  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 esti-mators for treatment effect
estimators on continuous outcomes. Dose-response functions (DRF) 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 developped 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 to the
nominal value, particularly when the proportion of the variation in the
quantitative exposure explained by the covariates was 1 large. The stratified
estimator was more stable, and variance estima-tors (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.
