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 auxiliary variables 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 null treatments 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.
翻译:在社会、生物和医学科学中,发现在未经测量的混乱情况下的治疗效果是一个长期存在的问题。在多重治疗环境中的未经测量的混乱问题,在统计遗传学和生物信息学环境中最为常见。在统计遗传学和生物信息学环境中,研究人员制定了许多成功的统计战略,但没有深入涉及问题的因果关系。最近,有人试图弥合这些统计方法与因果推断之间的差距,但这些尝试要么有缺陷,要么完全依赖完全的参数假设。在本文中,我们提出了两种战略,用以查明和估计在未经测量的混乱环境中的多种治疗的因果关系。辅助变量方法利用了与结果没有因果关系的变量;在不具有因果关系的情况下,我们的方法只需要一种辅助变量,而不像现有的工具变量方法那样需要很多的处理方法。替代的无效处理方法所依据的假设是,即至少有一半的理果疗法对结果没有因果关系影响,但并不要求事先对哪些治疗的因果关系进行模型,而是要求事先对哪些治疗的假设进行不进行精确的假设。我们确定的方法仅需要一种辅助变量,而不是将现有结果的模型与通常的假设联系起来。