Dose response nonlinear

Although now there are numerous articles citing hormesis in various scientific databases, there are numerous other terms that have been used to describe dose-response relationships with the same quantitative features of the hormetic dose response. These similar descriptive terms include Yerkes-Dodson Law, nonmonotonic dose-response, nonlinear dose response, J-shaped dose-response, U-shaped dose-response, biphasic dose-response, BELL- haped dose-response, functional antagonism, hormologosis, overcompensation, rebound effect, bitonic, dual effect, bidirectional effect, bimodal effects, Amdt- chulz Law, Hueppe s Rule, and subsidy... 

One shortcoming of Schild analysis is an overemphasized use of the control dose-response curve (i.e., the accuracy of every DR value depends on the accuracy of the control EC o value). An alternative method utilizes nonlinear regression of the Gaddum equation (with visualization of the data with a Clark plot [10], named for A. J. Clark). This method, unlike Schild analysis, does not emphasize control pECS0, thereby giving a more balanced estimate of antagonist affinity. This method, first described by Lew and Angus [11], is robust and theoretically more sound than Schild analysis. On the other hand, it is not as visual. Schild analysis is rapid and intuitive, and can be used to detect nonequilibrium steady states in the system that can corrupt... 

There are statistical methods to determine the verisimilitude of experimental data to models. One major procedure to do this is nonlinear curve fitting to dose-response curves predicted by receptor models. 

Radiation is carcinogenic. The frequency of death from cancer of the thyroid, breast, lung, esophagus, stomach, and bladder was higher in Japanese survivors of the atomic bomb than in nonexposed individuals, and carcinogenesis seems to be the primary latent effect of ionizing radiation. The minimal latent period of most cancers was <15 years and depended on an individual s age at exposure and site of cancer. The relation of radiation-induced cancers to low doses and the shape of the dose-response curve (linear or nonlinear), the existence of a threshold, and the influence of dose rate and exposure period have to be determined (Hobbs and McClellan 1986). 

The PBPK model development for a chemical is preceded by the definition of the problem, which in toxicology may often be related to the apparent complex nature of toxicity. Examples of such apparent complex toxic responses include nonlinearity in dose-response, sex and species differences in tissue response, differential response of tissues to chemical exposure, qualitatively and/or quantitatively difference responses for the same cumulative dose administered by different routes and scenarios, and so on. In these instances, PBPK modeling studies can be utilized to evaluate the pharmacokinetic basis of the apparent complex nature of toxicity induced by the chemical. One of the values of PBPK modeling, in fact, is that accurate description of target tissue dose often resolves behavior that appears complex at the administered dose level. 

Note that in actuality, dose-response relationships are often not linear and instead we must use either a transform (to linearlize the data) or a nonlinear regression method (Gallant, 1975). 

Concentration response data are analyzed by a nonlinear regression logistic dose response model. Each of the crude extracts are fractionated into 10-15 subfractions. For each crude extract and the associated subfractions, ICsos and IC90S are determined as outlined above. All crude and subfractions of a particular marine organism are assayed simultaneously (within one assay) and include ribavirin as reference drugs using only A/WY/03/2003 virus. 

W. K. Lutz, S. Vamvakas, A. Kopp-Schneider, J. Schlatter and H. Stopper, Deviation from additivity in mixture toxicity relevance of nonlinear dose-response relationships and cell line differences in genotoxicity assays with combinations of chemical mutagens and g-radiation. Environmental Health Perspectives Supplements, 2002,110(6), 915-918. 

BMD approach can provide information on the nonlinear region of the dose-response. 

Dose-response assessment today is generally performed in two steps (1) assessment of observed data to derive a dose descriptor as a point of departure and (2) extrapolation to lower dose levels for the mmor type under consideration. The extrapolation is based on extension of a biologically based model (see Section 6.2.1) if supported by substantial data. Otherwise, default approaches that are consistent with current understanding of mode of action of the agent can be applied, including approaches that assume linearity or nonlinearity of the dose-response relationship, or both. The default approach is to extend a straight line to the human exposure doses. 

The second step of the dose-response assessment is an extrapolation to lower dose levels, i.e., below the observable range. The purpose of low-dose extrapolation is to provide as much information as possible about risk in the range of doses below the observed data. The most versatile forms of low-dose extrapolation are dose-response models that characterize risk as a probability over a range of environmental exposure levels. Otherwise, default approaches for extrapolation below the observed data range should take into account considerations about the agent s mode of action at each tumor site. Mode-of-action information can suggest the likely shape of the dose-response curve at these lower doses. Both linear and nonlinear approaches are available. 

