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Parameterising and inferring the effect of a continuous exposure using average derivative effects

Centre for Statistical Methodology seminar series - missing data and causal inference theme 

There is an increased awareness of the importance of non-parametrically defining the causal effect measure of interest prior to any modelling of the data. This is relatively easily done when the exposure is binary, but much less straightforward when continuous exposures are considered. 

With clear interventions in mind, initially, the focus on estimands that express the effect of shifting the exposure distribution in a certain, pre-specified way. However, in an exploratory phase of the study, or when shift interventions are not immediately intended to be rolled out, there is a need for estimands that capture the effect of exposure on outcome in a more generic way.  

In this talk, we will summarise conditional exposure effects based on weighted average derivative effects. These express the effect of a small change in the exposure and, depending on the chosen weights, encompass several estimands that have been previously proposed in the literature. The proposed estimands have several appealing properties when the conditional mean outcome is smooth in the exposure (in the sense of being differentiable with respect to the exposure): they can be causally expressed in terms of counterfactuals when standard exchangeability assumptions are met and can moreover be linked to parameters indexing a novel class of models. However, they remain well-defined when the conditional mean outcome lacks sufficient smoothness. We develop data-adaptive inference for the considered estimands by deriving their efficient influence function and using it as the basis for a one-step estimator. We moreover show that the recently proposed R-learner delivers an estimator of an (optimal) exposure effect in our class. 

This talk is relevant to statisticians and epidemiologists interested in non-parametric estimation for continuous exposures.    

Speaker 

Oliver Hines, PhD student, Medical Statistics department, London School of Hygiene & Tropical Medicine (LSHTM)

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