  Capturing complex dependence structures between outcome variables (e.g.,
study endpoints) is of high relevance in contemporary biomedical data problems
and medical research. Distributional copula regression provides a flexible tool
to model the joint distribution of multiple outcome variables by disentangling
the marginal response distributions and their dependence structure. In a
regression setup each parameter of the copula model, i.e. the marginal
distribution parameters and the copula dependence parameters, can be related to
covariates via structured additive predictors. We propose a framework to fit
distributional copula regression models via a model-based boosting algorithm.
Model-based boosting is a modern estimation technique that incorporates useful
features like an intrinsic variable selection mechanism, parameter shrinkage
and the capability to fit regression models in high dimensional data setting,
i.e. situations with more covariates than observations. Thus, model-based
boosting does not only complement existing Bayesian and maximum-likelihood
based estimation frameworks for this model class but rather enables unique
intrinsic mechanisms that can be helpful in many applied problems. The
performance of our boosting algorithm in the context of copula regression
models with continuous margins is evaluated in simulation studies that cover
low- and high-dimensional data settings and situations with and without
dependence between the responses. Moreover, distributional copula boosting is
used to jointly analyze and predict the length and the weight of newborns
conditional on sonographic measurements of the fetus before delivery together
with other clinical variables.
