A Latent Variable Approach for Causal Effect Estimation Under Misclassified Treatment Assignment

Misclassification in treatment assignment is a common issue in causal inference with observational studies, often leading to biased estimates of causal effects if unaddressed. Several methods have been developed to handle this issue by making use of a validation dataset. This paper proposes a robust latent variable approach for causal effect estimation without the need of validation data. By employing a potential outcome modeling framework that incorporates true treatment assignment as a latent variable, we construct a likelihood function that involves three models: the outcome model, the measurement error model for misclassification, and the propensity score model for treatment assignment. To enhance the robustness against misspecification of the measurement error mechanism, we further incorporate neural networks into the estimation of the measurement error model. The simulation results show that our method performed well under various misclassification assumptions, and that using neural networks reduced the impact of misspecification of functional form for the measurement error model. We illustrate the method using a synthetic dataset derived from the Right Heart Catheterization (RHC) study. This flexible framework mitigates bias and improves the reliability of causal inference when treatment assignment is subject to misclassification and no validation data is available.