Relationship between response

Assuming a hyperbolic relationship between response and the amount of agonist-receptor complex, response is defined as... 

During validation, the relationship between response and concentration is established. Checks also are made to ensure that the linearity of the method does not make too large a contribution to the measurement uncertainty (the uncertainty due to the calibration should contribute less than about 20% of the largest uncertainty component). The calibration schedule required during routine operation of the method is also established. It is wise to carry out sufficient checks on some or all of the following performance parameters, in order to establish that their values meet any specified limits. 

Calibration is also used to describe the process where several measurements are necessary to establish the relationship between response and concentration. From a set of results of the measurement response at a series of different concentrations, a calibration graph can be constructed (response versus concentration) and a calibration function established, i.e. the equation of the line or curve. The instrument response to an unknown quantity can then be measured and the prepared calibration graph used to determine the value of the unknown quantity. See Figure 5.2 for an example of a calibration graph and the linear equation that describes the relationship between response and concentration. For the line shown, y = 53.22x + 0.286 and the square of the correlation coefficient (r2) is 0.9998. 

Toxicogenomics The study of the relationship between responses to toxic substances and the resulting genetic changes. 

Relationship between response, design matrix and coefficients... 

Figure 9.35. Relationship between responses at different organizational levels.

Kramer WG, Kolibash AJ, Lewis RP, Bathala MS, Visconti lA, Reuning RH. Pharmacokinetics of digoxin Relationship between response intensity and predicted compartmental drug levels in man. J Pharmacokinet Biopharm 1979 7 47-61. 

Wagner JG. Kinetics of pharmacologic response I. Proposed relationships between response and drug concentration in the intact animal and man. J Theor Biol 1968 20 173-201. 

With the aim of achieving a better understanding of the relationships between response and predictors, the interpretability, simplicity and comparability of a model can always add useful information about its validity. 

We use the method of standard additions when it is difficult or impossible to duplicate the sample matrix. In general, the sample is spiked with a known amount or amounts of a standard solution of the analyte. In the single-point standard addition method, two portions of the sample are taken. One portion is measured as usual, but a known amount of standard analyte solution is added to the second portion. The responses for the two portions are then used to calculate the unknown concentration, assuming a linear relationship between response and analyte concentration (see Example 8-8). In the multiple additions method, additions of known amounts of standard analyte solution are made to several portions of the sample, and a multiple additions cahbration eurve is obtained. The multiple additions method gives some... 

Indirect response models require differential equations and numerical integration algorithms to describe the nonlinear inhibition or stimulation. Partially integrated solutions for these models have been developed (50, 51), which allow qualitative examination of the relationships between response... 

The mathematical equation used to describe the relationship between response and predictor variables is called regression model [Frank and Friedman, 1993 Wold, 1995 Ryan, 1997 Draper and Smith, 1998]. 

Kleinman MT (1984) Sulfur dioxide and exercise Relationships between response and absorption in upper airways. J Air Pollut Control Assoc 34 32-37. 

Linearity and range. The linearity of an analytical procedure is its ability to produce results that are directly proportional to the concentration of analyte in the samples. The range of the procedure is an expression of the lowest and highest levels of analyte that have been demonstrated to be determinable with acceptable precision, accuracy, and linearity. These characteristics are determined by application of the procedure to a series of samples having analyte concentrations spanning the claimed range of the procedure. When the relationship between response and concentration is not linear, standardization may be provided by means of a calibration curve. 

With simultaneous strategies, the relationship between responses and factors is studied by ruiming an experimental design. 

In contrast to the simultaneous factorial design study, experimentation by variation of one variable at a time is limited to the estimation of main effects, and no interactions, as are common in analytical chemistry, can be found. What cannot be evaluated with screening designs are curved dependences, that is, for more complicated relationships between responses and factors, designs at three or more factor levels are needed. 

In order to describe the relationship between responses and factors quantitatively, we will use mechanistic (physicochemical) or empirical models, for example, polynomial models. These mathematical models should be able to describe linear and curved response surfaces similarly. Curved dependences can be modeled if the factor levels have at least been investigated at three levels. 

RSMs are very useful in order to quantify and interpret the relationships between responses and factor effects. In analytical chemistry, the relationships can be based on physical or physicochemical models that are generalized by statisticians as the so-called mechanistic models. Another way is empirical modeling, where the parameters have no mechanistic meaning. 

Models are constructed in analytics to describe the relationship between responses and factors. This is, for example, important for optimization of analytical methods on the basis of response surface methods (cf. Section 4.2). Models are also needed for cahbration of analytical methods. There, calibration of a single analyte in dependence on one or several wavelengths might be of interest. If, in the first example, the straight-line model would be adequate, for the second task of multiwavelength spectroscopy, multivariate approaches are needed. Calibrations in the case of unselective analytical methods must also be performed. These methods are termed simultaneous multicomponent analysis. In near-infrared (NIR) spectroscopy, the contents of water and protein in whole grain wheat are determined that way. 

Performing a least squares regression analysis on the experimental calibration data to evaluate instrument linearity over a range of concentrations of interest and to establish the best relationship between response and concentration. 

As discussed in Chapter 2, after coUechng data, it should be plotted to assess if there are any trends or relationships between response variables and factors that should be identified. Uncertainhes should be calculated to verify that trends are due to physical phenomena and not random processes. Theories and relationships can then be derived between the responses—independent variables—and the factors—dependent variables—as shown in Figure 3.2. 

In many situations, the relationship between response variables and factors is unclear. Linear regression analysis is a first step in identifying significant factors. However, many physical processes vary nonlinearly with factors and thus much of the variance in the data may not be accounted for with simple linear regression. To account for nonlinear behavior, response variables may be... 

The relationships between response variables, y, and factors, x, are represented through mathematical expressions that take the form of correlations or regression equations. These linear or nonlinear mathematical expressions are often expressed as a polynomial, logarithmic, exponential, or trigonometric function. For example, the variation of the specific heats of gases, Cp, has been expressed as a third-order polynomial with respect to temperature ... 

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