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Dose-incidence modeling: consequences of linking quantal measures of response to depletion of critical tissue targets.

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 links 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 may arise from normal distributions for BED and nonlinear kinetics between BED and administered dose. These conclusions are important for developing biologically based dose response (BBDR) models that link incidences of toxicity or other biological responses to measures of BED.