Semiparametric Correlation Estimation in Multivariate BWAS

Music City Center 

Multivariate brain-wide association studies (BWAS) use machine learning (ML) models to predict phenotypes from high-dimensional brain imaging. For continuous predicted features, Pearson's correlation between the predicted feature and actual feature is often used to quantify model accuracy in test data; however, the parameter this is meant to estimate is not explicit. We rigorously define multiple parameters and show that the standard Pearson estimator is biased for the typical parameter of interest in multivariate BWAS studies. Using flexible ML models affects the rate of convergence to the true parameter, and the sample size needed to converge is often larger than existing neuroimaging datasets. Additionally, the typical Fisher confidence intervals for Pearson's correlation undercover. We use semiparametric theory to present a new estimator based on the efficient influence function of the target parameter. This estimator converges to the parameter in reasonable sample sizes and admits a confidence interval procedure that achieves nominal or near-nominal coverage. We show how researchers can provide estimates, confidence intervals, and p-values (without the need for permutation testing) for model accuracy.

machine learning

brain-wide association studies

correlation

semiparametric

prediction

neuroimaging 

Section on Statistics in Imaging