Drug Information Journal - March 2009 - (Page 144) 144 MEDICAL INFORMATION Dijkman, Fraser, Treasure, Kapke STUDY POPULATION Reference intervals are usually derived from reference samples collected from a reference sample population. The LRL is, by convention, often set at the 2.5% percentile. This analysis is based on a clinical trial data set, which will likely, for many analytes, be different from the usual reference population. The method to be described is empirical because it uses the data as seen in the data set. TWO LOCAL LOWER LIMITS The ith local laboratory is now associated with two LRLs: 1. Li is the LRL that the local laboratory has derived and actually uses in practice: the actual local LRL. 2. Λi is the LRL that the local laboratory should use to cut off the same fraction of the results locally as the central laboratory LRL (Lc) does globally, according to the current data set. GLOBAL CUTOFF FRACTION For each analyte Q, there is a central laboratory-defined lower reference limit Lc. The central laboratory reference interval has a rational basis, as described under Reference Intervals. Over the whole data set for all laboratories, a fraction F of the results falls below the LRL: F is defined as the global cutoff fraction. This fraction differs from the cutoff fraction that would derive from an apparently healthy population since F is derived from this study population, which, for some analytes, such as leucocyte count, may be different. F = # of samples < Lc # of samples (1) EMPIRICAL LOCAL LOWER LIMITS If the distribution of values were identical for each local laboratory, then the fraction of results below the central laboratory LRL would be the global cutoff fraction F for each laboratory. In any real data set, the observed distribution will not be identical over all local laboratories. This can be characterized by calculating, for each laboratory, what the LRL should be in order to achieve the cutoff with the identical fraction F. This is the empirical local LRL and, for the ith local laboratory, will be denoted Λi. Mathematically, Λi is calculated to satisfy: F = # of results from ith laboratory < Λi # of results from ith laboratory POTENTIAL RELATIONSHIP BETWEEN Li AND Λi Suppose the local laboratories selected the actual local LRL (Li) on a rational basis: that is, Li is derived on the basis of the reference sample population actually examined at that laboratory, as was done for the central laboratory reference interval. If that local population generally had results that were, for example, higher than those of the global population, then the local laboratory should derive a higher value of Li (whatever algorithm is actually used to do the calculation). Since the population for that laboratory has generally higher results, the results in the database will also tend to be higher and so the empirical lower limit Λi will also be higher (in order to keep cutting off the same fraction F). In summary, if the local laboratory has derived Li rationally from the reference sample population selected by them for derivation of reference intervals, then Λi would be close to Li. If this held true over the whole set of laboratories, there would be a significant correlation between Λi and Li. Conversely, if there is no objective justification for the local laboratory’s choice of Li, there should be no significant correlation observed between Λi and Li. The hypothesis that there is no objective population justification for local reference limits is tested with the available data. DATA TRANSFORMATIONS Raw Data. For a specified analyte Q, the jth observation from the ith laboratory is denoted Xij. Logarithmic Transformation. All the results are by definition positive. For several analytes, particularly those harmonized, results had pos- where the global cutoff fraction F is calculated from the whole data set as in Eq. (1) above.
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