A generalization of moderated statistics to data adaptive semiparametric estimation in high-dimensional biology
The widespread availability of high-dimensional biological sequencing data has made the simultaneous screening of numerous biological characteristics a central statistical problem in computational biology. While the dimensionality of such data sets continues to increase, the problem of teasing out the effects of biomarkers in studies measuring baseline confounders while avoiding model misspecification remains only partially addressed. Efficient estimators constructed from data adaptive estimates of nuisance functions provide an avenue for avoiding model misspecification; however, in the context of high-dimensional problems requiring simultaneous estimation of numerous parameters, standard variance estimators have proven unstable, resulting in unreliable Type-I error control under standard multiple testing corrections. We present the formulation of a general approach for applying variance moderation strategies to asymptotically linear estimators of parameters defined in the nonparametric model, for which a standard variance estimator is constructed from estimation of an influence function. A methodology for nonparametric variable importance analysis for use with high-dimensional biological data sets with modest sample sizes is introduced and the proposed technique is demonstrated to be robust in small samples even when relying on data adaptive estimators that eschew parametric forms. The general methodology is demonstrated in the context of targeted minimum loss estimation, with simulation studies comparing the merits of the proposed variance moderation approach to both the standard variance estimator and a linear modeling strategy with moderated inference. Application to an observational study of occupational exposure is presented to demonstrate the construction of stabilized variable importance measures of individual biomarkers.