  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.
