Dose-response curve nonlinearities

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 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. 

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. 

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 ... 

The most promising compounds, or actives, typically numbering from 1000 to 5000, are then tested in a secondary screen which involves testing each compound at 5 to 10 different concentrations. These results are modeled with a nonlinear dose-response curve and for each molecule a summary measure is computed such as a 50% inhibitory concentration (IC50) or a 50% efficacious concentration (EC50). 

There is considerable controversy over the shape of the dose-response curve at the chronic low dose levels important for environmental contamination. Proposed models include linear models, nonlinear (quadratic) models, and threshold models. Because risks at low dose must be extrapolated from available data at high doses, the shape of the dose-response curve has important implications for the environmental regulations used to protect the general public. Detailed description of dosimetry models can be found in Cember (1996), BEIR IV (1988), and Harley (2001). 

Once a chemical s mode(s) of action has been identified, the risk assessor can proceed with the evaluation of carcinogenic potential, including consideration of the relevance of the mode of action to humans. Further consideration of mode of action distinguishes between a genotoxic (or sometimes more rigorously described as DNA-reactive) mode of action, for which there may be some risk at every nonzero dose, and nongenotoxic (or nonmutagenic) modes of action, for which threshold or nonlinear dose-response curves may apply. 

Figure 33-10 Dose-response curves. L/ne A illustrates the linear relationship between serum drug concentration and total daily dose of a drug that displays first-order kinetics typical of most drugs. Line B illustrates the dose-response relationship for a drug that displays capacity-limited kinetics because of a saturable enzyme or transport mechanism in this situation, serum concentration becomes independent of total daily dose, and the relationship of drug concentration to dose becomes nonlinear. (Modified from Pippenger CE. Practical pharmacokinetic appiications. Syvo Monitor, Son Jose Syva Co, January, i 979 1-4.)...

Fitting the data directly to either Equation 5.14 or Equation 5.15 eliminates bias in the data imposed by reciprocal linear curve fitting. Figure 5.21 shows the use of nonlinear curve fitting to measure the affinity of the a-adrenoceptor agonist oxymetazoline in rat anococcygeus muscle after alkylation of a portion of the receptors with phenoxybenzamine. This data shows how all three curves can be used for a better estimate of the affinity with nonlinear curve fitting, a technique not possible with the double reciprocal plot approach where only two dose-response curves can be used. The use of three curves increases the power of the analysis... 

A point of departure (POD) is a point on a dose-response curve at which the range of data is extended from the observable range to lower dose ranges by extrapolation. Such extrapolation can be by default hnear, predicted linear, or predicted nonlinear (to also include a threshold). 

Nonlinearity in the mutagenesis dose-response curve can occur even for chemicals that interact directly with DNA. Sofuni et al. (2000) evaluated the mutagenicity of the alkylating agents A-ethyl-A -nitro-A-nitrosoguanidine (ENNG), methyl methanesulfonate (MMS), dimethylnitrosamine (DMN), and ethylnitrosourea... 

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