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Identifying alert concentrations using a model‐based bootstrap approach

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  • Kathrin Möllenhoff
  • Kirsten Schorning
  • Franziska Kappenberg

Abstract

The determination of alert concentrations, where a pre‐specified threshold of the response variable is exceeded, is an important goal of concentration–response studies. The traditional approach is based on investigating the measured concentrations and attaining statistical significance of the alert concentration by using a multiple t‐test procedure. In this paper, we propose a new model‐based method to identify alert concentrations, based on fitting a concentration–response curve and constructing a simultaneous confidence band for the difference of the response of a concentration compared to the control. In order to obtain these confidence bands, we use a bootstrap approach which can be applied to any functional form of the concentration–response curve. This particularly offers the possibility to investigate also those situations where the concentration–response relationship is not monotone and, moreover, to detect alerts at concentrations which were not measured during the study, providing a highly flexible framework for the problem at hand.

Suggested Citation

  • Kathrin Möllenhoff & Kirsten Schorning & Franziska Kappenberg, 2023. "Identifying alert concentrations using a model‐based bootstrap approach," Biometrics, The International Biometric Society, vol. 79(3), pages 2076-2088, September.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:3:p:2076-2088
    DOI: 10.1111/biom.13799
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    References listed on IDEAS

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    1. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers 29/13, Institute for Fiscal Studies.
    2. Holger Dette & Kathrin Möllenhoff & Stanislav Volgushev & Frank Bretz, 2018. "Equivalence of Regression Curves," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 711-729, April.
    3. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. F. Bretz & J. C. Pinheiro & M. Branson, 2005. "Combining Multiple Comparisons and Modeling Techniques in Dose-Response Studies," Biometrics, The International Biometric Society, vol. 61(3), pages 738-748, September.
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