It is challenging to evaluate causal effects when the outcomes of interest suffer from truncation-by-death in many clinical studies; that is, outcomes cannot be observed if patients die before the time of measurement. To address this problem, it is common to consider average treatment effects by principal stratification, for which, the identifiability results and estimation methods with a binary treatment have been established in previous literature. However, in multiarm studies with more than two treatment options, estimation of causal effects becomes more complicated and requires additional techniques. In this article, we consider identification, estimation, and bounds of causal effects with multivalued ordinal treatments and the outcomes subject to truncation-by-death. We define causal parameters of interest in this setting and show that they are identifiable either using some auxiliary variable or based on linear model assumption. We then propose a semiparametric method for estimating the causal parameters and derive their asymptotic results. When the identification conditions are invalid, we derive sharp bounds of the causal effects by use of covariates adjustment. Simulation studies show good performance of the proposed estimator. We use the estimator to analyze the effects of a four-level chronic toxin on fetal developmental outcomes such as birth weight in rats and mice, with data from a developmental toxicity trial conducted by the National Toxicology Program. Data analyses demonstrate that a high dose of the toxin significantly reduces the weights of pups.

中文翻译：

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多臂研究中因死亡而截断结果的因果推断

在许多临床研究中，当感兴趣的结果因死亡而截断时，评估因果效应具有挑战性；也就是说，如果患者在测量时间之前死亡，则无法观察到结果。为了解决这个问题，通常通过主要分层来考虑平均处理效果，为此，在以前的文献中已经建立了二元处理的可识别性结果和估计方法。然而，在有两种以上治疗方案的多臂研究中，因果效应的估计变得更加复杂，需要额外的技术。在本文中，我们考虑了多值序数处理的因果效应的识别、估计和界限，以及受死亡截断影响的结果。我们在此设置中定义了感兴趣的因果参数，并表明它们可以使用一些辅助变量或基于线性模型假设来识别。然后，我们提出了一种半参数方法来估计因果参数并推导出它们的渐近结果。当识别条件无效时，我们通过使用协变量调整得出因果效应的明确界限。仿真研究表明所提出的估计器具有良好的性能。我们使用估算器分析四级慢性毒素对大鼠和小鼠胎儿发育结果（例如出生体重）的影响，数据来自国家毒理学计划进行的发育毒性试验。数据分析表明，高剂量的毒素会显着降低幼崽的体重。