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@ARTICLE{Berger:279354,
      author       = {Berger, Moritz and Klein, Nadja and Wagner, Michael and
                      Schmid, Matthias},
      title        = {{M}odeling the ratio of correlated biomarkers using copula
                      regression.},
      journal      = {Statistical methods in medical research},
      volume       = {34},
      number       = {5},
      issn         = {0962-2802},
      address      = {London [u.a.]},
      publisher    = {Sage},
      reportid     = {DZNE-2025-00731},
      pages        = {968 - 985},
      year         = {2025},
      abstract     = {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 commonly based on oversimplified assumptions,
                      assuming e.g. independence or strictly positive associations
                      between the components. In this paper, we overcome such
                      limitations and propose a regression model where the
                      marginal distributions of the two components are linked by a
                      copula. A key feature of our model is that it allows for
                      both positive and negative associations 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.},
      keywords     = {Biomarkers / Humans / Alzheimer Disease: diagnosis /
                      Amyloid beta-Peptides / tau Proteins / Models, Statistical /
                      Regression Analysis / Computer Simulation / Copula model
                      (Other) / distributional regression (Other) / gamma
                      distribution (Other) / negative dependence (Other) / ratio
                      outcome (Other) / Biomarkers (NLM Chemicals) / Amyloid
                      beta-Peptides (NLM Chemicals) / tau Proteins (NLM
                      Chemicals)},
      cin          = {AG Wagner},
      ddc          = {610},
      cid          = {I:(DE-2719)1011201},
      pnm          = {353 - Clinical and Health Care Research (POF4-353)},
      pid          = {G:(DE-HGF)POF4-353},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:39930915},
      pmc          = {pmc:PMC12177203},
      doi          = {10.1177/09622802241313293},
      url          = {https://pub.dzne.de/record/279354},
}