The prediction reliability is of primary concern in many clinical studies when the objective is to develop new predictive models or improve existing risk scores. In fact, before using a model in any clinical decision making, it is very important to check its ability to discriminate between subjects who are at risk of, for example, developing certain disease in a near future from those who will not. To that end, the time‐dependent receiver operating characteristic (ROC) curve is the most commonly used method in practice. Several approaches have been proposed in the literature to estimate the ROC nonparametrically in the context of survival data. But, except one recent approach, all the existing methods provide a nonsmooth ROC estimator whereas, by definition, the ROC curve is smooth. In this article we propose and study a new nonparametric smooth ROC estimator based on a weighted kernel smoother. More precisely, our approach relies on a well‐known kernel method used to estimate cumulative distribution functions of random variables with bounded supports. We derived some asymptotic properties for the proposed estimator. As bandwidth is the main parameter to be set, we present and study different methods to appropriately select one. A simulation study is conducted, under different scenarios, to prove the consistency of the proposed method and to compare its finite sample performance with a competitor. The results show that the proposed method performs better and appear to be quite robust to bandwidth choice. As for inference purposes, our results also reveal the good performances of a proposed nonparametric bootstrap procedure. Furthermore, we illustrate the method using a real data example.

中文翻译：

---

平滑的随时间变化的接收器操作特征曲线，用于正确审查生存数据。

当目标是开发新的预测模型或改善现有风险评分时，预测可靠性是许多临床研究中最关注的问题。实际上，在任何临床决策中使用模型之前，检查其区分能力的能力非常重要，例如，这些能力会将处于危险中的受试者（例如，在不久的将来患上某些疾病的受试者）与不会患有该疾病的受试者区分开。为此，与时间有关的接收机工作特性（ROC）曲线是实践中最常用的方法。文献中已经提出了几种方法来在生存数据的背景下非参数地估计ROC。但是，除了最近的一种方法之外，所有现有方法都提供了不平滑的ROC估计量，而根据定义，ROC曲线是平滑的。在本文中，我们提出并研究了一种基于加权核平滑器的新型非参数平滑ROC估计器。更准确地说，我们的方法依赖于众所周知的核方法，该方法用于估计具有有限支持量的随机变量的累积分布函数。我们推导了估计器的一些渐近性质。由于带宽是要设置的主要参数，因此，我们介绍并研究不同的方法以适当地选择一种。在不同情况下进行了仿真研究，以证明该方法的一致性，并将其有限样本性能与竞争对手进行比较。结果表明，所提出的方法性能更好，并且对于带宽选择而言似乎很健壮。出于推理目的，我们的结果还揭示了拟议的非参数引导程序的良好性能。