The identification of biomarkers with high predictive accuracy is a crucial task in medical research, as it can aid clinicians in making early decisions, thereby reducing morbidity and mortality in high-risk populations. Time-dependent receiver operating characteristic (ROC) curves are the main tool used to assess the accuracy of prognostic biomarkers for outcomes that evolve over time. Recognising the need to account for patient heterogeneity when evaluating the accuracy of a prognostic biomarker, we introduce a novel penalised-based estimator of the time-dependent ROC curve that accommodates a possible modifying effect of covariates. We consider flexible models for both the hazard function of the event time given the covariates and biomarker and for the location-scale regression model of the biomarker given covariates, enabling the accommodation of non-proportional hazards and nonlinear effects through penalised splines, thus overcoming limitations of earlier methods. The simulation study demonstrates that our approach successfully recovers the true functional form of the covariate-specific time-dependent ROC curve and the corresponding area under the curve across a variety of scenarios. Comparisons with existing methods further show that our approach performs favourably in multiple settings. Our approach is applied to evaluate the ability of the Global Registry of Acute Coronary Events risk score to predict mortality over different time periods after discharge in patients who have suffered an acute coronary syndrome and to investigate how this ability may vary with the left ventricular ejection fraction. An R package, CondTimeROC, implementing the proposed method is provided.

翻译：在医学研究中，识别具有高预测准确性的生物标志物是一项关键任务，因为它可以帮助临床医生做出早期决策，从而降低高风险人群的发病率和死亡率。时间依赖性受试者工作特征（ROC）曲线是评估随时间演变结局的预后生物标志物准确性的主要工具。认识到在评估预后生物标志物准确性时需要考虑患者异质性，我们引入了一种新颖的基于惩罚的时间依赖性ROC曲线估计量，该估计量能够适应协变量可能存在的修饰效应。我们考虑了给定协变量和生物标志物的事件时间风险函数的灵活模型，以及给定协变量的生物标志物的位置-尺度回归模型的灵活模型，通过惩罚样条能够适应非比例风险和非线性效应，从而克服了早期方法的局限性。模拟研究表明，我们的方法在各种场景下成功恢复了协变量特异性时间依赖性ROC曲线的真实函数形式及其相应的曲线下面积。与现有方法的比较进一步表明，我们的方法在多种设置下表现良好。我们将该方法应用于评估全球急性冠状动脉事件注册风险评分在预测急性冠状动脉综合征患者出院后不同时间段内死亡率的能力，并研究这种能力如何随左心室射血分数变化。提供了实现所提出方法的R软件包CondTimeROC。