  The generalized propensity score (GPS) is an extension of the propensity
score for use with quantitative or continuous exposures (e.g., dose of
medication or years of education). Current GPS methods allow estimation of the
dose-response relationship between a single continuous exposure and an outcome.
However, in many real-world settings, there are multiple exposures occurring
simultaneously that could be causally related to the outcome. We propose a
multivariate GPS method (mvGPS) that allows estimation of a dose-response
surface that relates the joint distribution of multiple continuous exposure
variables to an outcome. The method involves generating weights under a
multivariate normality assumption on the exposure variables. Focusing on
scenarios with two exposure variables, we show via simulation that the mvGPS
method can achieve balance across sets of confounders that may differ for
different exposure variables and reduces bias of the treatment effect estimates
under a variety of data generating scenarios. We apply the mvGPS method to an
analysis of the joint effect of two types of intervention strategies to reduce
childhood obesity rates.
