Estimation of a non-parametric variable importance measure of a continuous exposure
Chambaz, Antoine ; Neuvial, Pierre ; Van Der Laan, Mark
HAL, hal-00629899 / Harvested from HAL
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.
Publié le : 2012-07-05
Classification:  [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST],  [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]
@article{hal-00629899,
     author = {Chambaz, Antoine and Neuvial, Pierre and Van Der Laan, Mark},
     title = {Estimation of a non-parametric variable importance measure of a continuous exposure},
     journal = {HAL},
     volume = {2012},
     number = {0},
     year = {2012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00629899}
}
Chambaz, Antoine; Neuvial, Pierre; Van Der Laan, Mark. Estimation of a non-parametric variable importance measure of a continuous exposure. HAL, Tome 2012 (2012) no. 0, . http://gdmltest.u-ga.fr/item/hal-00629899/