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Pooling imprecision for interpretative purposes
Clinica Chimica Acta 378 (2007) 231 www.elsevier.com/locate/clinchim
Letter to the Editor
Pooling imprecision for interpretative purposes
Many clinical laboratories, especially emergency laboratories, measure some biological quantities using indistinctly (at random) two or more measurement systems. Ideally, the imprecision and the systematic errors of these measurement systems, if they exist, should be the same. However, in real life, these measurement systems frequently have different imprecision or different systematic errors, or both, and measurement results usually are transferred to the laboratory information system without matching each result with the corresponding measurement system. Measurement results of a biological quantity obtained in this way may correspond to consecutive measurements in the same patient. The goal of such consecutive measurements is often to detect a significant change in the value of the quantity under consideration; this change is significant when the difference between the two consecutive results is greater than a “reference change” or “critical difference” (dc) calculated as follows [1,2]: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dc ¼ 2; 33 s2M þ s2Bw where, sM is the metrological (usually day-to-day) standard deviation of the measurement procedure, and sBw is the withinsubject biological variation of the biological quantity under measurement. In these cases, the metrological standard deviation used in the formula above should be the pooled metrological standard deviation of the different measurement systems indistinctly used. For a given biological quantity, the pooled standard deviation should be calculated from the individual standard deviation of each measurement system, which is estimated using the same patient samples or the same control materials, provided that these control materials are commutable with human samples. Pooling standard deviation requires different approaches depending on the metrological differences between the two or more measurement systems used. When only differences in imprecision occur, the pooled imprecision will have an intermediate value between individual imprecision, and should
0009-8981/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cca.2006.12.007
be calculated using the formula A [3]. When there are differences in systematic error only, or in both imprecision and systematic error, the pooled imprecision may be higher than the higher individual imprecision, and should be calculated using the formula B [4]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rðni −1Þs2i formula A: sP ¼ Rðni −1Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rðni −1Þs2i þ Rni ð x¯i − x¯ Þ2 where formula B: sB ¼ Rðni −1Þ P ni ¯xi ¯x ¼ Pi i ni and sP is the metrological pooled standard deviation; ni, and x¯i, are, respectively, the sample size and the mean of data used in estimating each individual metrological standard deviation. References [1] Harris EK, Yasaka T. On the calculation of a “reference change” for comparing two consecutive measurements. Clin Chem 1983;29:25–30. [2] Harris EK, Boyd JC. Statistical bases of reference values in laboratory medicine. New York: Marcel Dekker; 1995. p. 221–58. [3] International Union of Pure and Applied Chemistry. Compendium of chemical terminology (“Gold book”). Oxford: Blackwell Science; 1997. http://www. chem.qmul.ac.uk/iupac/bibliog/gold.html (Accessed October 2006). [4] Hyvärinen A. A model for the statistical description of analytical errors occurring in clinical chemical laboratories with time. Scand J Clin Lab Med 1985;45(Suppl 175):1–84.
Raül Rigo-Bonnin Ariadna Padró-Miquel José Valero-Politi Xavier Fuentes-Arderiu* Laboratori Clínic, IDIBELL-Hospital Universitari de Bellvitge, 08907 L´Hospitalet de Llobregat, Catalonia, Spain E-mail address: [email protected]. * Corresponding author. 16 November 2006
Letter to the Editor
Pooling imprecision for interpretative purposes
Many clinical laboratories, especially emergency laboratories, measure some biological quantities using indistinctly (at random) two or more measurement systems. Ideally, the imprecision and the systematic errors of these measurement systems, if they exist, should be the same. However, in real life, these measurement systems frequently have different imprecision or different systematic errors, or both, and measurement results usually are transferred to the laboratory information system without matching each result with the corresponding measurement system. Measurement results of a biological quantity obtained in this way may correspond to consecutive measurements in the same patient. The goal of such consecutive measurements is often to detect a significant change in the value of the quantity under consideration; this change is significant when the difference between the two consecutive results is greater than a “reference change” or “critical difference” (dc) calculated as follows [1,2]: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dc ¼ 2; 33 s2M þ s2Bw where, sM is the metrological (usually day-to-day) standard deviation of the measurement procedure, and sBw is the withinsubject biological variation of the biological quantity under measurement. In these cases, the metrological standard deviation used in the formula above should be the pooled metrological standard deviation of the different measurement systems indistinctly used. For a given biological quantity, the pooled standard deviation should be calculated from the individual standard deviation of each measurement system, which is estimated using the same patient samples or the same control materials, provided that these control materials are commutable with human samples. Pooling standard deviation requires different approaches depending on the metrological differences between the two or more measurement systems used. When only differences in imprecision occur, the pooled imprecision will have an intermediate value between individual imprecision, and should
0009-8981/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cca.2006.12.007
be calculated using the formula A [3]. When there are differences in systematic error only, or in both imprecision and systematic error, the pooled imprecision may be higher than the higher individual imprecision, and should be calculated using the formula B [4]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rðni −1Þs2i formula A: sP ¼ Rðni −1Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rðni −1Þs2i þ Rni ð x¯i − x¯ Þ2 where formula B: sB ¼ Rðni −1Þ P ni ¯xi ¯x ¼ Pi i ni and sP is the metrological pooled standard deviation; ni, and x¯i, are, respectively, the sample size and the mean of data used in estimating each individual metrological standard deviation. References [1] Harris EK, Yasaka T. On the calculation of a “reference change” for comparing two consecutive measurements. Clin Chem 1983;29:25–30. [2] Harris EK, Boyd JC. Statistical bases of reference values in laboratory medicine. New York: Marcel Dekker; 1995. p. 221–58. [3] International Union of Pure and Applied Chemistry. Compendium of chemical terminology (“Gold book”). Oxford: Blackwell Science; 1997. http://www. chem.qmul.ac.uk/iupac/bibliog/gold.html (Accessed October 2006). [4] Hyvärinen A. A model for the statistical description of analytical errors occurring in clinical chemical laboratories with time. Scand J Clin Lab Med 1985;45(Suppl 175):1–84.
Raül Rigo-Bonnin Ariadna Padró-Miquel José Valero-Politi Xavier Fuentes-Arderiu* Laboratori Clínic, IDIBELL-Hospital Universitari de Bellvitge, 08907 L´Hospitalet de Llobregat, Catalonia, Spain E-mail address: [email protected]. * Corresponding author. 16 November 2006