Boosting Distributional Copula Regression for Bivariate Binary, Discrete and Mixed Responses

TL;DR

This paper introduces a scalable boosting method for modeling complex bivariate responses with arbitrary marginals and copulas, enabling flexible, data-driven analysis of diverse biomedical data.

Contribution

It develops a novel boosting framework for joint distribution modeling with covariate effects on both marginals and copula parameters, integrating variable selection and shrinkage.

Findings

Effective modeling of diverse biomedical data types

Implementation in R package gamboostLSS

Versatile application to genetic and healthcare data

Abstract

Motivated by challenges in the analysis of biomedical data and observational studies, we develop statistical boosting for the general class of bivariate distributional copula regression with arbitrary marginal distributions, which is suited to model binary, count, continuous or mixed outcomes. In our framework, the joint distribution of arbitrary, bivariate responses is modelled through a parametric copula. To arrive at a model for the entire conditional distribution, not only the marginal distribution parameters but also the copula parameters are related to covariates through additive predictors. We suggest efficient and scalable estimation by means of an adapted component-wise gradient boosting algorithm with statistical models as base-learners. A key benefit of boosting as opposed to classical likelihood or Bayesian estimation is the implicit data-driven variable selection mechanism as well as shrinkage without additional input or assumptions from the analyst. To the best of our knowledge, our implementation is the only one that combines a wide range of covariate effects, marginal distributions, copula functions, and implicit data-driven variable selection. We showcase the versatility of our approach on data from genetic epidemiology, healthcare utilization and childhood undernutrition. Our developments are implemented in the R package gamboostLSS, fostering transparent and reproducible research.