With rapidly increasing data sources, statistical methods that make use of external information are gradually becoming popular tools in medical research. In this article, we efficiently synthesize the auxiliary survival information and propose a semiparametric estimation method for the combined empirical likelihood in the framework of the nonmixture cure model, to enhance inference about the associations between exposures and disease outcomes. The auxiliary survival probabilities from external sources are first summarized as unbiased estimation equations, which help produce more efficient estimates of the effects of interest and improve the prediction accuracy for the risk of the event. Then we develop a Bernstein-based sieve empirical likelihood method to estimate the parametric and nonparametric components simultaneously. Such an estimation procedure allows us to reduce the computation burden while preserving the shape constraint on the baseline distribution function. The resulting estimators for the true associations are strongly consistent and asymptotically normal. Instead of collecting substantial exposure data, the auxiliary survival information at multiple time points is incorporated, which further reduces the mean squared error of the estimators. This contributes to biomarker evaluation and treatment effect analysis within smaller studies. We show how to choose the number of auxiliary survival probabilities appropriately and provide a guideline for practical applications. Simulation studies demonstrate that the estimators enjoy large gains in efficiency. A melanoma dataset is analyzed for illustrating the methodology.

中文翻译：

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具有辅助生存信息的非混合治愈模型的半参数估计

随着数据源的迅速增加，利用外部信息的统计方法逐渐成为医学研究中的流行工具。在本文中，我们有效地综合了辅助生存信息，并在非混合治愈模型的框架下提出了一种组合经验似然的半参数估计方法，以增强对暴露与疾病结果之间关联的推断。来自外部来源的辅助生存概率首先被总结为无偏估计方程，这有助于对感兴趣的影响产生更有效的估计，并提高对事件风险的预测准确性。然后我们开发了一种基于 Bernstein 的筛经验似然方法来同时估计参数和非参数分量。这种估计过程允许我们减少计算负担，同时保留对基线分布函数的形状约束。真实关联的最终估计量是高度一致的并且渐近正态。不是收集大量的暴露数据，而是结合了多个时间点的辅助生存信息，这进一步降低了估计器的均方误差。这有助于在较小的研究中进行生物标志物评估和治疗效果分析。我们展示了如何适当地选择辅助生存概率的数量，并为实际应用提供指导。模拟研究表明，估计器在效率方面享有很大的收益。分析黑色素瘤数据集以说明该方法。