Doubly robust identification for bivariate causal discovery under unmeasured confounding

Summary Learning causal relationships between pairs of complex traits from observational studies is of great interest in many scientific fields. However, most existing methods assume the absence of unmeasured confounding and restrict causal relationships between two traits to be unidirectional, which may be violated in real-world systems. In this paper, we address the problem of bivariate causal discovery in the presence of unmeasured confounding and potential feedback loops, leveraging possibly invalid instrumental variables. We propose a novel doubly robust identification framework that guarantees identifiability of the causal direction as long as one of two complementary assumptions holds, without requiring knowledge of which assumption is correct. Moreover, the causal effects are point identified in the unidirectional case and identifiable up to two candidate solutions in the bidirectional case unless additional information is available. Building on this framework, we develop a finite-sample procedure to detect the causal direction and conduct inference on causal effects. We prove that our method consistently recovers the true causal direction and yields valid confidence intervals for causal effects. Extensive simulations demonstrate its superior performance compared to existing methods. We finally apply our approach to analyze real data sets from UK Biobank.