[Paper Review] Causal inference for multiple continuous exposures via the multivariate generalized propensity score

Justin Williams, Catherine M. Crespi|arXiv (Cornell University)|Aug 31, 2020

Advanced Causal Inference Techniques4 citations

TL;DR

This paper proposes the multivariate generalized propensity score (mvGPS) method to estimate causal effects of multiple continuous exposures on an outcome using observational data. By assuming multivariate normality of exposures, mvGPS generates balancing weights to estimate a dose-response surface, reducing bias and improving covariate balance in simulations and a real-world study on childhood obesity interventions.

ABSTRACT

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.

Motivation & Objective

• To address the lack of methods for estimating joint causal effects of multiple continuous exposures in observational studies.
• To develop a multivariate extension of the generalized propensity score (GPS) that handles multiple simultaneous continuous exposures.
• To improve covariate balance across confounders that may differ in their association with each exposure.
• To estimate a dose-response surface for joint exposure effects using weighted regression.
• To validate the method through simulations and apply it to a real-world study on childhood obesity interventions.

Proposed method

• Assumes multivariate normality of the joint distribution of multiple continuous exposure variables.
• Uses conditional densities of each exposure given the others to derive weights via the multivariate normal distribution.
• Generates inverse probability weights based on the multivariate generalized propensity score (mvGPS) to balance confounders.
• Applies weighted regression to estimate the outcome as a function of the joint exposure values.
• Employs a convex hull-based approach to define estimable regions where exposure combinations are supported by observed data.
• Uses the multivariate normal density to compute the conditional probability of exposure given confounders, enabling weight calculation.

Experimental results

Research questions

• RQ1 Can the mvGPS method achieve better covariate balance across confounders that are differentially associated with each exposure?
• RQ2 How does mvGPS perform in reducing bias in treatment effect estimation compared to univariate GPS or unweighted methods?
• RQ3 What is the shape and interpretation of the dose-response surface for joint effects of two continuous exposures in a real-world setting?
• RQ4 How does the method perform under violations of multivariate normality or in high-dimensional exposure spaces?
• RQ5 Can mvGPS be used to identify optimal combinations of exposure levels that maximize or minimize the outcome?

Key findings

• The mvGPS method achieved superior balance compared to univariate GPS, reducing the maximum absolute correlation between confounders and exposures to below 0.1 and the average absolute correlation to nearly zero.
• In simulations, mvGPS reduced bias in treatment effect estimates across various data-generating scenarios, including when confounders had different associations with each exposure.
• The estimated dose-response surface from mvGPS weights differed substantially from the unweighted surface, indicating the presence of significant confounding in the original data.
• In the childhood obesity application, the most effective intervention combination was found to be higher levels of micro-strategies and lower levels of macro-strategies.
• The method demonstrated robustness to positivity issues within the convex hull of observed exposure combinations, though performance may degrade in higher dimensions.
• Despite assumptions of multivariate normality and SUTVA, the method provided a practical framework for estimating joint causal effects in non-randomized studies with multiple continuous exposures.