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Double robust variance estimation with parametric working models.

Bonnie E Shook-Sa1, Paul N Zivich2, Chanhwa Lee1

  • 1Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States.

Biometrics
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Summary

Doubly robust variance estimators offer reliable causal inference. The empirical sandwich and bootstrap methods provide valid variance estimates when outcome or exposure models are correct, unlike traditional influence functions.

Keywords:
M-estimationaugmented inverse probability weightingcausal inferencedouble robustnessempirical sandwich variance

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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.