Basil Jarvis1, Cordula Wilrich2, Peter-Theodor Wilrich3. 1. Ross Biosciences Ltd, Upton Bishop, Ross-on-Wye HR9 7UR, United Kingdom. 2. Bundesanstalt für Materialforschung und -prüfung, Unter den Eichen 87, D-12205 Berlin, Germany. 3. Freie Universität Berlin, Institut für Statistik und Ökonometrie, Garystrasse 21, D-14195 Berlin, Germany.
Abstract
Background: We deal with interlaboratory experiments (collaborative studies) in which k participating laboratories, selected randomly from a population of laboratories, use samples from one and the same material or matrix. They perform binary microbiological measurements for which the measurement results are either "0" (target microorganisms not detected) or "1" (target microorganisms detected). The performance of such a measurement method is described by its probability of detection (POD) function, i.e., the POD as a function of the contamination of the sample (CFU per gram or CFU per milliliter), or by the level of detection (LODp), i.e., the contamination level of the sample that is detected (measurement result "1") with a specified probability p. Objective: We derive an approximate statistical analysis that is simple enough to be implemented in a spreadsheet application. Methods: Under the assumption of a Poisson distribution of the number of CFU in the samples, we estimate the mean POD function of the laboratories and the SD of the laboratory effect based on a complementary log-log model, a special case of the Generalized Linear Model in the special situation in which the contamination level is known by means other than the POD. The estimates are obtained by maximization of the Laplace approximation of the likelihood function. By simulation, a bias correction factor for the estimate of the SD is obtained. With the estimated POD function, LODs can be estimated. The model can also be used to evaluate the relative LOD of an alternative method with repect to a reference method. Results: The EXCEL program PODLOD-interlab_ver1.xls for this method of statistical analysis can be downloaded from <ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich">http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich</ext-link>. Highlights: A simple approximate statistical method for the estimation of the POD and LOD is derived. The method also allows the estimation of the RLOD of an alternative method with respect to reference method. The method is implemented in an EXCEL program that can be downloaded from <ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="url" xlink:href="http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich">http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich</ext-link>.
Background: We deal with interlaboratory experiments (collaborative studies) in which k participating laboratories, selected randomly from a population of laboratories, use samples from one and the same material or matrix. They perform binary microbiological measurements for which the measurement results are either "0" (target microorganisms not detected) or "1" (target microorganisms detected). The performance of such a measurement method is described by its probability of detection (POD) function, i.e., the POD as a function of the contamination of the sample (CFU per gram or CFU per milliliter), or by the level of detection (LODp), i.e., the contamination level of the sample that is detected (measurement result "1") with a specified probability p. Objective: We derive an approximate statistical analysis that is simple enough to be implemented in a spreadsheet application. Methods: Under the assumption of a Poisson distribution of the number of CFU in the samples, we estimate the mean POD function of the laboratories and the SD of the laboratory effect based on a complementary log-log model, a special case of the Generalized Linear Model in the special situation in which the contamination level is known by means other than the POD. The estimates are obtained by maximization of the Laplace approximation of the likelihood function. By simulation, a bias correction factor for the estimate of the SD is obtained. With the estimated POD function, LODs can be estimated. The model can also be used to evaluate the relative LOD of an alternative method with repect to a reference method. Results: The EXCEL program PODLOD-interlab_ver1.xls for this method of statistical analysis can be downloaded from <ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich">http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich</ext-link>. Highlights: A simple approximate statistical method for the estimation of the POD and LOD is derived. The method also allows the estimation of the RLOD of an alternative method with respect to reference method. The method is implemented in an EXCEL program that can be downloaded from <ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="url" xlink:href="http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich">http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich</ext-link>.