Objectives: Estimation of areas under receiver operating characteristic curves (AUCs) and their differences is a key task in diagnostic studies. We aimed to derive, evaluate, and implement simple sample size formulas for such studies with a focus on estimation rather than hypothesis testing. Materials and Methods: Sample size formulas were developed by explicitly incorporating pre-specified precision and assurance, with precision denoted by the lower limit of confidence interval and assurance denoted by the probability of achieving that lower limit. A new variance function was proposed for valid estimation allowing for unequal variances of observations in the disease and non-disease groups. Performance of the proposed formulas was evaluated through simulation. Results: Closed-form sample size formulas were obtained. Simulation results demonstrated that the proposed formulas produced empirical assurance probability close to the pre-specified assurance probability and empirical coverage probability close to the nominal 95%. Real-world worked examples were presented for illustration. Conclusions: Sample size formulas based on estimation of AUCs and their differences were developed. Simulation results suggested good performance in terms of achieving pre-specified precision and assurance probability. An online calculator for implementing the proposed formulas is openly available at https://dishu.page/calculator/.

中文翻译：

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重新审视接受者操作特征研究的样本量规划：一种具有精确性和保证性的置信区间方法

目标：估计受试者工作特征曲线 (AUC) 下的面积及其差异是诊断研究中的一项关键任务。我们旨在为此类研究推导、评估和实施简单的样本量公式，重点是估计而不是假设检验。材料和方法：样本量公式是通过明确结合预先指定的精度和保证来开发的，精度由置信区间的下限表示，保证由达到该下限的概率表示。为有效估计提出了一种新的方差函数，允许在疾病组和非疾病组中观察到不相等的方差。通过仿真评估了所提出公式的性能。结果：获得了封闭式样本量公式。仿真结果表明，所提出的公式产生的经验保证概率接近预先指定的保证概率，经验覆盖概率接近标称的 95%。提供了真实世界的工作示例以进行说明。结论：开发了基于 AUC 估计及其差异的样本量公式。模拟结果表明在达到预先指定的精度和保证概率方面表现良好。用于实施建议公式的在线计算器可在 https://dishu.page/calculator/ 上公开获得。开发了基于 AUC 估计及其差异的样本量公式。模拟结果表明在达到预先指定的精度和保证概率方面表现良好。用于实施建议公式的在线计算器可在 https://dishu.page/calculator/ 上公开获得。开发了基于 AUC 估计及其差异的样本量公式。模拟结果表明在达到预先指定的精度和保证概率方面表现良好。用于实施建议公式的在线计算器可在 https://dishu.page/calculator/ 上公开获得。