Neural Networks to Estimate Generalized Propensity Scores for Continuous Treatment Doses

Abstract

Background: The generalized propensity score (GPS) addresses selection bias due to observed confounding variables and provides a means to demonstrate causality of continuous treatment doses with propensity score analyses. Estimating the GPS with parametric models obliges researchers to meet improbable conditions such as correct model specification, normal distribution of variables, and large sample sizes. Objectives: The purpose of this Monte Carlo simulation study is to examine the performance of neural networks as compared to full factorial regression models to estimate GPS in the presence of Gaussian and skewed treatment doses and small to moderate sample sizes. Research design: A detailed conceptual introduction of neural networks is provided, as well as an illustration of selection of hyperparameters to estimate GPS. An example from public health and nutrition literature uses residential distance as a treatment variable to illustrate how neural networks can be used in a propensity score analysis to estimate a dose–response function of grocery spending behaviors. Results: We found substantially higher correlations and lower mean squared error values after comparing true GPS with the scores estimated by neural networks. The implication is that more selection bias was removed using GPS estimated with neural networks than using GPS estimated with classical regression. Conclusions: This study proposes a new methodological procedure, neural networks, to estimate GPS. Neural networks are not sensitive to the assumptions of linear regression and other parametric models and have been shown to be a contender against parametric approaches to estimate propensity scores for continuous treatments.