Bantis Leonidas E, Nakas Christos T, Reiser Benjamin, Myall Daniel, Dalrymple-Alford John C
1 Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX, USA.
2 Laboratory of Biometry, University of Thessaly, Volos, Greece.
Stat Methods Med Res. 2017 Jun;26(3):1429-1442. doi: 10.1177/0962280215581694. Epub 2015 Apr 24.
The three-class approach is used for progressive disorders when clinicians and researchers want to diagnose or classify subjects as members of one of three ordered categories based on a continuous diagnostic marker. The decision thresholds or optimal cut-off points required for this classification are often chosen to maximize the generalized Youden index (Nakas et al., Stat Med 2013; 32: 995-1003). The effectiveness of these chosen cut-off points can be evaluated by estimating their corresponding true class fractions and their associated confidence regions. Recently, in the two-class case, parametric and non-parametric methods were investigated for the construction of confidence regions for the pair of the Youden-index-based optimal sensitivity and specificity fractions that can take into account the correlation introduced between sensitivity and specificity when the optimal cut-off point is estimated from the data (Bantis et al., Biomet 2014; 70: 212-223). A parametric approach based on the Box-Cox transformation to normality often works well while for markers having more complex distributions a non-parametric procedure using logspline density estimation can be used instead. The true class fractions that correspond to the optimal cut-off points estimated by the generalized Youden index are correlated similarly to the two-class case. In this article, we generalize these methods to the three- and to the general k-class case which involves the classification of subjects into three or more ordered categories, where ROC surface or ROC manifold methodology, respectively, is typically employed for the evaluation of the discriminatory capacity of a diagnostic marker. We obtain three- and multi-dimensional joint confidence regions for the optimal true class fractions. We illustrate this with an application to the Trail Making Test Part A that has been used to characterize cognitive impairment in patients with Parkinson's disease.
当临床医生和研究人员希望根据连续诊断标志物将受试者诊断或分类为三个有序类别之一时，三类方法用于进行性疾病。这种分类所需的决策阈值或最佳切点通常被选择以最大化广义约登指数（中田等人，《统计医学》2013年；32: 995 - 1003）。可以通过估计其相应的真实类别比例及其相关的置信区域来评估这些选定切点的有效性。最近，在两类情况下，研究了参数和非参数方法来构建基于约登指数的最佳敏感性和特异性比例对的置信区域，当从数据中估计最佳切点时，该方法可以考虑敏感性和特异性之间引入的相关性（班蒂斯等人，《生物计量学》2014年；70: 212 - 223）。基于Box - Cox正态变换的参数方法通常效果良好，而对于具有更复杂分布的标志物，可以使用基于对数样条密度估计的非参数程序。与广义约登指数估计的最佳切点相对应的真实类别比例与两类情况类似地相关。在本文中，我们将这些方法推广到三类和一般的k类情况，其中涉及将受试者分类为三个或更多有序类别，在这种情况下，通常分别采用ROC曲面或ROC流形方法来评估诊断标志物的鉴别能力。我们获得了最佳真实类别比例的三维和多维联合置信区域。我们通过将其应用于用于表征帕金森病患者认知障碍的连线测验A部分来说明这一点。
