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@ARTICLE{HollandLetz:136030,
      author       = {T. Holland-Letz$^*$ and N. Gunkel and E. Amtmann$^*$ and A.
                      Kopp-Schneider$^*$},
      title        = {{P}arametric modeling and optimal experimental designs for
                      estimating isobolograms for drug interactions in
                      toxicology.},
      journal      = {Journal of biopharmaceutical statistics},
      volume       = {28},
      number       = {4},
      issn         = {1520-5711},
      address      = {Philadelphia, PA},
      publisher    = {Taylor $\&$ Francis},
      reportid     = {DKFZ-2018-00730},
      pages        = {763 - 777},
      year         = {2018},
      abstract     = {In toxicology and related areas, interaction effects
                      between two substances are commonly expressed through a
                      combination index [Formula: see text] evaluated separately
                      at different effect levels and mixture ratios. Often, these
                      indices are combined into a graphical representation, the
                      isobologram. Instead of estimating the combination indices
                      at the experimental mixture ratios only, we propose a simple
                      parametric model for estimating the underlying interaction
                      function. We integrate this approach into a joint model
                      where both the parameters of the dose-response functions of
                      the singular substances and the interaction parameters can
                      be estimated simultaneously. As an additional benefit, this
                      concept allows to determine optimal statistical designs for
                      combination studies optimizing the estimation of the
                      interaction function as a whole. From an optimal design
                      perspective, finding the interaction parameters generally
                      corresponds to a [Formula: see text]-optimality resp.
                      [Formula: see text]-optimality design problem, while
                      estimation of all underlying dose response parameters
                      corresponds to a [Formula: see text]-optimality design
                      problem. We show how optimal designs can be obtained in
                      either case as well as how combination designs providing
                      reasonable performance in regard to both criteria can be
                      determined by putting a constraint on the efficiency in
                      regard to one of the criteria and optimizing for the other.
                      As all designs require prior information about model
                      parameter values, which may be unreliable in practice, the
                      effect of misspecifications is investigated as well.},
      cin          = {C060 / G404},
      ddc          = {570},
      cid          = {I:(DE-He78)C060-20160331 / I:(DE-He78)G404-20160331},
      pnm          = {313 - Cancer risk factors and prevention (POF3-313)},
      pid          = {G:(DE-HGF)POF3-313},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:29173022},
      doi          = {10.1080/10543406.2017.1397005},
      url          = {https://inrepo02.dkfz.de/record/136030},
}