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.
Keywords: generalized propensity score; observational study; quantitative exposure; variance estimator.
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