Generalized Variance Moderation for Locally Efficient Estimation in High-Dimensional Biology

Abstract

Exploratory analysis of high-dimensional biological data has received much attention since the explosion of high-throughput biotechnology enabled the simultaneous screening of thousands of molecular characteristics (genomics, metabolomics, proteomics, microbiomics, metallomics). Such analyses pose numerous challenges for statisticians and scientists. We focus on (1) how to derive estimation of independent associations (variable importance measures) in the context of many competing causes in a semiparametric statistical model, and (2) the use of robust variance estimators to enable small-sample inference when data-adaptive techniques are leveraged in such settings. We present an approach that constructs locally efficient estimators of causal parameters, rooted in the Targeted Learning framework, in the construction of nonparametric variable importance measures. The resultant estimates are equipped with scientifically convenient interpretations, under the standard assumptions of causal models, and are robust to model misspecification, since ensemble machine learning may be used in estimating relevant factors of the data-generating distribution. The estimators we present have closed-form representations based on influence functions, allowing for variance moderation to be applied in constructing robust hypothesis tests and confidence intervals. We illustrate the methodology by applying these approaches to high-dimensional data sets of relatively modest sample size, combining existing targeted maximum likelihood learning methods with a simple generalization of empirical Bayes approaches to improve the stability of estimators in small samples. The result is a machine learning-based approach that can estimate independent associations of biomarkers within high-dimensional data, teasing apart the effects of potential confounds and protecting against the unreliability introduced by small-sample inference. Time-permitting, we also discuss recently developed software (the biotmle R package: https://bioconductor.org/packages/biotmle) as well as methods to circumvent the statistical pitfalls of multiple comparisons.