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ToxSci Advance Access published online on October 19, 2005
Toxicological Sciences, doi:10.1093/toxsci/kfj024
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© The Author 2005. Published by Oxford University Press on behalf of the Society of Toxicology. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
Received August 1, 2005
Accepted October 10, 2005

Risk Assessment

Dose-Incidence Modeling: Consequences of Linking Quantal Measures of Response to Depletion of Critical Tissue Targets

Melvin E. Andersen 1*, Roman W. Lutz 2, Kai H. Liao 1, and Werner K. Lutz 3

1 CIIT Centers for Health Research, Research Triangle Park, North Carolina 27709
2 Seminar for Statistics, Swiss Federal Institute of Technology, 8092 Zürich, Switzerland
3 Department of Toxicology, University of Würzburg, 97078 Würzburg, Germany

* To whom correspondence should be addressed.
Melvin E. Andersen, E-mail: Mandersen{at}ciit.org


  Abstract

In developing mechanistic PK-PD models, incidence of toxic responses in a population has to be described in relation to measures of biologically effective dose (BED). We have developed a simple dose-incidence model that link incidence with BED for compounds that cause toxicity by depleting critical cellular target molecules. The BED in this model was the proportion of target molecule adducted by the dose of toxic compound. Our modeling approach first estimated the proportion depleted for each dose and then calculated the tolerance distribution for toxicity in relation to either administered dose or log of administered dose. We first examined cases where the mean of the tolerance distribution for toxicity occurred when a significant proportion of target had been adducted (i.e., more than half). When a normal distribution was assumed to exist for the relationship of incidence and BED, the tolerance distribution based on administered dose for these cases becomes asymmetrical and logarithmic transformations of the administered dose axis lead to a more symmetrical distribution. These linked PK-PD models for tissue reactivity, consistent with conclusions from other work for receptor binding models (Lutz et al., 2005), indicate that log normal distributions with administered dose are expected to arise from normal distributions for BED and nonlinear kinetics between BED and administered dose. These conclusions are important for developing BBDR models that link toxic and other biological responses to measures of BED.

Keywords: Dose-incidence relationship; logarithm; individual susceptibility; biologically effective dose; pharmacodynamic modeling; pharmacokinetic modeling.

#Definition: If a variable is normally distributed when represented on a logarithmical scale, the distribution is called "log normal".


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