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Likelihood ratio tests for a dose-response effect using multiple nonlinear regression models.

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Titel: Likelihood ratio tests for a dose-response effect using multiple nonlinear regression models.
Autoren: Gutjahr, Georg, Bornkamp, Björn
Quelle: Biometrics; Mar2017, Vol. 73 Issue 1, p197-205, 9p
Schlagwörter: LIKELIHOOD ratio tests, DOSE-response relationship in biochemistry, NONLINEAR regression, DIFFERENTIAL geometry, BIG data
Abstract: We consider the problem of testing for a dose-related effect based on a candidate set of (typically nonlinear) dose-response models using likelihood-ratio tests. For the considered models this reduces to assessing whether the slope parameter in these nonlinear regression models is zero or not. A technical problem is that the null distribution (when the slope is zero) depends on non-identifiable parameters, so that standard asymptotic results on the distribution of the likelihood-ratio test no longer apply. Asymptotic solutions for this problem have been extensively discussed in the literature. The resulting approximations however are not of simple form and require simulation to calculate the asymptotic distribution. In addition, their appropriateness might be doubtful for the case of a small sample size. Direct simulation to approximate the null distribution is numerically unstable due to the non identifiability of some parameters. In this article, we derive a numerical algorithm to approximate the exact distribution of the likelihood-ratio test under multiple models for normally distributed data. The algorithm uses methods from differential geometry and can be used to evaluate the distribution under the null hypothesis, but also allows for power and sample size calculations. We compare the proposed testing approach to the MCP-Mod methodology and alternative methods for testing for a dose-related trend in a dose-finding example data set and simulations. [ABSTRACT FROM AUTHOR]
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  Data: Likelihood ratio tests for a dose-response effect using multiple nonlinear regression models.
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  Data: Biometrics; Mar2017, Vol. 73 Issue 1, p197-205, 9p
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  Data: We consider the problem of testing for a dose-related effect based on a candidate set of (typically nonlinear) dose-response models using likelihood-ratio tests. For the considered models this reduces to assessing whether the slope parameter in these nonlinear regression models is zero or not. A technical problem is that the null distribution (when the slope is zero) depends on non-identifiable parameters, so that standard asymptotic results on the distribution of the likelihood-ratio test no longer apply. Asymptotic solutions for this problem have been extensively discussed in the literature. The resulting approximations however are not of simple form and require simulation to calculate the asymptotic distribution. In addition, their appropriateness might be doubtful for the case of a small sample size. Direct simulation to approximate the null distribution is numerically unstable due to the non identifiability of some parameters. In this article, we derive a numerical algorithm to approximate the exact distribution of the likelihood-ratio test under multiple models for normally distributed data. The algorithm uses methods from differential geometry and can be used to evaluate the distribution under the null hypothesis, but also allows for power and sample size calculations. We compare the proposed testing approach to the MCP-Mod methodology and alternative methods for testing for a dose-related trend in a dose-finding example data set and simulations. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Biometrics is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1111/biom.12563
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      – Code: eng
        Text: English
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        PageCount: 9
        StartPage: 197
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      – SubjectFull: LIKELIHOOD ratio tests
        Type: general
      – SubjectFull: DOSE-response relationship in biochemistry
        Type: general
      – SubjectFull: NONLINEAR regression
        Type: general
      – SubjectFull: DIFFERENTIAL geometry
        Type: general
      – SubjectFull: BIG data
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              Text: Mar2017
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              Y: 2017
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