Health econometric evaluation of the effects of a continuous treatment: a machine learning approach

When the treatment under evaluation is continuous rather than binary, the marginal causal effect can be reported from the estimated dose-response function. Here, regression methods can be employed that specify a model for the endpoint, given the treatment and covariates. An alternative is to estimate the generalised propensity score (GPS), which can adjust by the conditional density of the treatment, given the covariates. Witheither regression or GPS approaches, model misspecification can lead to biased estimates. This paper introduces a machine learning approach, the “Super Learner†, to estimate both the GPS and the dose-response function. The Super Learner selects the convex combination of candidate estimation algorithms, to create new estimators. We take a two stage estimation approach whereby the Super Learner selects a GPS, and then a dose-response function conditional on the GPS. We compare this approach to parametric implementations of the GPS and regression methods. We contrast the methods in the Risk Adjustment In Neurocritical care (RAIN) cohort study, in which we estimate the marginal causal effects of increasing transfer time from emergency departments to specialised neuroscience centres, for patients with traumatic brain injury. With parametric models for the outcome we find that dose-response curves differ according to choice of parametric 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 outcome.