Quantile Graph Discovery through QuACC: Quantile Association via Conditional Concordance

Abstract

Graphical structure learning is an effective way to assess and visualize cross-biomarker dependencies in biomedical settings. Standard approaches to estimating graphs rely on conditional independence tests that may not be sensitive to associations that manifest at the tails of joint distributions, i.e., they may miss connections among variables that exhibit associations mainly at lower or upper quantiles. In this work, we propose a novel measure of quantile-specific conditional association called QuACC: Quantile Association via Conditional Concordance. For a pair of variables and a conditioning set, QuACC quantifies agreement between the residuals from two quantile regression models, which may be linear or more complex, e.g., quantile forests. Using this measure as the basis for a test of null (quantile) association, we introduce a new class of quantile-specific graphical models. Through simulation we show our method is powerful for detecting dependencies under dependencies that manifest at the tails of distributions. We apply our method to biobank data from All of Us and identify quantile-specific patterns of conditional association in a multivariate setting. This is joint work with Zain Khan, Daniel Malinsky, Martin Picard, Alan A. Cohen and Columbia’s Columbia SOH Group.

• Department of Biomecical Engineering, Columbia University, New York, USA [zk2243@cumc.columbia.edu]

• Department of Biostatistics, Columbia University, New York, USA [dsm2128@cumc.columbia.edu]

• Robert N. Butler Columbia Aging Center, Columbia University, New York, USA [mp3484@cumc.columbia.edu]

• Robert N. Butler Columbia Aging Center,Columbia University, New York, USA [ad41@cumc.columbia.edu]

• Department of Biostatistics, Columbia University, New York, USA [yw2148@cumc.columbia.edu]

Keywords: Quantile Regression – Graphic Model – Robustness