The Most Probable Curve method - A robust approach to estimate kinetic models from low plate count data resulting in reduced uncertainty

A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model that makes a separation between the “true” microbial concentration according to the model, the “actual” concentration in the media considering...

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Vydané v:	International journal of food microbiology Ročník 380; s. 109871
Hlavní autori:	Garre, Alberto, Zwietering, Marcel H., van Boekel, Martinus A.J.S.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 02.11.2022
Predmet:	Bayesian statistics food microbiology Gamma-Poisson regression Kinetic modelling kinetics liquids Listeria monocytogenes Microbial inactivation Pasteurization plate count Poisson distribution Poisson regression Predictive microbiology regression analysis Robust statistics stress tolerance uncertainty Robust statistics Bayesian statistics Predictive microbiology Kinetic modelling Pasteurization Gamma-Poisson regression Microbial inactivation Poisson regression
ISSN:	0168-1605, 1879-3460, 1879-3460
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Abstract	A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model that makes a separation between the “true” microbial concentration according to the model, the “actual” concentration in the media considering chance, and the actual counts on the plate. It is based on the assumptions that stress resistance is homogeneous within a microbial population, and that there is no aggregation of microbial cells. Under these assumptions, the number of colonies in/on a plate follows a Poisson distribution with expected value depending on the proposed kinetic model, the number of dilutions and the plated volume. The novel method is compared against (non)linear regression based on a normal likelihood distribution (traditional method), Poisson regression and gamma-Poisson regression using data on the inactivation of Listeria monocytogenes. The conclusion is that the traditional method has limitations when the data includes plates with low (or zero) cell counts, which can be mitigated using more complex (discrete) likelihoods. However, Poisson regression uses an unrealistic likelihood function, making it unsuitable for survivor curves with several log-reductions. Gamma-Poisson regression uses a more realistic likelihood function, even though it is based mostly on empirical hypotheses. We conclude that the MPC method can be used reliably, especially when the data includes plates with low or zero counts. Furthermore, it generates a more realistic description of uncertainty, integrating the contribution of the plating error and reducing the uncertainty of the primary model parameters. Consequently, although it increases modelling complexity, the MPC method can be of great interest in predictive microbiology, especially in studies focused on variability analysis. •Models fitted using normal likelihood functions have limitations for low plate counts.•Poisson regression is unsuitable to describe survivor curves with multiple log-reductions.•Gamma-Poisson provides a suitable empirical extension of Poisson regression.•The Most Probable Curve (MPC) method estimates kinetic parameters from low plate counts reliably.•The MPC method can integrate the uncertainty resulting from serial dilutions and plating.
AbstractList	A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model that makes a separation between the “true” microbial concentration according to the model, the “actual” concentration in the media considering chance, and the actual counts on the plate. It is based on the assumptions that stress resistance is homogeneous within a microbial population, and that there is no aggregation of microbial cells. Under these assumptions, the number of colonies in/on a plate follows a Poisson distribution with expected value depending on the proposed kinetic model, the number of dilutions and the plated volume. The novel method is compared against (non)linear regression based on a normal likelihood distribution (traditional method), Poisson regression and gamma-Poisson regression using data on the inactivation of Listeria monocytogenes. The conclusion is that the traditional method has limitations when the data includes plates with low (or zero) cell counts, which can be mitigated using more complex (discrete) likelihoods. However, Poisson regression uses an unrealistic likelihood function, making it unsuitable for survivor curves with several log-reductions. Gamma-Poisson regression uses a more realistic likelihood function, even though it is based mostly on empirical hypotheses. We conclude that the MPC method can be used reliably, especially when the data includes plates with low or zero counts. Furthermore, it generates a more realistic description of uncertainty, integrating the contribution of the plating error and reducing the uncertainty of the primary model parameters. Consequently, although it increases modelling complexity, the MPC method can be of great interest in predictive microbiology, especially in studies focused on variability analysis. •Models fitted using normal likelihood functions have limitations for low plate counts.•Poisson regression is unsuitable to describe survivor curves with multiple log-reductions.•Gamma-Poisson provides a suitable empirical extension of Poisson regression.•The Most Probable Curve (MPC) method estimates kinetic parameters from low plate counts reliably.