Drug Information Journal - March 2009 - (Page 145) Local Laboratory Reference Intervals MEDICAL INFORMATION 145 itively skewed distributions. Therefore, it was decided to work with the natural logarithm of the raw data: ln(Xij). There would be no difference in the conclusions if base 10 had been used. Standardization Across Age and Gender. Because reference intervals may vary according to age and gender and since local laboratories and central laboratories use different population fractions to partition their reference values according to age, the data were normalized for age and gender. The data were standardized to the appropriate central laboratory reference limit (LRL or URL depending on the appropriate application). Taking the LRL: each result Xij has associated with it a central laboratory LRL (Lc, which now may vary according to age and gender) and the result is divided by Lc for analysis. The data actually analyzed are Yij = ln(Xij/Lc). The local LRLs are standardized using the same method. The mean of each laboratory’s LRL is taken over all the results to obtain Li. The empirical lower limits Λi follow directly from the Yij and so are automatically standardized. The figures are therefore comparing like with like. The same procedure, adjusted as necessary, is used when dealing with the URL. The following provides an example of the calculation, which may make the underlying theory clearer. The analyte hemoglobin is used and the LRL is considered. There are 16,350 valid hemoglobin results in the data set and, of them, 9,761 (59.6%) were below the central laboratory LRL. Only 16 results (0.1%) were above the central laboratory URL. This is a reflection of the clinical origin of the data set and reflects that a meaningful analysis of the local laboratory URL cannot be performed. The first valid hemoglobin observation in the data set for laboratory 533 is for a 58-yearold female with a hemoglobin of 131 g/L. The central laboratory reference interval for younger females is 1 16–164 g/L and the local laboratory reference interval for females of all ages was 120–160 g/L. This hemoglobin result is standardized by the formula Yij = ln(Xij/Lc), where: i = 533 as the laboratory identifier is 533 j = 1 as it is the first result for that laboratory Xij = 1 as the actual concentration observed 31 Lc = 1 the central laboratory LRL 16, resulting in (remembering natural logarithms are used) Yij = 0.122. The Yij are calculated for all the observations in that laboratory and arranged in increasing order. Λi for this laboratory is the standardized value, which cuts off the same fraction of this laboratory’s data as the central laboratory LRL cuts off from the whole data set. It was seen above that 59.6% of the whole data set was below the appropriate central laboratory LRL. There are 275 usable hemoglobin observations for laboratory 533. Out of 275, 59.6% is 164.1, so the empirical cutoff is between the 164th and 165th lowest standardized hemoglobin results. The 164th and 165th lowest standardized hemoglobin results were both –0.04839 and so Λi for laboratory 533 is also –0.04839. (The minus sign here indicates that the hemoglobin results from laboratory 533 are slightly lower than the data set as a whole.) The empirical LRL limits are to be compared with the actual laboratory LRL. However, a laboratory may use LRL limits specific for age and gender, and these may change with time. Taking the laboratory LRL for each observation, standardizing it by dividing it by the central laboratory LRL and taking the natural logarithm, and then calculating the mean of the standardized LRL, a single lower limit Li for each laboratory is obtained. The central laboratory and local laboratory LRL for the 58-year-old female mentioned above are 1 and 120 g/L re16 spectively, so the standardized LRL is ln(120/ 1 16)L = 0.034. This data transformation as well as the meaning of the global cutoff fraction F and the local empirical reference limit Λ is illustrated in Figure 3. The mean of the standardized limits (Li) for laboratory 533 is 0.04835 (this laboratory’s LRLs are in general higher than the central laboratory’s LRLs). The local laboratory LRLs are assessed by correlating the empirical LRL (Λi) with the actual LRL (Li). If the local laboratories have chosen their LRL rationally with respect to their Drug Information Journal
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