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Dose response signal detection under model uncertainty

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  • Holger Dette
  • Stefanie Titoff
  • Stanislav Volgushev
  • Frank Bretz

Abstract

type="main" xml:lang="en"> We investigate likelihood ratio contrast tests for dose response signal detection under model uncertainty, when several competing regression models are available to describe the dose response relationship. The proposed approach uses the complete structure of the regression models, but does not require knowledge of the parameters of the competing models. Standard likelihood ratio test theory is applicable in linear models as well as in nonlinear regression models with identifiable parameters. However, for many commonly used nonlinear dose response models the regression parameters are not identifiable under the null hypothesis of no dose response and standard arguments cannot be used to obtain critical values. We thus derive the asymptotic distribution of likelihood ratio contrast tests in regression models with a lack of identifiability and use this result to simulate the quantiles based on Gaussian processes. The new method is illustrated with a real data example and compared to existing procedures using theoretical investigations as well as simulations.

Suggested Citation

  • Holger Dette & Stefanie Titoff & Stanislav Volgushev & Frank Bretz, 2015. "Dose response signal detection under model uncertainty," Biometrics, The International Biometric Society, vol. 71(4), pages 996-1008, December.
    • Handle: RePEc:bla:biomet:v:71:y:2015:i:4:p:996-1008
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    Cited by:

    1. Frank Schaarschmidt & Christian Ritz & Ludwig A. Hothorn, 2022. "The Tukey trend test: Multiplicity adjustment using multiple marginal models," Biometrics, The International Biometric Society, vol. 78(2), pages 789-797, June.
    2. Georg Gutjahr & Björn Bornkamp, 2017. "Likelihood ratio tests for a dose-response effect using multiple nonlinear regression models," Biometrics, The International Biometric Society, vol. 73(1), pages 197-205, March.

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