A Dose-Response Model Incorporating Nonlinear Kinetics

Abstract

This paper introduces a dose-response model for toxic quantal response data based on hit theory applied to the dose unit as transformed by a nonlinear kinetic equation. When spontaneous background response is included in the model, the resulting dose-response model has four parameters. The maximum likelihood estimators and their large-sample properties are given. Likelihood ratio tests of interest are developed, including one for whether the model is one-hit in the transformed dose and one to check whether nonlinear kinetics is operative. The use of the model for low-dose extrapolation is presented. Finally, the procedures developed are illustrated on data from three animal carcinogenicity bioassays that show, respectively, concave, linear, and convex dose-response curves in the observed data.

Assessing the effects of metabolism of environmental agents on cancer tumor development by a two-stage model of carcinogenesis.

“…, where is a constant, (2) and b -d is the natural background difference of cell proliferation rate and cell differentiation rate ofinitiated cells.…”

“…For example, Hoel, Kaplan, and Anderson (1) have shown that it is not the exposed dose but the DNA adduct of agents that gives a linear dose-response curve for small doses. By using Michaelis-Menten kinetics, Van Ryzin and Rai (2) To provide a mathematical description of the carcinogenic process which can be used to interpret the results of experimental animal and human epidemiologic studies, Moolgavkar and Venzon (5) and Moolgavkar and Knudson (6) proposed a two-stage model of carcinogenesis. They modeled only two stages because no more than two distinct stages have been experimentally demonstrated.…”

Pattern–Mixture Models with Incomplete Informative Cluster Size: Application to a Repeated Pregnancy Study

“…Modelling clustered data with informative cluster size is an active area of statistical research. Ryzin and Rai () first proposed to adjust for the cluster size directly as a covariate in the regression model and directly interpreted the cluster‐size‐adjusted regression model. Hoffman et al .…”

Simplified models to analyse time- and dose-dependent responses of populations to toxicants

“…The mathematical model chosen was first used by Leonor Michaelis and Maud Menten in the early 20th century for a different purpose: to calculate the rate of enzyme-mediated reactions. The Michaelis-Menten kinetic model is usually invoked to explain uptake and elimination processes in toxicology (Newman 1998), but Van Ryzin andRai (1987) used it for describing the dose-response resulting from toxic effects in organisms. Apart from one isolated mention in the literature (Meister and Van den Brink 2000), to our knowledge this mathematical model has not been used to describe the time response of toxicants nor the kinetics of inhibition.…”