Partitioning of reference values

The aim of partitioning is to provide a better basis for comparison of clinicai laboratory results class-specific reference intervals (e.g., age- and gender-specific reference intervals). 

Various statistical criteria for partitioning have been suggested. For example, an intuitive criterion states that partitioning is necessaiy if differences between classes are statistically significant (rejection of the nuU hypothesis of equal distributions). The distribution of reference values in the classes may show different locations (mean values vary) or different intraclass variations (standard deviations vary). 

These differences may be tested by statistical methods, which are not described here. The reader is referred to Chapter 14 and to standard textbooks of parametric and nonpara-metric statistics.  

The differences of location or variation, however, may be statistically significant and still too small to justify replacing a single total reference interval with several class-specific intervals. Alternately, statistically nonsignificant differences can lead to situations in which the proportions of each subclass above the upper or below the lower reference limits (witlrout partitioning) are much different from the desired 2.5% on each side. Harris and Boyd therefore suggested criteria based on the ratio between the subclass standard deviations, a normal deviate test of means, and calculation of critical decision values dependent on the sample size. 

Lahti and co-workers focused on distances between reference limits instead of distances between means, and suggested new distance and proportion criteria for partitioning. Their model also makes it possible to account for unequal subclass prevalences and is applicable to distributions of various types. 

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This section deals with two main topics the partitioning of reference values into more homogeneous classes and the determination of reference limits and intervals. The subject matter is presented in the order in which data often are treated. Figure 16-2 gives an outline and refers to the corresponding sections in the text. Before the presentation of the... 

Figure 16-2 The statistical treatment of reference values.The boxes in the flow chart refer to sections in the text. NB = Nota bene The order of the three first actions (partitioning, inspection, and detection and/or handling of outliers) may vary, dependent on the distribution and the statistical methods applied. Y, Yes N, no.

Partitioning requires large samples of reference values. If not, the subclass sizes may be too small for refiable estimates of reference intervals. 

As shown by the above formulas, SED can be partitioned into two errors (a) a systematic difference (bias) between the two sets of analysis values calculated as the difference between the means of the two sets of values, and (b) SED corrected for bias (SED(C)) or unexplained error, caused by using an equation not designed specifically for the samples being tested. The slope of reference values regressed on predicted values usually differs from 1, and is included in unexplained error. 

Although experimental partition coefficients are the values of reference, drug design often necessitates log evaluations before the compound has been synthesized. Consequently, various methods have been developed to predict lipophilicity [188], and they generally apply only to neutral compounds in the water-OCT system. 

For the studies summarized in Table I and discussed in the following sections of the text, physicochemical properties (including partition coefficients) were collected from a variety of reference documents or estimated according to available equations (Table III). Acceptable daily doses were calculated from toxicological data (Table III). When more than one equation was available, judgment was used to determine which to apply. Table III excludes those contaminants footnoted in Table I. A default value of 1.0 was adopted for K for the first nine compounds of Table III (4). For PBBs, the value of log KQC was calculated from the solubility in creek water (7.96 x 10-4 pM), according to the equation (1,3)1... 

The first step Is to use Equation 7 to compute the two weighted means v and w 2 Since all of the starting Uj j are either 0 or 1, in this case v- and v 2 are just the usual mean values, or centers, of the corresponding hard partition of the input data. When the Uj j, Include values between 0 and 1, the are often referred to... 

However, before more comprehensive data sets of measured values become available, the calculation of KOA from Kow and KAW is the most viable approach. Indeed, most of the investigations of plant-air partitioning to date have been done with calculated KqA values, and hence the derived correlations are valid only with calculated values. In order to avoid confusion, this chapter will refer to calculated KqA values as KoW/KAW. 

An advantage of defining the problem in this manner is that the partition coefficient has become a central property in quantitative structure-activity relationships (QSAR) and a large data base of P values is available in the medicinal chemistry literature (22-24). In particular, if a correlation (Equation 15) between the polymer-water and octanol-water partition coefficients can be established for a series of solutes, it becomes possible to utilize log P (oc-tanol/water) value as a reference point from which to calculate the polymer-water value. 

Another obvious conclusion that follows from Fig. 18 is that the EDM (-> MEC) are localized, as are the MEC modes that they resemble. This is particularly so in Part b of the figure, where modes a = 14 and 15 represent the corresponding CH fragments of toluene. A reference to the kva values, which reflect a partitioning of the external CT, d/V, for the most important CT-active... 

Note that in Eq. 8-24 we have used the typical approximation to factorize the partition function [28,32] and hence Qv,s, Qv are the (quantum) vibrational partition functions of the solvent and solute molecule, respectively, and U = + AUvfi with < > the system potential energy (i.e., electronic ground state energy surface) and NUv,o the system vibrational ground state energy shift from a reference value [28,32], typically negligible. 

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