Double robust variance estimation with parametric working models

Area of Science:

• Epidemiology
• Biostatistics
• Causal Inference

Background:

• Doubly robust (DR) estimators are popular in causal inference for consistent estimates when outcome or exposure models are correctly specified.
• Traditional influence function-based variance estimators for DR estimators lack robustness, requiring correct specification of both models for consistency.
• This limitation is particularly relevant for nonrandomized exposures where model misspecification is common.

Purpose of the Study:

• To evaluate the doubly robust properties of empirical sandwich and nonparametric bootstrap variance estimators.
• To compare the performance of these estimators against the traditional influence function-based estimator.
• To assess the validity of variance estimation and confidence interval coverage under model misspecification.

Main Methods:

• The study theoretically demonstrates that empirical sandwich and nonparametric bootstrap variance estimators are doubly robust.
• Simulation studies were conducted assuming parametric working models to compare the performance of different variance estimators.
• The estimators were applied to real-world data from the Improving Pregnancy Outcomes with Progesterone (IPOP) study.

Main Results:

• Empirical sandwich and nonparametric bootstrap variance estimators demonstrated doubly robust properties.
• These methods provide valid variance estimates and nominal confidence interval coverage when at least one working model (outcome or exposure) is correctly specified.
• Simulation results confirmed the theoretical findings, highlighting the robustness of these alternative variance estimators.

Conclusions:

• Empirical sandwich and nonparametric bootstrap variance estimators offer more reliable variance estimation in causal inference compared to the traditional influence function-based approach, especially with nonrandomized exposures.
• These robust methods enhance the validity of confidence intervals when working models may be misspecified.
• The findings support the use of these doubly robust variance estimators for improved causal effect estimation in observational studies.