Constitution statistical evaluation

The traditional acute, subchronic, and chronic toxicity studies performed in rodents and other species also can be considered to constitute multiple endpoint screens. Although the numerically measured continuous variables (body weight, food consumption, hematology values) generally can be statistically evaluated individually by traditional means, the same concerns of loss of information present in the interrelationship of such variables apply. Generally, traditional multivariate methods are not available, efficient, sensitive, or practical (Young, 1985). 

Changes in constitution and conformation also have significant effects on the statistical evaluation of data sets. The following examples of small molecule data sets... 

The terms similarity and diversity can have quite different meanings in chemical investigations. Describing the diversity of a data collection with a general valid measure is almost impossible. Descriptor flexibility allows the characterization of similarity by means of statistics for different tasks. The statistical evaluation of descriptors shows that it is recommended to interpret correlation coefficients together with the symmetry of distribution. In contrast to correlation coefficients, skewness and kurtosis are sensitive indicators to constitutional and conformational changes in a molecule. This feature allows a more precise evaluation of structural similarity or diversity of molecular data sets. 

The chemical measurement process is constituted by several steps field sampling, sample handling, laboratory sample preparation, separation and quantitation, data handling and statistical evaluation, results interpretation and conclusion suggestion, and finally required action [46]. 

Unperturbed dimensions and dipole moments of polydialkylsiloxanes are investigated using RIS theory. Polymers are treated as branched molecules in which each silicon atom constitutes a tetrafunctional branch point. All significant first- and second-order interactions are included in the configuration partition function. Higher order interactions not suppressed by second-order interactions are also evaluated and accounted for in the statistical weights used. 

The study of a particular adsorption process requires the knowledge of equilibrium data and adsorption kinetics [4]. Equilibrium data are obtained firom adsorption isotherms and are used to evaluate the capacity of activated carbons to adsorb a particular molecule. They constitute the first experimental information that is generally used as a tool to discriminate among different activated carbons and thereby choose the most appropriate one for a particular application. Statistically, adsorption from dilute solutions is simple because the solvent can be interpreted as primitive, that is to say as a structureless continuum [3]. Therefore, all equations derived firom monolayer gas adsorption remain vafid. Some of these equations, such as the Langmuir and Dubinin—Astakhov, are widely used to determine the adsorption capacity of activated carbons. Batch equilibrium tests are often complemented by kinetics studies, to determine the external mass transfer resistance and the effective diffusion coefficient, and by dynamic column studies. These column studies are used to determine system size requirements, contact time, and carbon usage rates. These parameters can be obtained from the breakthrough curves. In this chapter, I shall deal mainly with equilibrium data in the adsorption of organic solutes. 

In a broad sense, the term computational chemistry includes several fields such as quantum chemistry, statistical molecular mechanics, molecular modeling, approaches based on graph invariants, molecular graphics and visualization, evaluation of experimental data in X-ray crystallography, NMR spectroscopy, and, in general, spectroscopic techniques moreover, in this broad sense, analysis, exploration, and modeling performed by chemometrics on experimental data, searching for structure-response correlations, information retrieval from chemical databases, and expert chemical systems are also included in computational chemistry, as constitutive parts of —> chemoinformatics. 

Documentation on assumptions should address those assumptions implicit in the pharmacokinetic or pharmacodynamic model and the statistical methodology chosen to evaluate the data. It should also state the assumed sensitivity of the parameters required to define the model relative to the data space being evaluated as well as any preconceived notions regarding biomarkers or surrogate markers evaluated as responses or covariates in the analysis. Hypotheses should be defined based on what was held a priori as true before the study or analysis, what was developed from preliminary or exploratory data analysis, and what would constitute a difference or equivalence in an effect or outcome, hi some instances the criteria for difference as opposed to equivalence can be defined from a statistical viewpoint independent of the actual study design. This approach does not always confer regulatory acceptance, however. 

For situations with more than two variances, one statistical test that may be employed is the Hartley F-max procedure. This is a test that may be applied to a balanced database. I.C.. the same number of values in each of the data sets, each set constituting a certain level of a factor in a test program. The variance of each of n data sets to be tested for equivalent variance is evaluated, and the ratio of. S /max), S (min) is calculated and designated as F-max(calc). The value of this is compared to F-ma.x(crit) at a selected P level (0.05 or O.Ot) in tables of the F-max distribution for n factor levels (data sets) and for the common (// for each vairianee estimate. Table AH is i Hartley F-max table. The null hypothesis is... 

---