Inference of a non-parametric covariate-adjusted variable importance measure of a continuous exposure

We consider a setting where a real-valued variable of cause X affects a real-valued variable of effect Y in the presence of a context variable W. The objective is to assess to what extent (X, W) influences Y while making as few assumptions as possible on the unknown distribution of (W, X, Y). Based on a user-supplied marginal structural model, our new variable importance measure is non-parametric and context-adjusted. It generalizes the variable importance measure introduced by Chambaz et al. [4]. We show how to infer it by targeted minimum loss estimation (TMLE), conduct a simulation study and present an illustration of its use.