Exploratory analysis of high dimensional u22omicsu22 data has received much attention since the explosion of high-throughput technology allows simultaneous screening of tens of thousands of characteristics (genomics, metabolomics, proteomics, adducts, etc., etc.). Part of this trend has been an increase in the dimension of exposure data in studies of environmental exposure and associated biomarkers. Though some of the general approaches, such as GWAS, are transferable, what has received less focus is 1) how to derive estimation of independent associations in the context of many competing causes, without resorting to a misspecified model, and 2) how to derive accurate small-sample inference when data adaptive techniques are used in this context. This paper focuses on semi-parametric variable importance analysis of high dimensional data sets of modest sample size (e.g., gene expression, mRNA, etc). Though the methodology we propose is generally applicable to similar situations, we present the method in the context of a study of miRNA expression for an environmental exposure. Specifically, the analysis is faced with not just a large number of comparisons, but also trying to tease out of association of the expression of miRNA with an exposure apart from confounds such as age, race, smoking conditions, BMI, etc. Our goal is to propose a method that is reasonably robust in small samples, but does not rely on misspecified (arbitrary) parametric assumptions, and thus will be based on data-adaptive methods. The methodology proposed is we believe a powerful combination of existing semi-parametric statistical methods and theory, as well as a simple framework for use of commonly used empirical Bayes approaches to aid in small sample inference. Specifically, We propose using targeted maximum likelihood estimation (TMLE) for estimating variable importance measures along with a general adaptation of the commonly used Limma approach, which relies on specification of the so-called influence curve of the proposed estimator. The result is a machine-based approach that can estimate independent associations in high dimensional data, but protects against the unreliability of small-sample inference that can result when using data adaptive estimation in relatively small samples.
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