Boosting Multivariate Structured Additive Distributional Regression Models

TL;DR

This paper introduces a boosting method for multivariate distributional regression that models all distribution parameters simultaneously, handles high-dimensional data, and captures associations between multiple outcomes, demonstrated through diverse biomedical applications.

Contribution

It presents a novel boosting approach for multivariate distributional regression that models all parameters and their associations, with data-driven variable selection in high-dimensional settings.

Findings

Successfully identified genetic variants linked to disease association.

Effectively modeled healthcare demand with count data.

Revealed age and regional differences in childhood undernutrition correlations.

Abstract

We develop a model-based boosting approach for multivariate distributional regression within the framework of generalized additive models for location, scale, and shape. Our approach enables the simultaneous modeling of all distribution parameters of an arbitrary parametric distribution of a multivariate response conditional on explanatory variables, while being applicable to potentially high-dimensional data. Moreover, the boosting algorithm incorporates data-driven variable selection, taking various different types of effects into account. As a special merit of our approach, it allows for modelling the association between multiple continuous or discrete outcomes through the relevant covariates. After a detailed simulation study investigating estimation and prediction performance, we demonstrate the full flexibility of our approach in three diverse biomedical applications. The first is based on high-dimensional genomic cohort data from the UK Biobank, considering a bivariate binary response (chronic ischemic heart disease and high cholesterol). Here, we are able to identify genetic variants that are informative for the association between cholesterol and heart disease. The second application considers the demand for health care in Australia with the number of consultations and the number of prescribed medications as a bivariate count response. The third application analyses two dimensions of childhood undernutrition in Nigeria as a bivariate response and we find that the correlation between the two undernutrition scores is considerably different depending on the child's age and the region the child lives in.