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

Georg Gutjahr1, Björn Bornkamp2

  • 1Department of Mathematics, University of Bremen, Germany.

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|July 12, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a novel numerical algorithm to accurately approximate the null distribution for likelihood-ratio tests in dose-response modeling. This method overcomes limitations of existing approaches, enabling reliable power and sample size calculations for dose-related effect testing.

Keywords:
Dose-findingEmax modelNon-identifiabilityNon-linear modelsVolume of tubes

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Area of Science:

  • Biostatistics
  • Pharmacometrics
  • Statistical modeling

Background:

  • Testing for dose-related effects often involves nonlinear dose-response models and likelihood-ratio tests.
  • A key challenge is that the null distribution depends on non-identifiable parameters, invalidating standard asymptotic results.
  • Existing asymptotic solutions are complex, require simulations, and may be unreliable for small sample sizes.

Purpose of the Study:

  • To develop a robust numerical algorithm for approximating the exact null distribution of the likelihood-ratio test in nonlinear dose-response models.
  • To provide a method that overcomes the numerical instability and parameter non-identifiability issues of previous approaches.
  • To enable accurate power and sample size calculations for testing dose-related trends.

Main Methods:

  • Derivation of a numerical algorithm based on differential geometry principles.
  • Approximation of the exact null distribution for likelihood-ratio tests under multiple models.
  • Application to normally distributed data.

Main Results:

  • The proposed algorithm provides a stable and accurate approximation of the null distribution.
  • The method facilitates reliable power and sample size calculations.
  • Comparison with existing methods like MCP-Mod demonstrates the utility of the new approach.

Conclusions:

  • The developed numerical algorithm offers a significant advancement for testing dose-related effects using likelihood-ratio tests.
  • This approach addresses critical limitations in existing statistical methods for dose-response modeling.
  • The methodology is applicable to dose-finding studies and provides a more reliable basis for statistical inference.