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On the correlation coefficient between the TD50 and the MTD

M Razzaghi1, D W Gaylor

  • 1National Center for Toxicological Research, Bloomsburg University, Pennsylvania 17815, USA.

Risk Analysis : an Official Publication of the Society for Risk Analysis
|February 1, 1996
PubMed
Summary

Researchers explored the link between carcinogenic potency (TD50) and maximum tolerated dose (MTD). A new, more general method was developed to better quantify this correlation, improving upon existing analytical expressions.

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Area of Science:

  • Toxicology and Carcinogenesis
  • Biostatistics
  • Quantitative Risk Assessment

Background:

  • The correlation between carcinogenic potency (TD50) and maximum tolerated dose (MTD) is crucial for toxicological risk assessment.
  • Previous studies, such as Krewski et al., proposed analytical expressions to quantify this correlation based on specific distributional assumptions.
  • These existing models may not fully capture the variability and complexity of the relationship in real-world bioassay data.

Purpose of the Study:

  • To critically evaluate the accuracy of existing analytical expressions for the correlation coefficient between TD50 and MTD.
  • To derive a more general expression for the correlation coefficient that encompasses previous models as a special case.
  • To demonstrate the potential for existing methods to either overestimate or underestimate the true correlation.

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Main Methods:

  • Review and analysis of the distributional assumptions underlying Krewski et al.'s analytical expression.
  • Development of a generalized mathematical framework to derive a more robust correlation coefficient expression.
  • Application and validation of the proposed method using a real-world dataset from toxicological bioassays.

Main Results:

  • The analytical expression derived by Krewski et al. was found to be a special case of the newly proposed, more general expression.
  • Demonstrated instances where the Krewski et al. expression can lead to overestimation of the correlation coefficient.
  • Identified scenarios where the Krewski et al. expression can result in underestimation of the correlation coefficient, highlighting its limitations.
  • The proposed method provided a more accurate quantification of the correlation when applied to the real dataset.

Conclusions:

  • Existing analytical expressions for the correlation between carcinogenic potency and maximum tolerated dose may be imprecise due to underlying assumptions.
  • The newly derived, generalized expression offers a more accurate and flexible approach to quantifying this critical toxicological relationship.
  • This improved methodology enhances the reliability of risk assessment by providing a better understanding of the interplay between carcinogenicity and dose.