Inference on Effects of Multiple Causes With an Unobserved Confounder
摘要：Unmeasured confounding often arises in observational studies, such as in socioeconomic, biomedical, and epidemiological researches. Unmeasured confounding may jeopardize causal inference, and leads to misleading results. For inference about the effect of a single cause, instrumental variables and negative controls are commonly used to remove unmeasured confounding, however, the situation becomes complicated when effects of multiple causes are of interest. In this paper, we focus on identifying the effect of multiple causes that may be confounded by an unobserved confounder. We offer two approaches to remove unmeasured confounding by using auxiliary variables and by imposing a sparsity effects assumption, respectively. We propose sufficient conditions for identification of the causal effects, describe estimation methods that are convenient to implement, and evaluate their performance via numerical examples.