Epidemiologic Methodology for Biomarkers (including ROC curve)

正如氧化应激有许多标志一样，生物技术的快速发展意味着研究人员越来越多地必须考虑在他们的研究中使用哪种筛查或诊断测试。我对ROC曲线的研究旨在为做出这些选择提供基于证据的方法。ROC曲线同时绘制了在不同的测试分界点被正确诊断的异常受试者和正常受试者的比例。这种图形显示便于选择最佳阈值，并能够轻松比较不同测试的能力。ROC曲线越来越多地被用于基于人群的环境中，而不是在个人已经进行了某种程度的预先筛查的环境中。然而，ROC曲线方法并没有被开发来解决常见的问题，如丢失数据、测量误差、线性组合、混淆、推荐偏差、LOD和其他挑战。 我们提出了K样本U统计量(其中ROC曲线下的面积(AUC)是特例)的均值的估计式，当感兴趣的结果的数据在某些样本单元中缺失且辅助变量在整个样本中可用时。拟议的估计数利用辅助资料中现有的信息，而不需要对辅助资料和结果的联合分布作出假设。所提出的估计量的性质是由K样本U统计量均值的有效半参数估计的一般结果导出的，该估计具有随机结果缺失、观测辅助变量和已知缺失概率。 随机测量误差会削弱生物标记物区分患病和未患病人群的能力。我们提出了一种估计正态分布生物标记物的Youden指数、AUC及其相关的最佳切割点的方法，该方法修正了正态分布的随机测量误差。我们还利用Delta方法给出了这些修正估计的可信区间，并通过对各种情况的模拟得出了覆盖概率。将这些技术应用于生物标记物硫代巴比妥酸反应物质(TBARS)，这是一种衡量氧化应激的指标，已被建议作为不孕不育的区分指标，在最佳切割点上，诊断效率提高了50%。这一结果可能会导致曾经被天真地认为无效的生物标志物成为有用的诊断工具。 由于多个标记物经常可用，我们考虑将它们结合起来以提高诊断的准确性。Su和Liu(1993)得出的最大化AUC的线性组合在特定的期望特异度范围内可能具有令人不满意的低灵敏度。我们考虑了在一定的特异度范围内的灵敏度最大化，并提出了在高(或低)特异度范围内具有更高灵敏度的可选的线性组合。此外，我们在假设多个标记或其变换服从多变量正态分布的情况下，评估了协变量对这种线性组合的影响。我们估计了经协变量和相应AUC的近似可信区间调整后的这种标记的线性组合的ROC曲线。 在评估新的诊断测试的研究中经常遇到的另一个问题是，由于测试的费用和/或侵入性，并不是所有的患者都要接受疾病验证。事实上，让患者接受验证测试的决定通常取决于新测试的结果和其他疾病状态的预测因素。在诊断性测试中，AUC估计仅基于已确认疾病状态的患者，通常的估计值是有偏差的。我们开发了针对这种偏差进行调整的估计器。 当疾病状态信息缺失时，有必要对缺失数据或导致缺失的过程进行建模，以获得AUC的良好行为估计。我们已经描述了一种双稳健估计器，当疾病或缺失的模型正确时，它是无偏的。这种估计器不需要EM类型的迭代，并且使用标准软件很容易计算。它既可以容纳离散的标记，也可以容纳连续的标记，并允许对验证的选择是不可忽视的可能性。此外，与目前可用的其他方法相比，双稳健估计器提供了更多针对模型误指定的保护。 我们已经应用了上述方法来证明TBARS，具有比机会更好的辨别能力。这项工作已在同行评议的期刊上发表了23篇文章，其中包括《比丘利斯卡》和《美国统计协会杂志》。

Just as there are many markers of oxidative stress, the rapid growth of biotechnology means that researchers increasingly must consider which screening or diagnostic test to use in their research. My work with ROC curves is aimed at providing evidence-based approaches for making these choices. The ROC curve simultaneously plots the proportion of both abnormal and normal subjects correctly diagnosed at various test cutoff points. This graphical display facilitates the selection of an optimal threshold and enables easy comparison of the abilities of different tests. Increasingly, ROC curves are used in population based settings as opposed to settings where individuals have been pre-screened to some degree. However, ROC curve methods were not developed to account for common problems such as missing data, measurement error, linear combinations, confounding, referral bias, LODs, and other challenges. We have proposed estimators of the mean of a K-sample U-statistic (of which the area under the ROC curve (AUC) is a special case) when data on the outcomes of interest are missing in some sampled units and auxiliary variables are available in the entire sample. The proposed estimators exploit the information available in the auxiliaries without requiring assumptions about the joint distribution of the auxiliaries and outcomes. The properties of the proposed estimators are derived from general results on efficient semi-parametric estimation of the mean of a K-sample U-statistic with missing at random outcomes, observed auxiliary variables and known missingness probabilities. Random measurement error can attenuate a biomarkers ability to discriminate between diseased and non-diseased populations. We present an approach for estimating the Youden index, the AUC and its associated optimal cut-point for a normally distributed biomarker that corrects for normally distributed random measurement error. We also developed confidence intervals for these corrected estimates using the delta method and coverage probability through simulation of a variety of situations. Applying these techniques to the biomarker thiobarbituric acid reaction substance (TBARS), a measure of oxidative stress that has been proposed as a discriminating measurement for infertility, yields a 50% increase in diagnostic effectiveness at the optimal cut-point. This result may lead to biomarkers that were once naively considered ineffective becoming useful diagnostic devices. Since multiple markers are often available, we considered combining them to improve diagnostic accuracy. The linear combinations derived by Su and Liu (1993) that maximize the AUC may have unsatisfactorily low sensitivity over a certain range of desired specificity. We considered maximization of sensitivity over a range of specificity, and presented alternative linear combinations that have higher sensitivity over a range of high (or low) specificity. Additionally, we evaluated covariate effects on this linear combination assuming that the multiple markers or a transformation thereof, follow a multivariate normal distribution. We estimated the ROC curve of this linear combination of markers adjusted for covariates and approximate confidence intervals for the corresponding AUC. Another frequently encountered problem in studies that evaluate new diagnostic tests is that not all patients undergo disease verification due to the expense and/or invasiveness of the test. In fact, the decision to subject patients to verification testing often depends on the results of the new test and other predictors of disease status. For diagnostic tests where AUC estimation is based only on patients with verified disease status, the usual estimators are biased. We developed estimators that adjust for this bias. When information on disease status is missing, it is necessary either to model the missing data or the process leading to the missingness to obtain well-behavedestimators of the AUC. We have described a doubly robust estimator that is unbiased when the model for disease or the missingness is correct. This estimator does not require EM-type iterations and is easy to compute using standard software. It can accommodate both discrete and continuous markers and allows for the possibility that selection to verification is non-ignorable. In addition, the doubly robust estimator offers more protection against model misspecification than other currently available methods. We have applied the methods described above to show that TBARS, has discriminating abilities above and beyond chance. This work has yielded 23 publications in peer reviewed journals including Biometrika and the Journal of the American Statistical Association.