Inverse probability of treatment weights (IPTWs) are commonly used to control for confounding when estimating causal effects of point exposures from observational data. When planning a study that will be analyzed with IPTWs, determining the required sample size for a given level of statistical power is challenging because of the effect of weighting on the variance of the estimated causal means. This paper considers the utility of the design effect to quantify the effect of weighting on the precision of causal estimates. The design effect is defined as the ratio of the variance of the causal mean estimator divided by the variance of a naïve estimator if, counter to fact, no confounding had been present and weights were not needed. A simple, closed-form approximation of the design effect is derived that is outcome invariant and can be estimated during the study design phase. Once the design effect is approximated for each treatment group, sample size calculations are conducted as for a randomized trial, but with variances inflated by the design effects to account for weighting. Simulations demonstrate the accuracy of the design effect approximation, and practical considerations are discussed.

中文翻译：

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点曝光效应观察研究的功效和样本量

在根据观察数据估计点暴露的因果效应时，治疗权重的逆概率 (IPTW) 通常用于控制混杂。在计划将使用 IPTW 进行分析的研究时，确定给定统计功效水平所需的样本量具有挑战性，因为加权对估计因果均值的方差有影响。本文考虑了设计效果的效用量化加权对因果估计精度的影响。如果与事实相反，不存在混杂且不需要权重，则设计效果定义为因果均值估计量的方差除以朴素估计量的方差的比率。导出了设计效果的简单、封闭形式的近似值，它是结果不变的，可以在研究设计阶段进行估计。一旦对每个治疗组的设计效果进行了近似计算，就可以像随机试验一样进行样本量计算，但方差会因设计效果而膨胀以说明权重。仿真证明了设计效果近似的准确性，并讨论了实际考虑因素。