Modeling dose response using generalized linear models

Authors

  • David R. Kerr,

    1. Department of Statistics, University of Washington, Seattle, Washington 98195, USA
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  • James P. Meador

    Corresponding author
    1. Environmental Conservation Division, Northwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, 2725 Montlake Blvd. E., Seattle, Washington 98112, USA
    • Environmental Conservation Division, Northwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, 2725 Montlake Blvd. E., Seattle, Washington 98112, USA
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Abstract

This paper describes a method to determine and model dose–response relationships from binomial response data using generalized linear models (GLM). The main advantage of this technique is that it allows LCp or LDp to be determined without an initial linearizing transformation. (LCp and LDp are the lethal concentration or dose that causes p proportion of test animals to die at a specified time period.) Thus, the method of GLM is an appropriate way to analyze a dose–response relationship because it utilizes the inherent S-shaped feature of the toxicologic response and incorporates the sample size of each trial in parameter estimation. This method is also much better behaved when the extremes of the response probability are considered because responses of 0% and 100% are included in the model. Another advantageous feature of this method is that confidence intervals (C.I.s) for both the dose estimate and response probabilities can be computed with GLM, which provides a more complete description of the estimates and their inherent uncertainty. Because C.I.s for both the dose estimate and response probabilities can be constructed, the lowest observed effect concentration (LOEC) can also be determined.

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