{"title":"Variance estimation for average treatment effects estimated by g-computation","authors":"Stefan Nygaard Hansen, Morten Overgaard","doi":"10.1007/s00184-024-00962-4","DOIUrl":null,"url":null,"abstract":"<p>The average treatment effect is used to evaluate effects of interventions in a population. Under certain causal assumptions, such an effect may be estimated from observational data using the g-computation technique. The asymptotic properties of this estimator appears not to be well-known and hence bootstrapping has become the preferred method for estimating its variance. Bootstrapping is, however, not an optimal choice for multiple reasons; it is a slow procedure and, if based on too few bootstrap samples, results in a highly variable estimator of the variance. In this paper, we consider estimators of potential outcome means and average treatment effects using g-computation. We consider these parameters for the entire population but also in subgroups, for example, the average treatment effect among the treated. We derive their asymptotic distributions in a general framework. An estimator of the asymptotic variance is proposed and shown to be consistent when g-computation is used in conjunction with the M-estimation technique. The proposed estimator is shown to be superior to the bootstrap technique in a simulation study. Robustness against model misspecification is also demonstrated by means of simulations.</p>","PeriodicalId":49821,"journal":{"name":"Metrika","volume":"17 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Metrika","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00184-024-00962-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
The average treatment effect is used to evaluate effects of interventions in a population. Under certain causal assumptions, such an effect may be estimated from observational data using the g-computation technique. The asymptotic properties of this estimator appears not to be well-known and hence bootstrapping has become the preferred method for estimating its variance. Bootstrapping is, however, not an optimal choice for multiple reasons; it is a slow procedure and, if based on too few bootstrap samples, results in a highly variable estimator of the variance. In this paper, we consider estimators of potential outcome means and average treatment effects using g-computation. We consider these parameters for the entire population but also in subgroups, for example, the average treatment effect among the treated. We derive their asymptotic distributions in a general framework. An estimator of the asymptotic variance is proposed and shown to be consistent when g-computation is used in conjunction with the M-estimation technique. The proposed estimator is shown to be superior to the bootstrap technique in a simulation study. Robustness against model misspecification is also demonstrated by means of simulations.
平均治疗效果用于评估干预措施在人群中的效果。在某些因果假设条件下,可以使用 g 计算技术从观察数据中估算出平均治疗效果。这种估计方法的渐近特性似乎并不为人所知,因此引导法成为估计其方差的首选方法。然而,由于多种原因,自举法并不是最佳选择;它是一个缓慢的过程,而且如果基于过少的自举样本,会导致方差估计值的高度可变性。在本文中,我们考虑使用 g 计算来估计潜在结果均值和平均治疗效果。我们不仅考虑了整个人群的这些参数,还考虑了子群中的这些参数,例如,受治疗者的平均治疗效果。我们在一般框架下推导出它们的渐近分布。我们提出了一个渐近方差估计器,并证明当 g 计算与 M 估计技术结合使用时,该估计器是一致的。模拟研究表明,所提出的估计方法优于自举技术。此外,还通过模拟研究证明了该方法对模型错误规范的稳健性。
期刊介绍:
Metrika is an international journal for theoretical and applied statistics. Metrika publishes original research papers in the field of mathematical statistics and statistical methods. Great importance is attached to new developments in theoretical statistics, statistical modeling and to actual innovative applicability of the proposed statistical methods and results. Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.