High-dimensional model-assisted inference for treatment effects with multi-valued treatments

Area of Science:

• Statistics
• Causal Inference
• Econometrics

Background:

• Estimating average treatment effects (ATE) with multi-valued treatments in high-dimensional settings presents challenges.
• Existing methods using augmented inverse probability weighted (IPW) estimators often struggle with separate fitting of outcome regression and propensity score models.
• Regularized likelihood-based estimation can lead to difficulties in subsequent treatment parameter inference.

Purpose of the Study:

• To develop a novel regularized calibrated estimation framework for fitting propensity score and outcome regression models.
• To ensure valid confidence intervals under potential model misspecification.
• To generalize the augmented IPW estimator for multi-valued treatments and achieve covariate balance.

Main Methods:

• Employing sparsity-including penalties for variable selection in high-dimensional settings.
• Utilizing carefully chosen loss functions for valid statistical inference.
• Generalizing the augmented IPW estimator with new calibration equations for just-identification.
• Developing practical algorithms using group Lasso and Fisher scoring for computation.
• Providing rigorous high-dimensional analysis under sparsity conditions.

Main Results:

• The proposed regularized calibrated estimation facilitates variable selection while ensuring valid confidence intervals.
• The generalized augmented IPW estimator achieves just-identification and covariate balance.
• Rigorous theoretical analysis confirms the validity of the estimators under sparsity.
• Simulation studies and an empirical application demonstrate the practical utility of the methods.

Conclusions:

• Regularized calibrated estimation offers a robust approach for ATE estimation with multi-valued treatments in high-dimensional data.
• The developed methods address limitations of existing techniques, particularly regarding model misspecification and inference.
• The R package mRCAL provides a practical implementation for researchers.