Discrimination measures such as concordance statistics (e.g. the c-index or the concordance probability) and the cumulative-dynamic time-dependent area under the ROC-curve (AUC) are widely used in the medical literature for evaluating the predictive accuracy of a scoring rule which relates a set of prognostic markers to the risk of experiencing a particular event. Often the scoring rule being evaluated in terms of discriminatory ability is the linear predictor of a survival regression model such as the Cox proportional hazards model. This has the undesirable feature that the scoring rule depends on the censoring distribution when the model is misspecified. In this work we focus on linear scoring rules where the coefficient vector is a nonparametric estimand defined in the setting where there is no censoring. We propose so-called debiased estimators of the aforementioned discrimination measures for this class of scoring rules. The proposed estimators make efficient use of the data and minimize bias by allowing for the use of data-adaptive methods for model fitting. Moreover, the estimators do not rely on correct specification of the censoring model to produce consistent estimation. We compare the estimators to existing methods in a simulation study, and we illustrate the method by an application to a brain cancer study.

翻译：在医学文献中，判别度量如一致性统计量（例如c指数或一致性概率）和累积动态时间依赖性ROC曲线下面积（AUC）被广泛用于评估评分规则的预测准确性，该评分规则将一组预后标志物与发生特定事件的风险相关联。通常，从判别能力角度评估的评分规则是生存回归模型（如Cox比例风险模型）的线性预测因子。当模型设定错误时，评分规则依赖于删失分布，这是一个不良特性。在本研究中，我们关注线性评分规则，其中系数向量是在无删失情况下定义的非参数估计量。我们针对此类评分规则提出了上述判别度量的所谓去偏估计器。所提出的估计器通过允许使用数据自适应方法进行模型拟合，从而高效利用数据并最小化偏差。此外，这些估计器不依赖于删失模型的正确设定即可产生一致的估计。我们在模拟研究中将所提出的估计器与现有方法进行比较，并通过脑癌研究的应用实例来说明该方法。