Bidirectional causal inference for binary outcomes in the presence of unmeasured confounding

TL;DR

This paper introduces a structural equation modeling approach to identify and estimate bidirectional causal effects between binary variables with unmeasured confounding, using instrumental variables and applied to health data.

Contribution

It proposes a novel method for causal inference with binary variables and unmeasured confounding, extending existing techniques to more complex biomedical scenarios.

Findings

Successfully identified bidirectional causal effects between heart disease and diabetes.

Developed an estimation method for causal parameters with sensitivity analysis.

Demonstrated practical utility in biomedical research context.

Abstract

Bidirectional causal relationships arising from mutual interactions between variables are commonly observed within biomedical, econometrical, and social science contexts. When such relationships are further complicated by unobserved factors, identifying causal effects in both directions becomes especially challenging. For continuous variables, methods that utilize two instrumental variables from both directions have been proposed to explore bidirectional causal effects in linear models. However, the existing techniques are not applicable when the key variables of interest are binary. To address these issues, we propose a structural equation modeling approach that links observed binary variables to continuous latent variables through a constrained mapping. We further establish identification results for bidirectional causal effects using a pair of instrumental variables. Additionally, we develop an estimation method for the corresponding causal parameters. We also conduct sensitivity analysis under scenarios where certain identification conditions are violated. Finally, we apply our approach to investigate the bidirectional causal relationship between heart disease and diabetes, demonstrating its practical utility in biomedical research.