不同方差比双正态ROC参数估计样本量确定方法准确性探讨

Discussion of the accuracy of the sample size determination required for binormal ROC parameter estimation

目的 探讨不同方差比双正态参数估计时样本量确定方法的准确性,对最常用样本量估计方法--双正态法所估计样本量的准确性进行评价与修正.方法 采用Monte Carlo模拟试验,分别利用参数法和非参数法计算获得曲线下面积的参数估计值,获得实际所需样本量,对Obuchowski和Mcclish给出的不同方差比双正态ROC参数估计所需样本量的准确性进行评价,依据试验数据采用曲线拟合方法给出修正公式.结果 Obuchowski和Mcclish给出的方法是假定患病组诊断变量XA和非患病组诊断变量XN服从正态分布,样本量计算公式是以ROC曲线下面积估计值服从正态分布为前提导出的,但事实上随ROC曲线实际面积θ逐渐增大,样本估计量偏离正态,导致样本量估计结果不够准确,与实际样本需要量有一定差距.在其他条件相同的情况下,患病组与非患病组诊断变量方差比越大实际所需样本量越多,在患病组与非患病组诊断变量方差比分别为2∶1及3∶1的情况下,用Obuchowski和Mcclish方法计算出的样本量与实际所需样本量相差不是很大.根据Monte Carlo模拟试验的结果,给出了Obuchowski和Mcclish方法计算样本量的修正公式,该修正公式可有效地应用于实际.结论 Obuchowski和Mcclish方法计算的样本量进行ROC参数估计时需要调整,采用Monte Carlo方法估计的样本量,可以有效地进行双正态ROC参数估计,达到诊断试验评价要求.

Objective To discuss the accuracy of sample size determination involving binormal ROC parameter estimation, and evaluate and adjust the accuracy of the Obuchowski and Mcclish sample size determination involving binormal ROC pa rameter estimation. Methods We conducted a Monte Carlo simulation study to obtain the sample size involving binormal ROC parameter estimation with parametric or nonparametric estimates respectively. We assessed the bias of the Obuchowski and Mcclish sample size determination according to the sample size of the simulation study. We preented an approach for adjusting the sample size involving binormal ROC parameter estimation. Results At present, one of the sample size determination methods used usually is the Obuchowski and Mcclish sample size determination involving binormal ROC. Let XN and XA denote the underlying continuous test results of the normal and abnormal patients respectively. Let t） denote the underlying continuous area underthe ROC curve. When it was used, we assumed that XN - N（μNv, σ^2N） ,XA - N（μA, σ^2A） and θ - N（μθ, σ^2θ ）. But in practice, the value of θ is not from a standard normal distribution that corresponds to a certain probability. So the sample size is not suitable for our study. The higher value of θ , the more sample size demanded. The higher ratio of variance of abnormal patients to normal patients, the more sample size we need. Conclusion The method mentioned in this article is effective to determine the sample size which satisfies the requirement of the assessment of diagnostic test involving binormal ROC parameter estimation.