Abstract

In this talk, we will define a new class of statistical parameters which we call non-parametric variable importance (NPVI) measures. They extend the notion of variable importance measure of a discrete ’cause’ onto an ’effect’ accounting for potential confounders to the case where the ’cause’ is continuous. They are non-parametric in the sense that it is not necessary to assume that a specific semi-parametric model holds. We will show how to carry out the estimation of such a NPVI measure following the targeted minimum loss estimation (TMLE) methodology. Some important asymptotic properties of the TMLE estimator (robustness, asymptotic normality) will be stated. The talk will be illustrated with a simulation study inspired by biological question of interest and a dataset from the Cancer Genome Atlas (TCGA) and with a real data application. Indeed, looking for genes whose DNA copy number (the ’cause’) is significantly associated with their expression level (’the effect’) in a cancer study can help pinpoint candidates implied in the disease and improve on our understanding of its molecular bases. DNA methylation (potential confounder) is an important player to account for in this setting, as it can down-regulate gene expression and may also influence DNA copy number. This is joint work with Pierre Neuvial and Mark van der Laan.