Propensity score methods are widely used in observational studies for evaluating marginal treatment effects. The generalized propensity score (GPS) is an extension of the propensity score framework, historically developed in the case of binary exposures, for use with quantitative or continuous exposures. In this paper, we proposed variance estimators for treatment effect estimators on continuous outcomes. Dose–response functions (DRFs) were estimated through weighting on the inverse of the GPS, or using stratification. Variance estimators were evaluated using Monte Carlo simulations. Despite the use of stabilized weights, the variability of the weighted estimator of the DRF was particularly high, and none of the variance estimators (a bootstrap-based estimator, a closed-form estimator especially developed to take into account the estimation step of the GPS, and a sandwich estimator) were able to adequately capture this variability, resulting in coverages below the nominal value, particularly when the proportion of the variation in the quantitative exposure explained by the covariates was large. The stratified estimator was more stable, and variance estimators (a bootstrap-based estimator, a pooled linearized estimator, and a pooled model-based estimator) more efficient at capturing the empirical variability of the parameters of the DRF. The pooled variance estimators tended to overestimate the variance, whereas the bootstrap estimator, which intrinsically takes into account the estimation step of the GPS, resulted in correct variance estimations and coverage rates. These methods were applied to a real data set with the aim of assessing the effect of maternal body mass index on newborn birth weight.

中文翻译：

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使用广义倾向评分的加权和分层线性剂量反应函数估计的方差估计

倾向评分方法广泛用于评估边际治疗效果的观察性研究。广义倾向得分 (GPS) 是倾向得分框架的扩展，历史上是在二元暴露的情况下开发的，用于定量或连续暴露。在本文中，我们提出了用于连续结果的治疗效果估计量的方差估计量。剂量反应函数 (DRFs) 通过对 GPS 的倒数加权或使用分层来估计。使用蒙特卡罗模拟评估方差估计量。尽管使用了稳定权重，但 DRF 的加权估计量的可变性特别高，并且没有一个方差估计量（基于 bootstrap 的估计量，一个封闭式估计器，特别是为了考虑 GPS 的估计步骤而开发的，以及一个三明治估计器）能够充分捕捉这种可变性，导致覆盖率低于标称值，特别是当定量暴露的变化比例由协变量解释的很大。分层估计器更稳定，方差估计器（基于引导的估计器、合并的线性化估计器和基于合并模型的估计器）在捕获 DRF 参数的经验可变性方面更有效。合并方差估计器倾向于高估方差，而自举估计器本质上考虑了 GPS 的估计步骤，导致正确的方差估计和覆盖率。