Robust inference of conditional average treatment effects using dimension reduction

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Personalized treatment requires understanding how treatment effects vary across individuals (CATE).
• Estimating CATE from observational data is challenging due to multivariate confounders and the curse of dimensionality.

Purpose of the Study:

• To develop a robust method for inferring CATE from observational data.
• To address the curse of dimensionality while retaining nonparametric advantages.

Main Methods:

• Propose double dimension reduction: identifying the central mean subspace of CATE and using nonparametric regression with prior dimension reduction for counterfactual imputation.
• Establish asymptotic properties of the proposed estimator considering the two-step double dimension reduction.
• Develop an effective bootstrapping procedure for valid inferences without bootstrapping the estimated central mean subspace.

Main Results:

• The proposed double dimension reduction method effectively reduces dimensionality.
• The imputation of counterfactual outcomes is stabilized.
• Asymptotic properties are established, and a valid bootstrapping procedure is proposed.
• Simulations and applications demonstrate superior performance compared to existing methods.

Conclusions:

• The proposed method offers a robust and efficient approach for CATE estimation from observational data.
• This facilitates more accurate personalized treatment strategies.
• The methodology addresses key challenges in high-dimensional causal inference.