Skip to main content
Estimation of a Non-Parametric Variable Importance Measure of a Continuous Exposure
U.C. Berkeley Division of Biostatistics Working Paper Series
  • Chambaz Antoine, MAPS, Université Paris Descartes and CNRS
  • Pierre Neuvial, Laboratoire Statistique et Génome, Université d'Evry Val d'Essonne, UMR CNRS 8071 -- USC INRA
  • Mark J. van der Laan, University of California, Berkeley; School of Public Health, Division of Biostatistics
Date of this Version

We define a new measure of variable importance of an exposure on a continuous outcome, accounting for potential confounders. The exposure features a reference level x0 with positive mass and a continuum of other levels. For the purpose of estimating it, we fully develop the semi-parametric estimation methodology called targeted minimum loss estimation methodology (TMLE) [van der Laan & Rubin, 2006; van der Laan & Rose, 2011]. We cover the whole spectrum of its theoretical study (convergence of the iterative procedure which is at the core of the TMLE methodology; consistency and asymptotic normality of the estimator), practical implementation, simulation study and application to a genomic example that originally motivated this article. In the latter, the exposure X and response Y are, respectively, the DNA copy number and expression level of a given gene in a cancer cell. Here, the reference level is x0=2, that is the expected DNA copy number in a normal cell. The confounder is a measure of the methylation of the gene. The fact that there is no clear biological indication that X and Y can be interpreted as an exposure and a response, respectively, is not problematic.

Citation Information
Chambaz Antoine, Pierre Neuvial and Mark J. van der Laan. "Estimation of a Non-Parametric Variable Importance Measure of a Continuous Exposure" (2011)
Available at: