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

Causal inference for multiple continuous exposures via the multivariate generalized propensity score