Estimation and testing for multiple regulation of multivariate mixed outcomes

TL;DR

This paper introduces a novel estimation and testing framework for identifying multiple regulators affecting diverse multivariate outcomes, handling different data types and scales, with proven asymptotic properties and improved performance over existing methods.

Contribution

It proposes a new estimation technique that standardizes effects across different outcome types, induces sparsity, and includes a multiple testing procedure with asymptotic control of error rates.

Findings

The estimator achieves consistent asymptotic properties.

Resampling methods effectively quantify uncertainty.

Simulation shows improved bias reduction and testing power.

Abstract

Considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies, either to capture the multidimensionality of complex disorders or to understand shared etiology of related disorders. We seek to identify {\em multiple regulators} or predictors that are associated with multiple outcomes when these outcomes may be measured on very different scales or composed of a mixture of continuous, binary, and not-fully-observed elements. We first propose an estimation technique to put all effects on similar scales, and we induce sparsity on the estimated effects. We provide standard asymptotic results for this estimator and show that resampling can be used to quantify uncertainty in finite samples. We finally provide a multiple testing procedure which can be geared specifically to the types of multiple regulators of interest, and we establish that, under standard regularity conditions, the familywise error rate will approach 0 as sample size diverges. Simulation results indicate that our approach can improve over unregularized methods both in reducing bias in estimation and improving power for testing.