For robust statistical inference it is crucial to obtain a good estimator of the variance of the proposed estimator of the statistical estimand. A commonly used estimator of the variance for an asymptotically linear estimator is the sample variance of the estimated influence function. This estimator has been shown to be anti-conservative in limited samples or in the presence of near-positivity violations, leading to elevated Type-I error rates and poor coverage. In this paper, capitalizing on earlier attempts at targeted variance estimators, we propose a one-step targeted variance estimator for the causal risk ratio (CRR) in scenarios involving treatment, outcome, and baseline covariates. While our primary focus is on the variance of log(CRR), our methodology can be extended to other causal effect parameters. Specifically, we focus on the variance of the IF for the log relative risk (log(CRR)) estimator, which requires deriving the efficient influence function for the variance of the IF as the basis for constructing the estimator. Several methods are available to develop efficient estimators of asymptotically linear parameters. In this paper, we concentrate on the so-called one-step targeted maximum likelihood estimator, which is a substitution estimator that utilizes a one-dimensional universal least favorable parametric submodel when updating the distribution. We conduct simulations with different effect sizes, sample sizes and levels of positivity to compare the estimator with existing methods in terms of coverage and Type-I error. Simulation results demonstrate that, especially with small samples and near-positivity violations, the proposed variance estimator offers improved performance, achieving coverage closer to the nominal level of 0.95 and a lower Type-I error rate.

翻译：为了进行稳健的统计推断，获得所提出的统计量估计量方差的一个良好估计量至关重要。对于渐近线性估计量，常用的方差估计量是估计影响函数的样本方差。已有研究表明，该估计量在有限样本或存在近似正性违例的情况下是反保守的，会导致I类错误率升高和覆盖率不佳。本文基于早期针对目标方差估计量的尝试，提出了一种在涉及处理、结果和基线协变量的场景中，用于因果风险比（CRR）的一步目标方差估计量。虽然我们的主要关注点是log(CRR)的方差，但我们的方法可以扩展到其他因果效应参数。具体而言，我们关注对数相对风险（log(CRR)）估计量的影响函数（IF）的方差，这需要推导出该IF方差的有效影响函数，作为构建估计量的基础。目前已有多种方法可用于开发渐近线性参数的有效估计量。在本文中，我们专注于所谓的一步目标最大似然估计量，这是一种替代估计量，在更新分布时使用一维通用最小有利参数子模型。我们通过模拟不同效应大小、样本量和正性水平，在覆盖率和I类错误方面将该估计量与现有方法进行比较。模拟结果表明，特别是在小样本和存在近似正性违例的情况下，所提出的方差估计量具有改进的性能，实现了更接近0.95名义水平的覆盖率以及更低的I类错误率。