Rank order function

This method can be used to obtain the reactions of a large number of stakeholders to alternative functions and features of a product or system concept. Typically, people are asked to rate the desirability and perceived feasibility of functions and features using, for example, scales of 1 to 10. Alternatively, people can be asked to rank order functions and features. 

Figure 8.2. Rank order function or Order Distribution Function for uniform random variable. Y variable ranges from 1 to 400 (or 1 to n) for 0 < x < 1.

A number of approaches to predict ionization based on structure have been published (for a review, see [53]) and some of these are commercially available. Predictions tend to be good for structures with already known and measured functional groups. However, predictions can be poor for new innovative structures. Nevertheless, pfCa predictions can still be used to drive a project in the desired direction and the rank order of the compounds is often correct. More recently training algorithms have also become available which use in-house data to improve the predictions. This is obviously the way forward. 

In non-metric MDS the analysis takes into account the measurement level of the raw data (nominal, ordinal, interval or ratio scale see Section 2.1.2). This is most relevant for sensory testing where often the scale of scores is not well-defined and the differences derived may not represent Euclidean distances. For this reason one may rank-order the distances and analyze the rank numbers with, for example, the popular method and algorithm for non-metric MDS that is due to Kruskal [7]. Here one defines a non-linear loss function, called STRESS, which is to be minimized ... 

The mechanistic simulation ACAT model was modified to account automatically for the change in small intestinal and colon k as a function of the local (pH-dependent) log D of the drug molecule. The rank order of %HIA from GastroPlus was directly compared with rank order experimental %HIA with this correction for the log D of each molecule in each of the pH environments of the small intestine. A significant Spearman rank correlation coefficient for the mechanistic simulation-based method of 0.58 (p < 0.001) was found. The mechanistic simulation produced 71% of %HIA predictions within 25% of the experimental values. 

The presence of a transporter can be assessed by comparing basolateral-to-apical with apical-to-basolateral transport of substrates in polarized cell monolayers. If P-gp is present, then basolateral-to-apical transport is enhanced and apical-to baso-lateral transport is reduced. Transport experiments are in general performed with radioactively labeled compounds. Several studies have been performed with Caco-2 cell lines (e.g. Ref. [85]). Since Caco-2 cells express a number of different transporters, the effects measured are most probably specific for the ensemble of transporters rather than for P-gp alone. P-gp-specific transport has been assayed across confluent cell layers formed by polarized kidney epithelial cells transfected with the MDR1 gene [86], Figure 20.11 shows experimental data obtained with these cell lines. A rank order for transport called substrate quality was determined for a number of compounds [86]. The substrate quality is a qualitative estimate, but nevertheless allows an investigation of the role of the air/water (or lipid/water) partition coefficient, log Kaw, for transport as seen in Fig. 20.11(A). For most of the compounds, a linear correlation is observed between substrate quality and log Kaw- However, four compounds are not transported at all despite their distinct lipophilicity. A plot of the substrate quality as a function of the potential of a... 

Ex vivo studies have revealed that trichothecenes can both inhibit and stimulate leukocyte function.12 For example, trichothecenes are toxic to alveolar macrophages,13 but drive differentiation of human myeloid leukemic cells.14 Dose-dependent decreases or increases in B- and T-cell mitogen responses are observable in lymphocytes from animals exposed to T-2 toxin, DON, or various macrocyclic trichothecenes these toxins similarly impair or enhance mitogen-induced lymphocyte proliferation in vitro.12 Rank order of inhibitor potency in rodent and human lymphocyte proliferation assays is Type D > Type A group > Type B group and is dependent on degree of acylation as well as of uptake and metabolism. 

The applicability of an in vitro assay to classify drug substances is verified by demonstrating a rank-order relationship between the extent of human absorption and experimental permeability values with 20 model drugs. The model drugs should represent ranges of 0-50%, 50-89%, and 90-100% absorption (/a) and the results should clearly differentiate between HP and LP drugs. The model can also be characterized for the presence of functional active transporters (e.g., amino acids, di/tripeptides, monocarboxylic acids, nucleosides) and efflux mechanisms (e.g., P-gp, MRP). 

As in the computation of all the scores, one needs to check to make sure that the rank-ordered compounds are reasonable. In the early stages of development of this prioritization method there was a great deal of adjustment to the scoring functions to match medicinal chemists and project team members opinions. 

Percutaneous penetration of 7V-nitrosodiethanolamine was measured using cryo-preserved human trunk skin and three vehicle formulations (isopropyl myristate, sunscreen cream or a 10% shampoo) containing 7V-nitroso[ C]diethanolamine. The absorption rate of a low dermal dose (10 ixg/cm ) of 7V-nitrosodiethanolamine was a linear function of the concentration (0.06, 0.2 or 0.6 Xg/ xL) applied to the skin. The peak rates for the isopropyl m uistate and shampoo vehicles were seen within five hours and for the sunscreen somewhat later. Total 48-h absorption ranged from 35 to 65% of the dose and was formulation-dependent (isopropyl m uistate > shampoo > sunscreen). A total absorption of 4-6 x JcaE was estimated to equate to an applied N-nitrosodiethanolamine dose of 10 x%lcaE. When applied as a large infinite dose (0.5 mg/cm ), total 7V-nitrosodiethanolamine absorption (4-35% of the applied dose) followed a different rank order (shampoo > isopropyl m uistate > sunscreen), probably due to the barrier-damaging properties of the vehicles. The permeability coefficient for isopropyl myristate was 3.5 X 10 cm/h (Franz etal., 1993). 

When comparing transmitter-gated ion channels on a functional level, one can discern between anion and cation channels. The former ones comprise the GABAa and glycine receptors, which display a rank order of anion selectivity of I- > Hr > Cl- and which are also permeable to HC()3. All other ionotropic receptors mentioned here are cation channels, which discriminate rather poorly between various monovalent cations, at least when compared with voltage-gated ion channels. Some... 

A probability distribution is a mathematical description of a function that relates probabilities with specified intervals of a continuous quantity, or values of a discrete quantity, for a random variable. Probability distribution models can be non-parametric or parametric. A non-parametric probability distribution can be described by rank ordering continuous values and estimating the empirical cumulative probability associated with each. Parametric probability distribution models can be fit to data sets by estimating their parameter values based upon the data. The adequacy of the parametric probability distribution models as descriptors of the data can be evaluated using goodness-of-fit techniques. Distributions such as normal, lognormal and others are examples of parametric probability distribution models. 

To go into this idea quantitatively, we need definitions of hardness and softness, and a rank order for acids and bases on a scale of hardness. This has been done in two ways one based on molecular orbital theory, and the other on density functional theory. 

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