Dose-response relationships, mathematical analysis

In this chapter, we have set forth a formal mathematical description of mutation-induction kinetics on the basis of certain simplifying assumptions. The resulting equations are sufficient for the analysis of many dose-response relationships found for radiations and chemicals. From this base, more elaborate mathematical methods could be developed to deal with more complex experimental situations or macromolecular processes than we have considered here. 

Fortunately, there are mathematical methods by which some of these difficulties can be circumvented. Probit analysis allows for mathematical gyrations to occur so that a sigmoidal relationship can be straightened into a line. As students of Euclidian geometry can testify, the shortest distance between any two points is a straight line, and conversely, any line can be described by only two points. As such, the entire dose-response curve can be accurately estimated using probit analysis when as few as two of the chemical doses provide... 

A regression analysis of all data obtained resulted in dose-response functions, i.e., mathematical relationships that express the rate of deterioration of a material as a function of concentration of one or more corrosion stimulators. Table 15.5 shows the parameters included in the dose-response functions obtained for selected materials. For reason of space only the function for zinc will be used as an illustration of the new dose-response function from the multi-pollutant exposure ... 

Response or effect surface analysis (RSA) uses multiple linear regressions to produce a statistically based mathematical relationship between the doses of each of the chemicals in a mixmre and the effect parameter. The equation for a mixmre containing three compounds would be... 

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