  Modeling the ratio of two dependent components as a function of covariates is
a frequently pursued objective in observational research. Despite the high
relevance of this topic in medical studies, where biomarker ratios are often
used as surrogate endpoints for specific diseases, existing models are based on
oversimplified assumptions, assuming e.g.\@ independence or strictly positive
associations between the components. In this paper, we close this gap in the
literature and propose a regression model where the marginal distributions of
the two components are linked by Frank copula. A key feature of our model is
that it allows for both positive and negative correlations between the
components, with one of the model parameters being directly interpretable in
terms of Kendall's rank correlation coefficient. We study our method
theoretically, evaluate finite sample properties in a simulation study and
demonstrate its efficacy in an application to diagnosis of Alzheimer's disease
via ratios of amyloid-beta and total tau protein biomarkers.