If a nonlinear dose-response function has been determined, it can be used with the expected exposure to estimate a risk. If an RfD or RfC is calculated, the hazard can be expressed as a Hazard Quotient (HQ), defined as the ratio of an exposure estimate over the RfD or RfC, i.e., HQ = Exposure/(RfD or RfC). 

When dose-response curves are nonlinear as is usually the case, the process becomes more complex and an envelope of additivity is calculated to define the area in which the interaction of the two agents could be additive depending on how the two agents interact. The method described by Peckham and Steele (27) is explained as follows with the assumption that the dose response does not vary that much beyond a linear response. In their analysis, drugs A and D were assumed to yield linear responses and B and C yielded nonlinear responses. 

Calibration curves were fitted, and EC50 values were derived using the nonlinear regression package pro Fit 5.5 (QuantumSoft, Zurich, Switzerland). The results of the calibration curve measurements were fitted to a sigmoidal dose-response function of the following form with a slope faetor of 1 ... 

For experimental studies of mixtmes, consideration is given to the possibility of changes in the physicochemical properties of the test substance during collection, storage, extraction, concentration and delivery. Chemical and toxicological interactions of the components of mixtmes may result in nonlinear dose-response relationships. 

Dose-response curves for PCB standard solutions are carried out. The curves are estimated by nonlinear regression using the following logistic equation [35] by GraphPad Prism 4 program ... 

Nonlinear pharmacokinetics. Nonlinear pharmacokinetics simply means that the relationship between dose and Cp is not directly proportional for all doses. In nonlinear pharmacokinetics, drug concentration does not scale in direct proportion to dose (also known as dose-dependent kinetics). One classic drug example of nonlinear pharmacokinetics is the anticonvulsant drug phenytoin.38 Clinicians have learned to dose pheny-toin carefully in amounts greater than 300 mg/day above this point, most individuals will have dramatically increased phenytoin plasma levels in response to small changes in the input dose. 

Pharmacokinetic models. An important advance in risk assessment for hazardous chemicals has been the application of pharmacokinetic models to interpret dose-response data in rodents and humans (EPA, 1996a Leung and Paustenbach, 1995 NAS/NRC, 1989 Ramsey and Andersen, 1984). Pharmacokinetic models can be divided into two categories compartmental or physiological. A compartmental model attempts to fit data on the concentration of a parent chemical or its metabolite in blood over time to a nonlinear exponential model that is a function of the administered dose of the parent. The model can be rationalized to correspond to different compartments within the body (Gibaldi and Perrier, 1982). 

The order in which the summations over the responses (r) and substances (i) of concern are executed in the second and third steps above is arbitrary. However, these steps must be executed before the MAX and INTEGER functions are applied to the result. If the risk index for substances causing deterministic responses were based on calculations of health risk per se, rather than dose, the INTEGER function in Equation 6.5 would not be necessary, because the risk would be zero whenever a dose is below the threshold. Again, however, evaluation of the risk index for substances that cause deterministic responses based on dose is recommended when the dose-response relationship is assumed to have a threshold. The use of dose is supported by the observation that the dose-response relationship above the threshold generally is nonlinear. 

The boundaries between different waste classes would be quantified in terms of limits on concentrations of hazardous substances using a quantity called the risk index, which is defined in Equation 6.1. The risk index essentially is the ratio of a calculated risk that arises from waste disposal to an allowable risk (a negligible or acceptable risk) appropriate to the waste class (disposal system) of concern. The risk index is developed taking into account the two types of hazardous substances of concern substances that cause stochastic responses and have a linear, nonthreshold dose-response relationship, and substances that cause deterministic responses and have a threshold dose-response relationship. The risk index for any substance can be expressed directly in terms of risk, but it is more convenient to use dose instead, especially in the case of substances that cause determinstic responses for which risk is a nonlinear function of dose and the risk at any dose below a nominal threshold is presumed to be zero. The risk index for mixtures of substances that cause stochastic or deterministic responses are given in Equations 6.4 and 6.5, respectively, and the simple rule for combining the two to obtain a composite risk index for all hazardous substances in waste is given in Equation 6.6 or 6.7 and illustrated in Equation 6.8. The risk (dose) that arises from waste disposal in the numerator of the risk index is calculated based on assumed scenarios for exposure of hypothetical... 

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