Doubly structured sparsity for grouped multivariate responses with application to functional outcome score modeling

TL;DR

This paper introduces a novel regularization method for modeling multivariate responses with known interrelationships, improving variable selection and effect estimation without assuming normality, demonstrated through simulations and pediatric health data.

Contribution

It develops a doubly structured sparsity approach that jointly selects variables and shrinks effects for related responses, applicable to non-normal data.

Findings

Method achieves asymptotic efficiency similar to oracle knowledge.

Performs well in simulations with structured multivariate data.

Successfully predicts pediatric functional status from health records.

Abstract

This work is motivated by the need to accurately model a vector of responses related to pediatric functional status using administrative health data from inpatient rehabilitation visits. The components of the responses have known and structured interrelationships. To make use of these relationships in modeling, we develop a two-pronged regularization approach to borrow information across the responses. The first component of our approach encourages joint selection of the effects of each variable across possibly overlapping groups related responses and the second component encourages shrinkage of effects towards each other for related responses. As the responses in our motivating study are not normally-distributed, our approach does not rely on an assumption of multivariate normality of the responses. We show that with an adaptive version of our penalty, our approach results in the same asymptotic distribution of estimates as if we had known in advance which variables were non-zero and which variables have the same effects across some outcomes. We demonstrate the performance of our method in extensive numerical studies and in an application in the prediction of functional status of pediatric patients using administrative health data in a population of children with neurological injury or illness at a large children's hospital.