Linearity example validation data

Table 11 Linearity Summary Statistics for the Example Validation Data...

Table 14 Lack-of-Fit Summary for Linearity of Example Validation Data with All Assays in the Linear Regression Analysis...

The first QSPR models for skin tried to establish linear relationships between the descriptors and the permeability coefficient. In many cases validation of these models using, for example, external data sets was not performed. Authors of more recent models took advantage of the progress in statistical methods and used nonlinear relationships between descriptors and predicted permeability and often tried to assess their predictive quality using some validation method. 

ICH Q2A suggested validation of the characteristics of accuracy, precision, specificity, linearity, and range for potency and content uniformity assay. A detailed discussion of each of these parameters is presented later in this chapter. Some examples of validation data are presented along with a brief critical discussion of the data. 

This is done to demonstrate the low level linearity of drug substance, which is used to quantitate impurities at certain levels. In most cases, quantitation of an impurity at 0.1% is required. It is imperative that the validation data demonstrate a sufficient LOD and LOQ. An example in Figure 3 shows the LOD at 0.05% and LOQ at 0.1% for a drug substance. Here, a nominal concentration of drug substance at 25.0mg/ml and a serial dilution of this solution to 0.5, 0.4, 0.3, 0.2, 0.1, and 0.05% relative to nominal concentration are made to demonstrate LOD and LOQ, as well as linearity. It has to be mentioned that sometimes the shape of drug substance band is somewhat compromised in order to fulfill the requirement of LOD and LOQ. 

The data are collected and recorded in tables (Tables 6A-D for hypothetical data). The validation characteristics of accuracy, precision, and linearity are analyzed from the data for this example validation. 

Results show very good estimation capacities using the first proposed scheme on validation data while succeeding to furnish only good water bed content estimations when working under the second scheme. The results confirm the capacity of this kind of neural model to track complex dynamic systems when a priori knowledge is conveniently introduced. Hence, the developed model can be used on-line, for example in a non linear model predictive control scheme. 

With real data, a more scientifically valid approach would be to correct the nonlinearity from physical theory. In the current case, for example, a scientifically valid approach would be to convert the data to transmission mode, subtract the stray light and reconvert to absorbance the nonlinear wavelengths would have become linear again. There are, of course, several things wrong with this procedure, all of them stemming from the fact that this data was created in a specific way for a specific purpose, not necessarily to be representative of real data ... 

In equation 3.4-18, the right side is linear with respect to both the parameters and the variables, j/the variables are interpreted as 1/T, In cA, In cB,.. . . However, the transformation of the function from a nonlinear to a linear form may result in a poorer fit. For example, in the Arrhenius equation, it is usually better to estimate A and EA by nonlinear regression applied to k = A exp( —EJRT), equation 3.1-8, than by linear regression applied to Ini = In A — EJRT, equation 3.1-7. This is because the linearization is statistically valid only if the experimental data are subject to constant relative errors (i.e., measurements are subject to fixed percentage errors) if, as is more often the case, constant absolute errors are observed, linearization misrepresents the error distribution, and leads to incorrect parameter estimates. 

Valid physical property relationships form an important feature of a process model. To validate a model, representative data must fit by some type of correlation using an optimization technique. Nonlinear regression instead of linear regression may be involved in the fitting. We illustrate the procedure in this example. 

Except for very simple systems, initial rate experiments of enzyme-catalyzed reactions are typically run in which the initial velocity is measured at a number of substrate concentrations while keeping all of the other components of the reaction mixture constant. The set of experiments is run again a number of times (typically, at least five) in which the concentration of one of those other components of the reaction mixture has been changed. When the initial rate data is plotted in a linear format (for example, in a double-reciprocal plot, 1/v vx. 1/[S]), a series of lines are obtained, each associated with a different concentration of the other component (for example, another substrate in a multisubstrate reaction, one of the products, an inhibitor or other effector, etc.). The slopes of each of these lines are replotted as a function of the concentration of the other component (e.g., slope vx. [other substrate] in a multisubstrate reaction slope vx. 1/[inhibitor] in an inhibition study etc.). Similar replots may be made with the vertical intercepts of the primary plots. The new slopes, vertical intercepts, and horizontal intercepts of these replots can provide estimates of the kinetic parameters for the system under study. In addition, linearity (or lack of) is a good check on whether the experimental protocols have valid steady-state conditions. Nonlinearity in replot data can often indicate cooperative events, slow binding steps, multiple binding, etc. 

One disadvantage of ANCOVA is that the modelling does involve a number of assumptions and if those assumptions are not valid then the approach could mislead. For example, it is assumed (usually) that the covariates affect outcome in a linear way there is invariably too little information in the data to be able to assess this assumption in any effective way. In contrast, with an adjusted analysis, assumptions about the way in which covariates affect outcome are not made and in that sense it can be seen as a more robust approach. In some regulatory circles adjusted analyses are preferred to ANCOVA for these reasons. 

EXAMPLE 6.2 Use of the Kelvin Equation for Determining Surface Tension. Figure 6.5 shows a plot of experimental data that demonstrates the validity of the Kelvin effect. Necks of liquid cyclohexane were formed between mica surfaces at 20°C, and the radius of curvature was measured by interferometry. Vapor pressures were measured for surfaces with different curvature. Use these data to evaluate 7 for cyclohexane. Comment on the significance of the fact that the linearity of Figure 6.5 extends all the way to a p/p0 value of 0.77. 

The method s performance characteristics should be based on the intended use of the method. For example, if the method will be used for qualitative trace-level analysis, there is no need to test and validate the method s linearity over the full dynamic range of the equipment. Initial parameters should be chosen according to the analyst s best judgment. Finally, parameters should be agreed upon between the lab generating the data and the client using the data. 

The more time-consuming experiments such as accuracy and ruggedness are put toward the end. Some of the parameters listed under items 2 through 5 can be measured in combined experiments. For example, when the precision of peak areas is measured over the full concentration range, the data can be used to validate the linearity. 

---