Population-Based Reference Regions

The topic of the previous sections of this chapter has been univariate population-based reference values and quantities derived from them. Such values do not, however, fit the common clinical situation in which observed values of several different laboratory tests are available for interpretation and decision making. For example, the average number of individual clinical chemistry tests requested on one specimen received in the author s laboratory is 9.7. There are two models for interpretation by comparison in this situation. We can compare each observed value with the corresponding reference values or inteiwal (i.e., we perform multiple, univariate comparisons) or we can consider the set of observed values as a single multivariate observation and interpret it as such by a multivariate comparison. In this section, the relative merits of these two approaches are discussed, and methods for the latter type of comparison are presented. 

A univariate observation, such as a single laboratory result, may be represented graphically as a point on a line, the axis. The results obtained by two different laboratory tests performed on the same specunen (a bivariate observation) may be displayed as a point in a plane defined by two perpendicular axes. With three results, we have a trivariate observation and a point in a space defined by three perpendicular axes, and so on. We lose the possibility for visualization of a multivariate observation when there are more than three dimensions. StiU, we can consider the multivariate observation as a point in a multidimensional hyperspace with as many mutually perpendicular axes as there are results of different tests. The prefix hyper signifies, in this context, more than three dimensions. Such multivariate observations are also 

The use of multivariate reference regions usually requires the assistance of a computer program, which takes a set of results obtained by several laboratory tests on the same clinical specimen and calculates an index. The interpretation of a multivariate observation in relation to reference values is then the task of comparing the index with a critical value estimated from the reference values. This, obviously, is much simpler than comparing each result with its proper reference interval. 

The index is essentially a distance measure, Mahalanobis squared distance (D ), which expresses the multivariate distance between the observation point and the common mean of the reference values, taldng into account the dispersion and correlation of the variables.More interpreta-tional guidance may be obtained from this distance by expressing it as a percentile analogous to the percentile presentation of univariate observed values. Also, the index of atypicality has a multivariate counterpart.  

Mahalanobis squared distance of an observation is the multivariate analog of the square of the SD unit (d ) discussed earlier  

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The extent of the survey is based on regional studies, with the requirements for data quality and quantity set forth in Refe [1,6]. The investigation is site-specific and covers an area within an approximately 50 km radius of the site. This area may be extended to compensate for lack of data in the time record (see Section 6.2). It may be smaller if the area is not populated and possible causes of events do not exist. The record length to be considered for site-specific evaluation is chosen with reference to the return period selected for the design basis. Appropriate extrapolation techniques have to be applied and validated. The projected growth of population around the site during the lifetime of the facility is evaluated. 

The conformational space sampled by the two-domain protein calmodulin has been explored by an approach based on four sets of NMR observables obtained on Tb " and Tm -substituted proteins. The observables are the pseudocontact shifts and residual dipolar couplings of the C-terminal domain when lanthanide substitution is at the N-terminal domain. Each set of observables provides independent information on the conformations experienced by the molecule. It was found that not all sterically allowed conformations are equally populated. For example, taking the N-terminal domain as the reference, the C-terminal domain preferentially resides in a region of space inscribed in a wide elliptical cone. 

Within a population, slight differences in individual DNA makes one organism uniquely different from others. Referred to as sequence polymorphisms, these are often the result of single base-pair changes that occur in regions of DNA that do not encode a gene but that are recognized and bound by restriction enzymes. 

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