TY - JOUR A1 - Jarvis, B. A1 - Wilrich, Cordula A1 - Wilrich, P.-Th. T1 - Estimation of the POD function and the LOD of a binary microbiological measurement method from an interlaboratory experiment N2 - 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 http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich. 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 Microbiological Methods Received December 11, 2018. Accepted by AH April 5, 2019. Estimation of the POD Function and the LOD of a Binary Microbiological Measurement Method from an Interlaboratory Experiment Basil Jarvis, Ross Biosciences Ltd, Upton Bishop, Ross-on-Wye HR9 7UR, United Kingdom; Cordula Wilrich, Bundesanstalt für Materialforschung und –prüfung, Unter den Eichen 87, D-12205 Berlin, Germany; Peter-Theodor Wilrich, Freie Universität Berlin, Institut für Statistik und Ökonometrie, Garystrasse 21, D-14195 Berlin, Germany. DOI: https://doi.org/10.5740/jaoacint.18-0412 method with respect to reference method. The method is implemented in an EXCEL program that can be downloaded from http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/wilrich. KW - Probability of detection KW - POD KW - Level of detection KW - Limit of detection KW - LOD KW - Interlaboratory experiment KW - Collaborative studies KW - Qualitative measurements KW - Binary measurement KW - Microbiological measurement PY - 2019 UR - https://aoac.publisher.ingentaconnect.com/contentone/aoac/jaoac/2019/00000102/00000005/art00042 U6 - https://doi.org/10.5740/jaoacint.18-0412 SN - 1060-3271 SN - 1944-7922 VL - 102 IS - 5 SP - 1617 EP - 1623 PB - AOAC International CY - Gaithersburg, USA, MD, 20877-2504 AN - OPUS4-48883 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Jarvis, B. A1 - Wilrich, Cordula A1 - Wilrich, P.-Th. T1 - Reconsideration of the derivation of most probable numbers, their standard deviations, confidence bounds and rarity values N2 - Aims: The purpose of this work was to derive a simple Excel spreadsheet and a set of standard tables of most probable number (MPN) values that can be applied by users of International Standard Methods to obtain the same output values for MPN, SD of the MPN, 95% confidence limits and test validity. With respect to the latter, it is considered that the Blodgett concept of 'rarity' is more valuable than the frequently used approach of improbability (vide de Man). Methods and Results: The paper describes the statistical procedures used in the work and the reasons for introducing a new set of conceptual and practical approaches to the determination of MPNs and their parameters. Examples of MPNs derived using these procedures are provided. The Excel spreadsheet can be downloaded from http://www.wiwiss.fu-berlin.de/institute/iso/mitarbeiter/wilrich/index.html. Conclusions: The application of the revised approach to the determination of MPN parameters permits those who wish to use tabulated values, and those who require access to a simple spreadsheet to determine values for nonstandard test protocols, to obtain the same output values for any specific set of multiple test results. The concept of 'rarity' is a more easily understood parameter to describe test result combinations that are not statistically valid. Provision of the SD of the log MPN value permits derivation of uncertainty parameters that have not previously been possible. Significance and Impact of the Study: A consistent approach for the derivation of MPNs and their parameters is essential for coherence between International Standard Methods. It is intended that future microbiology standard methods will be based on the procedures described in this paper. KW - Confidence bounds KW - Microbiological analyses KW - Most probable number KW - MPN KW - Rarity value PY - 2010 U6 - https://doi.org/10.1111/j.1365-2672.2010.04792.x SN - 1364-5072 VL - 109 IS - 5 SP - 1660 EP - 1667 PB - Wiley-Blackwell CY - Malden, Mass., USA AN - OPUS4-22168 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -