Free-response observer performance studies are of great importance for accuracy evaluation and comparison in tasks related to the detection and localization of multiple targets or signals. The free-response receiver operating characteristic (FROC) curve and many similar curves based on the free-response observer performance assessment data are important tools to display the accuracy of detection under different thresholds. The true positive rate at a fixed false positive rate and summary indices such as the area under the FROC curve are also commonly used as the figures of merit in the statistical evaluation of these studies. Motivated by a free-response observer performance assessment research of a Software as a Medical Device (SaMD), we propose a unified method based on the initial-detection-and-candidate model to simultaneously estimate a smooth curve and derive confidence intervals for summary indices and the true positive rate at a fixed false positive rate. A maximum likelihood estimator is proposed and its asymptotic normality property is derived. Confidence intervals are constructed based on the asymptotic normality of our maximum likelihood estimator. Simulation studies are conducted to evaluate the finite sample performance of the proposed method. We apply the proposed method to evaluate the diagnostic performance of the SaMD for detecting pulmonary lesions.

翻译：自由响应观察者性能研究对于多目标或多信号检测与定位任务中的准确性评估与比较具有重要意义。自由响应接收器操作特性（FROC）曲线以及基于自由响应观察者性能评估数据的诸多类似曲线，是展示不同阈值下检测准确性的重要工具。固定假阳性率下的真阳性率以及FROC曲线下面积等汇总指标，也常被用作此类研究统计评估的性能指标。受一项医疗设备软件（SaMD）自由响应观察者性能评估研究的启发，我们提出一种基于初始检测与候选模型的统一方法，能够同时估计平滑曲线，并为汇总指标及固定假阳性率下的真阳性率推导置信区间。本文提出了最大似然估计量并推导了其渐近正态性。基于最大似然估计量的渐近正态性构建了置信区间。通过模拟研究评估了所提方法在有限样本下的性能。我们将所提方法应用于评估SaMD检测肺部病变的诊断性能。