Identifying effects of multiple treatments in the presence of unmeasured confounding

Identification of treatment effects in the presence of unmeasured confounding is a persistent problem in the social, biological, and medical sciences. The problem of unmeasured confounding in settings with multiple treatments is most common in statistical genetics and bioinformatics settings, where researchers have developed many successful statistical strategies without engaging deeply with the causal aspects of the problem. Recently there have been a number of attempts to bridge the gap between these statistical approaches and causal inference, but these attempts have either been shown to be flawed or have relied on fully parametric assumptions. In this paper, we propose two strategies for identifying and estimating causal effects of multiple treatments in the presence of unmeasured confounding. The <i>auxiliary variables</i> approach leverages variables that are not causally associated with the outcome; in the case of a univariate confounder, our method only requires one auxiliary variable, unlike existing instrumental variable methods that would require as many instruments as there are treatments. An alternative <i>null treatments</i> approach relies on the assumption that at least half of the confounded treatments have no causal effect on the outcome, but does not require a priori knowledge of which treatments are null. Our identification strategies do not impose parametric assumptions on the outcome model and do not rest on estimation of the confounder. This paper extends and generalizes existing work on unmeasured confounding with a single treatment and models commonly used in bioinformatics.

在社会科学、生物学与医学领域，未观测混杂（unmeasured confounding）场景下的干预效应（treatment effects）识别问题是一项长期存在的共性难题。多干预（multiple treatments）场景下的未观测混杂问题在统计遗传学与生物信息学领域尤为常见，该领域研究者已开发出诸多行之有效的统计策略，但并未深入探讨该问题的因果维度。近年来，诸多研究尝试弥合此类统计方法与因果推断（causal inference）之间的鸿沟，但这些尝试要么被证实存在缺陷，要么依赖于完全参数化假设。针对未观测混杂情形下的多干预因果效应识别与估计问题，本文提出两种策略。辅助变量（auxiliary variables）法利用与结果变量无因果关联的变量；在单变量混杂情形下，该方法仅需一个辅助变量，而现有工具变量（instrumental variable）法所需工具变量的数量需与干预数目相当。另一种零干预（null treatments）法则基于如下假设：至少半数存在混杂的干预对结果无因果效应，但无需预先知晓哪些干预属于零效应干预。本文提出的识别策略既未对结果模型施加参数化假设，也无需对混杂变量进行估计。本文拓展并推广了现有关于单干预情形下未观测混杂的研究成果，以及生物信息学领域常用的相关模型。