Shook-Sa, B. E., Zivich, P. N., Lee, C., Xue, K., Ross, R. K., Edwards, J. K., Stringer, J. S. A., & Cole, S. R. (2024). Double robust variance estimation with parametric working models. arXiv preprint arXiv:2404.16166v2.
This paper aims to compare three variance estimation methods for doubly robust estimators of the average causal effect (ACE) with observational data: the influence function based variance estimator, the empirical sandwich variance estimator, and the nonparametric bootstrap. The authors seek to demonstrate the superior performance of the empirical sandwich and bootstrap methods, which are doubly robust, over the influence function method, which is not.
The authors first describe three common doubly robust estimators of the ACE: the classic augmented inverse probability weighted (AIPW) estimator, the weighted regression AIPW estimator, and targeted maximum likelihood estimation (TMLE). They then detail the three variance estimation approaches and apply them to data from the Improving Pregnancy Outcomes with Progesterone (IPOP) study to estimate the effect of maternal anemia on birth weight among women with HIV. Finally, they conduct a simulation study to compare the empirical properties of the three variance estimators under various model misspecification scenarios.
The simulation study demonstrates that both the empirical sandwich variance estimator and the nonparametric bootstrap provide valid estimates of the variance and achieve nominal confidence interval coverage when at least one of the working models (propensity score or outcome model) is correctly specified. In contrast, the influence function based variance estimator is biased and inconsistent when either model is misspecified, leading to either conservative or anti-conservative confidence intervals.
The authors conclude that the empirical sandwich variance estimator and the nonparametric bootstrap are preferable to the influence function based variance estimator for doubly robust estimation of the ACE with observational data. They advocate for wider adoption of these doubly robust variance estimators in practice and highlight the limitations of the commonly used influence function approach.
This research has important implications for causal inference in epidemiology and other fields where doubly robust estimators are employed. By demonstrating the limitations of the influence function based variance estimator and advocating for alternative doubly robust approaches, the authors contribute to more accurate and reliable estimation of causal effects in observational studies.
The study focuses on the average causal effect with a binary exposure and parametric working models. Future research could extend these findings to other estimands, exposures, and modeling approaches, including machine learning methods. Additionally, the authors acknowledge limitations in the IPOP data analysis, suggesting alternative estimands and methods for handling competing events in future work.
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by Bonnie E. Sh... at arxiv.org 11-06-2024
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