Nonparametric Estimation for Propensity Scores With Misclassified Treatments

ABSTRACT In the framework of causal inference, average treatment effect (ATE) is one of crucial concerns. To estimate it, the propensity score based estimation method and its variants have been widely adopted. However, most existing methods were developed by assuming that binary treatments are precisely measured. In addition, propensity scores are usually formulated as parametric models with respect to confounders. However, in the presence of measurement error in binary treatments and nonlinear relationship between treatments and confounders, existing methods are no longer valid and may yield biased inference results if these features are ignored. In this paper, we first analytically examine the impact of estimation of ATE and derive biases for the estimator of ATE when treatments are contaminated with measurement error. After that, we develop a valid method to address binary treatments with misclassification. Given the corrected treatments, we adopt the random forest method to estimate the propensity score with nonlinear confounders accommodated and then derive the estimator of ATE. Asymptotic properties of the error‐eliminated estimator are established. Numerical studies are also conducted to assess the finite sample performance of the proposed estimator, and numerical results verify the importance of correcting for measurement error effects.