Evaluation of the Effect of a Continuous Treatment: A Machine Learning Approach with an Application to Treatment for Traumatic Brain Injury.

Noémi Kreif,Iván Díaz,Richard Grieve,David Harrison

doi:10.1002/hec.3189

Abstract

SummaryFor a continuous treatment, the generalised propensity score (GPS) is defined as the conditional density of the treatment, given covariates. GPS adjustment may be implemented by including it as a covariate in an outcome regression. Here, the unbiased estimation of the dose–response function assumes correct specification of both the GPS and the outcome‐treatment relationship. This paper introduces a machine learning method, the ‘Super Learner’, to address model selection in this context. In the two‐stage estimation approach proposed, the Super Learner selects a GPS and then a dose–response function conditional on the GPS, as the convex combination of candidate prediction algorithms. We compare this approach with parametric implementations of the GPS and to regression methods. We contrast the methods in the Risk Adjustment in Neurocritical care cohort study, in which we estimate the marginal effects of increasing transfer time from emergency departments to specialised neuroscience centres, for patients with acute traumatic brain injury. With parametric models for the outcome, we find that dose–response curves differ according to choice of specification. With the Super Learner approach to both regression and the GPS, we find that transfer time does not have a statistically significant marginal effect on the outcomes. © 2015 The Authors. Health Economics Published by John Wiley & Sons Ltd.

Highlights

Public policymakers may be interested in evaluations that estimate the causal effects of treatments measured on a continuous scale
The methods are contrasted in an empirical example, in which we evaluate the marginal causal effect of increasing the transfer time from an emergency department to specialist neuroscience centres for critically ill patients with traumatic brain injury (TBI)
This paper provides a framework for estimating marginal causal effects of continuous treatments that does not require the model for the generalised propensity score (GPS) or the outcome regression to be correctly specified

Summary

Introduction

Public policymakers may be interested in evaluations that estimate the causal effects of treatments measured on a continuous scale. Evaluations may attempt to estimate the marginal causal effects of alternative financial incentives for health care providers, different levels of taxation on addictive substances and increasing doses of a new pharmaceutical. In such settings, the expected outcome at alternative levels of the treatment can be reported from the estimated dose–response function. Regression approaches can be simple, for example, ordinary least squares regression, or can take more flexible forms such as fractional polynomials

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