基于加权Youden指数确定最佳诊断界值下灵敏度、特异度及加权Youden指数的置信区间构建

The Confidence Interval Estimation for the Sensitivity,the Specificity,and the Weighted Youden Index with the Determined Optimal Cut-point based on the Weighted Youden Index

本研究旨在构建基于加权Youden指数确定最佳诊断界值后的灵敏度、特异度以及最大加权Youden指数的置信区间估计方法。方法在正态分布和logistic分布假设下,基于delta法估计各指标的方差并基于正态近似法构建其置信区间估计参数法,基于bootstrap法构建其非参数置信区间。采用Monte Carlo评价其统计性能。结果研究所构建各指标置信区间参数和非参数方法其置信区间覆盖率基本能达到预设水平,但是小样本下以及对加权Youden指标来讲,非参数的置信区间估计表现较差。在参数假设满足情况下,基于参数法估计的各指标在偏差及均方误差方面均优于非参数法。结论所提各指标参数置信区间估计方法能够满足应用需求,且当满足参数方法条件时,参数方法要优于非参数方法,非参数方法有待进一步改进。

Objective In the ROC(receiver-operator curve)analysis,when the optimal cut-point determined based on the Youden index,the corresponding sensitivity,specificity,and Youden index are usually reported.Our study aims to construct the confidence interval for sensitivity,specificity,and weighted Youden index after the optimal cut-point is determined based on the weighted Youden index.Methods Under the assumption that the test results are following normal or logistic distribution,the confidence intervals were parametrically constructed based on the normal approximation method,and the variances of sensitivity,specificity,weighted Youden index were estimated by the delta method.Under no assumption on the distribution of test results,the confidence intervals were non-parametrically estimated by the bootstrap method.The statistical performance of the proposed methods is evaluated by the Monte Carlo method.Results The simulation results showed that the confidence interval coverage of parametric and non-parametric methods can reach the preset level,but for the small sample size and the weighted Youden index,the performance of non-parametric methods are not satisfactory.Furthermore,we can recognize that if the assumption of the parametric method is satisfied,the parametric method is superior to the non-parametric method in terms of bias and mean square error.Conclusion The proposed parametric confidence interval estimation methods can meet the application requirements,and the parametric method is better than the non-parametric method when the parametric method is satisfied.