Parameterizing dose-response models to estimate relative potency functions directly
Biostatistics Branch, National Institute of Environmental Health Sciences (NIEHS), Research Triangle Park, North Carolina 27709.Toxicological Sciences (Impact Factor: 3.85). 06/2012; 129(2):447-55. DOI: 10.1093/toxsci/kfs209
Many comparative analyses of toxicity assume that the potency of a test chemical relative to a reference chemical is constant, but employing such a restrictive assumption uncritically may generate misleading conclusions. Recent efforts to characterize non-constant relative potency rely on relative potency functions and estimate them secondarily after fitting dose-response models for the test and reference chemicals. We study an alternative approach of specifying a relative potency model a priori and estimating it directly using the dose-response data from both chemicals. We consider a power function in dose as a relative potency model and find that it keeps the two chemicals' dose-response functions within the same family of models for families typically used in toxicology. When differences in the response limits for the test and reference chemicals are attributable to the chemicals themselves, the older two-stage approach is the more convenient. When differences in response limits are attributable to other features of the experimental protocol or when response limits do not differ, the direct approach is straightforward to apply with nonlinear regression methods and simplifies calculation of simultaneous confidence bands. We illustrate the proposed approach using Hill models with dose-response data from U.S. National Toxicology Program bioassays. Though not universally applicable, this method of estimating relative potency functions directly can be profitably applied to a broad family of dose-response models commonly used in toxicology.
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ABSTRACT: This article concerns the analysis of a stochastic model that we propose for the population that generates a response (response measure) to the dose with the multi-stage model. The parameter uncertainty is dealt with via random dose and random size of the population at risk. The response measure is modeled by a random sum of mixed bernoulli random variables with arbitrary distribution for the mixing parameters. Some extensions of the model are defined by new functionals of the infection probability, fulfilling some convexity properties. We analyze the response by stochastic comparisons under different stochastic relations on the random dosages and the random sizes of the population at risk; or on the random infection rates. We provide stochastic exact bounds of the mixture model for the response, using inequalities and the positive quadrant dependence. Numerical bounds of the response by a dose having a scalar value or having an exponential or uniform distributions are obtained. Some conclusions are derived: the lowerestimation of the response measure in the increasing convex order sense by replacing the dosages by their means; effects of the variation of the dose on the magnitude of the probability distribution of the response; effects of parameter correlation on the degree of variability of the response to any random dose; the low-dose region assessment; and also, the classical multi-stage model is compared versus the mixture model featuring independence and versus the mixture model with positive quadrant dependence.Mathematical biosciences 07/2014; 253(1). DOI:10.1016/j.mbs.2014.02.004 · 1.30 Impact Factor
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