断界值的理论尚不完善。本研究旨在假定检测结果服从logistic分布或正态分布,推导基于加权Youden指数的最优诊断界值,并构建其参数及非参数置信区间。方法在不同条件下使得加权Youden指数达到最大,推导相应最优诊断界值,基于delta法推导相应方差,利用正态近似法和bootstrap法分别构建相应参数及非参数置信区间。所提方法统计性能评估采用Monte Carlo方法。结果研究构建了单纯使加权Youden指数达到最大及限定灵敏度或特异度下限时,使加权Youden指数达到最大时相应的最优诊断界值,并推导得到了相应方差,构建了置信区间参数和非参数估计方法。模拟研究显示所提出的最优诊断界值平均偏差较小,在满足参数方法假设下参数方法优于非参数方法。所提置信区间覆盖率能达到预设水平。结论所提诊断界值确定方法及其置信区间能够满足应用需求,且当满足参数方法条件时,最优诊断界值参数方法要优于非参数方法。

Objective To determine the optimal cut-point for ROC curve analysis,the Youden index is often applied.To consider the weights of sensitivity and specificity,the weighted Youden index was proposed,but the theories of determining the optimal cut-point based on this new index are not yet established.The objective of this study was to establish parametric and non-parametric methods for the optimal cut-point selection based on the weighted Youden index and its variance and confidence interval estimation.Methods Under the criterion of maximizing the weighted Youden index,the parameter and non-parametric estimation methods were constructed to estimate the optimal cutpoints.The corresponding variances were derived based on the delta method,and the parametric and non-parametric confidence intervals were constructed using the normal approximation method and bootstrap method respectively.The statistical performance were assessed by the Monte Carlo method.Results Parametric and non-parametric methods based on weighted Youden index to determine optimal cut-point and its confidence interval were established.Meanwhile,a method to determine the optimal cut-point based on the weighted Youden index combined with the lower limit of sensitivity or specificity was also given.The simulation study shows that the bias of the proposed optimal cut-point is small,and the parametric method is better than the non-parametric method.The confidence interval coverage of the proposed confidence intervals can welly reach the preset level.Conclusion The proposed methods for determining the optimal cut-off point and its confidence interval can meet the application requirements.When the assumption of parameter methods is met,the parametric method is better than the non-parametric one.