A machine learning-based approach for estimating and testing associations with multivariate outcomes

TL;DR

This paper introduces a machine learning-based method to estimate and test associations between variable sets and multivariate outcomes, effectively capturing complex nonlinear relationships and interactions.

Contribution

It presents a novel ensemble machine learning approach for measuring and testing associations in multivariate data, outperforming traditional linear methods.

Findings

The proposed test has higher power than existing methods for nonlinear associations.

The method effectively captures complex relationships and interactions.

Application to cohort data demonstrates practical utility.

Abstract

We propose a method for summarizing the strength of association between a set of variables and a multivariate outcome. Classical summary measures are appropriate when linear relationships exist between covariates and outcomes, while our approach provides an alternative that is useful in situations where complex relationships may be present. We utilize ensemble machine learning to detect nonlinear relationships and covariate interactions and propose a measure of association that captures these relationships. A hypothesis test about the proposed associative measure can be used to test the strong null hypothesis of no association between a set of variables and a multivariate outcome. Simulations demonstrate that this hypothesis test has greater power than existing methods against alternatives where covariates have nonlinear relationships with outcomes. We additionally propose measures of variable importance for groups of variables, which summarize each groups' association with the outcome. We demonstrate our methodology using data from a birth cohort study on childhood health and nutrition in the Philippines.