Assessing causal treatment effect on a time-to-event outcome is of key interest in many scientific investigations. Instrumental variable (IV) is a useful tool to mitigate the impact of endogenous treatment selection to attain unbiased estimation of causal treatment effect. Existing development of IV methodology, however, has not attended to outcomes subject to interval censoring, which are ubiquitously present in studies with intermittent follow-up but are challenging to handle in terms of both theory and computation. In this work, we fill in this important gap by studying a general class of causal semiparametric transformation models with interval-censored data. We propose a nonparametric maximum likelihood estimator of the complier causal treatment effect. Moreover, we design a reliable and computationally stable expectation–maximization (EM) algorithm, which has a tractable objective function in the maximization step via the use of Poisson latent variables. The asymptotic properties of the proposed estimators, including the consistency, asymptotic normality, and semiparametric efficiency, are established with empirical process techniques. We conduct extensive simulation studies and an application to a colorectal cancer screening data set, showing satisfactory finite-sample performance of the proposed method as well as its prominent advantages over naive methods.

中文翻译：

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用区间删失数据估计因果治疗效果的工具变量

评估因果治疗对事件发生时间结果的影响是许多科学研究的主要兴趣所在。工具变量 (IV) 是一种有用的工具，可以减轻内生治疗选择的影响，从而实现对因果治疗效果的无偏估计。然而，IV 方法的现有发展并未关注受区间审查的结果，这些结果普遍存在于间歇性随访研究中，但在理论和计算方面都难以处理。在这项工作中，我们通过研究一类具有区间删失数据的因果半参数变换模型来填补这一重要空白。我们提出了依从者因果治疗效果的非参数最大似然估计。而且，我们设计了一种可靠且计算稳定的期望最大化 (EM) 算法，该算法通过使用泊松潜在变量在最大化步骤中具有易于处理的目标函数。所提出的估计量的渐近特性，包括一致性、渐近正态性和半参数效率，是通过经验过程技术建立的。我们进行了广泛的模拟研究，并将其应用于结直肠癌筛查数据集，展示了所提出方法令人满意的有限样本性能及其相对于朴素方法的显着优势。建立与经验过程技术。我们进行了广泛的模拟研究，并将其应用于结直肠癌筛查数据集，展示了所提出方法令人满意的有限样本性能及其相对于朴素方法的显着优势。建立与经验过程技术。我们进行了广泛的模拟研究，并将其应用于结直肠癌筛查数据集，展示了所提出方法令人满意的有限样本性能及其相对于朴素方法的显着优势。