Estimation of a non-parametric variable importance measure of a continuous exposure - Archive ouverte HAL
Article Dans Une Revue Electronic Journal of Statistics Année : 2012

Estimation of a non-parametric variable importance measure of a continuous exposure

Antoine Chambaz
Mark van Der Laan
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Résumé

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) [vanderLaan & 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.
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Dates et versions

hal-00629899 , version 1 (06-10-2011)

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Antoine Chambaz, Pierre Neuvial, Mark van Der Laan. Estimation of a non-parametric variable importance measure of a continuous exposure. Electronic Journal of Statistics , 2012, 6, pp.1059-1099. ⟨10.1214/12-EJS703⟩. ⟨hal-00629899⟩
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