Doubly robust estimators have gained popularity in the field of causal inference due to their ability to provide consistent point estimates when either an outcome or exposure model is correctly specified. However, for nonrandomized exposures the influence function based variance estimator frequently used with doubly robust estimators of the average causal effect is only consistent when both working models (i.e., outcome and exposure models) are correctly specified. Here, the empirical sandwich variance estimator and the nonparametric bootstrap are demonstrated to be doubly robust variance estimators. That is, they are expected to provide valid estimates of the variance leading to nominal confidence interval coverage when only one working model is correctly specified. Simulation studies illustrate the properties of the influence function based, empirical sandwich, and nonparametric bootstrap variance estimators in the setting where parametric working models are assumed. Estimators are applied 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.

翻译：在因果推断领域，双稳健估计量因其能够在结果模型或暴露模型中至少一个被正确设定时提供一致的点估计而广受欢迎。然而，对于非随机暴露，常用于平均因果效应双稳健估计量的基于影响函数的方差估计量，仅当两个工作模型（即结果模型和暴露模型）均被正确设定时才具有一致性。本文证明，经验三明治方差估计量与非参数自助法均为双稳健方差估计量。也就是说，当仅有一个工作模型被正确设定时，它们预期能提供有效的方差估计，从而获得名义置信区间覆盖率。模拟研究展示了在假定参数工作模型的设定下，基于影响函数的、经验三明治的以及非参数自助法方差估计量的性质。将估计量应用于"孕酮改善妊娠结局"研究的数据，以估计HIV感染孕妇中母体贫血对新生儿出生体重的影响。