School of Mathematical Sciences, Dalian University of Technology, Dalian, China.
Pharm Stat. 2020 Nov;19(6):955-974. doi: 10.1002/pst.2048. Epub 2020 Aug 10.
In medical studies, it is often observed that a portion of subjects will never experience the event of interest and thus can be treated as cured or long-term survivors. Many populations of early-stage cancer patients contain both uncured and cured individuals that should be modeled using cure models. In prognostic studies, the cure status (uncure or cure) is an issue of interest for medical practitioners, and the disease status (death or alive) of an individual is not a fixed characteristic and it varies along the time. These statuses are usually predicted by a prognostic risk score. The time-dependent receiver operating characteristic (ROC) curve is a powerful tool to evaluate these predicting performances dynamically. In the context with a cure fraction, quantifying and estimating the predictive performances of the risk score is a challenge since the disease status and cure status are both unknown among individuals who are censored. In this paper, to assess the predictive accuracy for the survival outcome with a cure fraction, we propose a time-dependent ROC curve semi-parametric estimator based on the sieve maximum likelihood (ML) estimation under the mixture cure model. We also apply a Bernstein-based smoothing method in the estimation procedure, and this estimator can lead to substantial gain in efficiency. In addition, we derive the time-dependent area under the ROC curve (AUC) to summarize the discriminatory capacity of the risk score globally. Finally, we evaluate the finite sample performance of the proposed methods by extensive simulations and illustrate the estimation using two real data sets, one from a melanoma study and the other from stomach cancer.
在医学研究中，我们经常观察到一部分研究对象从未经历过感兴趣的事件，因此可以将他们视为治愈或长期幸存者。许多早期癌症患者群体中既有未治愈的患者也有治愈的患者，这些患者应该使用治愈模型进行建模。在预后研究中，治愈状态（未治愈或治愈）是医学从业者关注的问题，而个体的疾病状态（死亡或存活）不是固定的特征，它会随着时间的推移而变化。这些状态通常通过预后风险评分来预测。时间依赖性接收者操作特征（ROC）曲线是一种强大的工具，可以动态地评估这些预测性能。在存在治愈分数的情况下，量化和估计风险评分的预测性能是一项挑战，因为在被删失的个体中，疾病状态和治愈状态都是未知的。在本文中，为了评估具有治愈分数的生存结局的预测准确性，我们在混合治愈模型下提出了一种基于筛最大似然（ML）估计的时间依赖性 ROC 曲线半参数估计量。我们还在估计过程中应用了基于 Bernstein 的平滑方法，该估计量可以显著提高效率。此外，我们推导出时间依赖性 ROC 曲线下面积（AUC）来概括风险评分的整体区分能力。最后，我们通过广泛的模拟评估了所提出方法的有限样本性能，并通过两个真实数据集来说明估计过程，一个来自黑色素瘤研究，另一个来自胃癌研究。
