Baker Alexander, Hsu Fang-Chi, Gayzik Scott
a Wake Forest Center for Injury Biomechanics , Winston-Salem , North Carolina.
b Department of Biostatistics , Wake Forest University School of Medicine , Winston-Salem , North Carolina.
Traffic Inj Prev. 2018 Feb 28;19(sup1):S174-S176. doi: 10.1080/15389588.2018.1426903.
Area under the receiver operating characteristic (AROC) is commonly used to evaluate an injury metric's ability to discriminate between injury and noninjury cases. However, AROC has limitations and may not handle censored data sets adequately. Survival methodology creates robust estimates of injury risk curves (IRCs) which accommodate censored data. We developed an observation-adjusted ROC (oaROC), an AROC-like statistic calculated from the IRC.
oaROC uses an observational distribution and an IRC to measure true positive rate (TPR) and false positive rate (FPR). The oaROC represents what the AROC would be with a large number of observations sampled from the IRC. We verified this using a limit test with simulated data sets at various sample sizes drawn from an assumed "true" IRC. For each sample size, 5,000 different data sets were created; a conventional AROC was calculated for each data set and compared with the single oaROC, which was calculated from the "true" IRC and not dependent on sample size.
The oaROC, calculated from the simulated IRC, was 0.911. At a sample size of 20, the mean AROC was 0.930 (2.0% difference). At a sample size of 1,000, the mean AROC was 0.9114 (0.02% difference).
We verified that AROC approaches the oaROC with increasing sample sizes, and oaROC presents a measure of IRC discriminatory ability. Survival methodology can estimate IRCs using censored observations and the oaROC was designed with this in mind. The oaROC may be a useful measure of discrimination for data sets containing censored data. Further investigation is needed to evaluate oaROC calculated from estimated IRCs.
受试者工作特征曲线下面积（AROC）常用于评估损伤指标区分损伤与非损伤病例的能力。然而，AROC存在局限性，可能无法充分处理删失数据集。生存分析方法能对损伤风险曲线（IRC）进行稳健估计，可处理删失数据。我们开发了一种观察调整后的ROC（oaROC），这是一种从IRC计算得出的类似AROC的统计量。
oaROC使用观察分布和IRC来测量真阳性率（TPR）和假阳性率（FPR）。oaROC代表从IRC中抽取大量观察值时的AROC。我们通过对从假定的“真实”IRC中抽取的不同样本量的模拟数据集进行极限检验来验证这一点。对于每个样本量，创建了5000个不同的数据集；为每个数据集计算传统的AROC，并与从“真实”IRC计算得出且不依赖于样本量的单个oaROC进行比较。
从模拟的IRC计算得出的oaROC为0.911。样本量为20时，平均AROC为0.930（差异2.0%）。样本量为1000时，平均AROC为0.9114（差异0.02%）。
我们验证了随着样本量增加，AROC趋近于oaROC，且oaROC体现了IRC的区分能力。生存分析方法可使用删失观察值估计IRC，而oaROC正是基于此设计的。对于包含删失数据的数据集，oaROC可能是一种有用的区分度量。需要进一步研究以评估从估计的IRC计算得出的oaROC。
