Variance estimation for the average treatment effects on the treated and on the controls

Area of Science:

• Causal Inference
• Biostatistics
• Epidemiology

Background:

• Doubly robust estimators, combining augmented inverse probability weighting with parametric models, offer consistent estimation of causal effects when at least one model is correctly specified.
• Estimating the variance of these doubly robust estimators involves uncertainties from treatment and outcome regression models, and treatment effect estimation.
• Common causal estimands include average treatment effect, average treatment effect of the treated, and average treatment effect on the controls.

Purpose of the Study:

• To propose and investigate methods for calculating the variance of normalized, doubly robust average treatment effect of the treated and average treatment effect on the controls estimators.
• To assess the finite sample properties of these proposed variance estimation methods.
• To address uncertainties in variance estimation for causal effect inference.

Main Methods:

• Proposed methods for variance calculation using estimating equations for asymptotic approximations.
• Investigated standard bootstrap and two wild bootstrap methods, utilizing perturbations of influence functions with independent random variables.
• Conducted an extensive simulation study varying treatment effect heterogeneity and active treatment group proportion.

Main Results:

• The proposed wild bootstrap methods offer an alternative to standard bootstrap by using perturbations of influence functions.
• Simulation studies provide insights into the finite sample properties of the proposed variance estimation techniques.
• The methods were illustrated using an observational study on right heart catheterization in critically ill patients.

Conclusions:

• The developed methods provide a robust framework for variance estimation in doubly robust causal inference.
• These techniques enhance the reliability of estimating treatment effects in observational data.
• The study contributes to the accurate application of causal inference methods in medical research.