  Weighted estimators are commonly used for estimating exposure effects in
observational settings to establish causal relations. These estimators have a
long history of development when the exposure of interest is binary and where
the weights are typically functions of an estimated propensity score. Recent
developments in optimization-based estimators for constructing weights in
binary exposure settings, such as those based on entropy balancing, have shown
more promise in estimating treatment effects than those methods that focus on
the direct estimation of the propensity score using likelihood-based methods.
This paper explores recent developments of entropy balancing methods to
continuous exposure settings and the estimation of population dose-response
curves using nonparametric estimation combined with entropy balancing weights,
focusing on factors that would be important to applied researchers in medical
or health services research. The methods developed here are applied to data
from a study assessing the effect of non-randomized components of an
evidence-based substance use treatment program on emotional and substance use
clinical outcomes.
