Multi-cause causal inference with unmeasured confounding and binary outcome

Unobserved confounding presents a major threat to causal inference in observational studies. Recently, several authors suggest that this problem may be overcome in a shared confounding setting where multiple treatments are independent given a common latent confounder. It has been shown that if additional data such as negative controls are available, then the causal effects are indeed identifiable. In this paper, we show that these additional data are not necessary for causal identification, provided that the treatments and outcome follow Gaussian and logistic structural equation models, respectively. Our novel identification strategy is based on the symmetry and tail properties of the observed data distribution. We further develop two-step likelihood-based estimation procedures. We illustrate our method through simulations and a real data application studying the causal relationship between the volume of various brain regions and cognitive scores.