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This work is motivated by the need to accurately model a vector of responsesrelated to pediatric functional status using administrative health data frominpatient rehabilitation visits. The components of the responses have known andstructured interrelationships. To make use of these relationships in modeling,we develop a two-pronged regularization approach to borrow information acrossthe responses. The first component of our approach encourages joint selectionof the effects of each variable across possibly overlapping groups relatedresponses and the second component encourages shrinkage of effects towards eachother for related responses. As the responses in our motivating study are notnormally-distributed, our approach does not rely on an assumption ofmultivariate normality of the responses. We show that with an adaptive versionof our penalty, our approach results in the same asymptotic distribution ofestimates as if we had known in advance which variables were non-zero and whichvariables have the same effects across some outcomes. We demonstrate theperformance of our method in extensive numerical studies and in an applicationin the prediction of functional status of pediatric patients usingadministrative health data in a population of children with neurological injuryor illness at a large children's hospital.

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