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Interval estimation of inverse dose-response

J M Alho1, E Valtonen

  • 1University of Joensuu, Department of Statistics, Finland.

Biometrics
|June 1, 1995
PubMed
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Likelihood ratio tests provide reliable interval estimates for LD50 and ED50, even with multiple exposure variables. This method improves upon classical Fieller limits, offering more stable results in statistical modeling.

Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Epidemiology

Background:

  • Interval estimation for toxicological and pharmacological dose-response parameters like LD50 and ED50 is crucial.
  • Existing methods, such as Fieller limits, can suffer from non-existence issues, particularly in small samples.
  • Generalized linear models provide a flexible framework for analyzing dose-response relationships.

Purpose of the Study:

  • To explore the practical application of likelihood ratio test (LRT)-based interval estimates for LD50, ED50, and related quantities.
  • To extend existing methods by incorporating additional explanatory variables relevant to epidemiologic studies.
  • To compare the performance of LRT-based intervals with classical Fieller limits.

Main Methods:

  • Utilizing a generalized linear model with a known scale parameter as the mathematical framework.

Related Experiment Videos

  • Applying Newton's method to compute the endpoints of LRT-based confidence intervals.
  • Investigating the computation of confidence sets, including cases of the whole real line or disjoint intervals.
  • Simulating data to compare LRT-based intervals with Fieller limits.

    • Main Results:

    • LRT-based interval estimates for LD50 and ED50 always exist, unlike Fieller limits which frequently fail in small samples.
    • While LRT-based limits are generally reliable, they can occasionally be slightly narrower than desired.
    • LRT-based limits are less prone to being infinite compared to Fieller limits.

    Conclusions:

    • LRT-based interval estimation offers a more robust and consistently available alternative to Fieller limits for dose-response parameters.
    • The method is adaptable for epidemiologic applications with multiple exposure variables.
    • Further research may be needed to refine the width of LRT-based intervals in certain scenarios.