•The MPC method can integrate the uncertainty resulting from serial dilutions and plating. A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model that makes a separation between the “true” microbial concentration according to the model, the “actual” concentration in the media considering chance, and the actual counts on the plate. It is based on the assumptions that stress resistance is homogeneous within a microbial population, and that there is no aggregation of microbial cells. Under these assumptions, the number of colonies in/on a plate follows a Poisson distribution with expected value depending on the proposed kinetic model, the number of dilutions and the plated volume. The novel method is compared against (non)linear regression based on a normal likelihood distribution (traditional method), Poisson regression and gamma-Poisson regression using data on the inactivation of Listeria monocytogenes. The conclusion is that the traditional method has limitations when the data includes plates with low (or zero) cell counts, which can be mitigated using more complex (discrete) likelihoods. However, Poisson regression uses an unrealistic likelihood function, making it unsuitable for survivor curves with several log-reductions. Gamma-Poisson regression uses a more realistic likelihood function, even though it is based mostly on empirical hypotheses. We conclude that the MPC method can be used reliably, especially when the data includes plates with low or zero counts. Furthermore, it generates a more realistic description of uncertainty, integrating the contribution of the plating error and reducing the uncertainty of the primary model parameters. Consequently, although it increases modelling complexity, the MPC method can be of great interest in predictive microbiology, especially in studies focused on variability analysis. A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model that makes a separation between the "true" microbial concentration according to the model, the "actual" concentration in the media considering chance, and the actual counts on the plate. It is based on the assumptions that stress resistance is homogeneous within a microbial population, and that there is no aggregation of microbial cells. Under these assumptions, the number of colonies in/on a plate follows a Poisson distribution with expected value depending on the proposed kinetic model, the number of dilutions and the plated volume. The novel method is compared against (non)linear regression based on a normal likelihood distribution (traditional method), Poisson regression and gamma-Poisson regression using data on the inactivation of Listeria monocytogenes. The conclusion is that the traditional method has limitations when the data includes plates with low (or zero) cell counts, which can be mitigated using more complex (discrete) likelihoods. However, Poisson regression uses an unrealistic likelihood function, making it unsuitable for survivor curves with several log-reductions. Gamma-Poisson regression uses a more realistic likelihood function, even though it is based mostly on empirical hypotheses. We conclude that the MPC method can be used reliably, especially when the data includes plates with low or zero counts. Furthermore, it generates a more realistic description of uncertainty, integrating the contribution of the plating error and reducing the uncertainty of the primary model parameters. Consequently, although it increases modelling complexity, the MPC method can be of great interest in predictive microbiology, especially in studies focused on variability analysis.A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model that makes a separation between the "true" microbial concentration according to the model, the "actual" concentration in the media considering chance, and the actual counts on the plate. It is based on the assumptions that stress resistance is homogeneous within a microbial population, and that there is no aggregation of microbial cells. Under these assumptions, the number of colonies in/on a plate follows a Poisson distribution with expected value depending on the proposed kinetic model, the number of dilutions and the plated volume. The novel method is compared against (non)linear regression based on a normal likelihood distribution (traditional method), Poisson regression and gamma-Poisson regression using data on the inactivation of Listeria monocytogenes. The conclusion is that the traditional method has limitations when the data includes plates with low (or zero) cell counts, which can be mitigated using more complex (discrete) likelihoods. However, Poisson regression uses an unrealistic likelihood function, making it unsuitable for survivor curves with several log-reductions. Gamma-Poisson regression uses a more realistic likelihood function, even though it is based mostly on empirical hypotheses. We conclude that the MPC method can be used reliably, especially when the data includes plates with low or zero counts. Furthermore, it generates a more realistic description of uncertainty, integrating the contribution of the plating error and reducing the uncertainty of the primary model parameters. Consequently, although it increases modelling complexity, the MPC method can be of great interest in predictive microbiology, especially in studies focused on variability analysis.
ArticleNumber	109871
Author	van Boekel, Martinus A.J.S. Zwietering, Marcel H. Garre, Alberto
Author_xml	– sequence: 1 givenname: Alberto surname: Garre fullname: Garre, Alberto organization: Food Microbiology, Wageningen University & Research, P.O. Box 17, 6700 AA Wageningen, the Netherlands – sequence: 2 givenname: Marcel H. surname: Zwietering fullname: Zwietering, Marcel H. organization: Food Microbiology, Wageningen University & Research, P.O. Box 17, 6700 AA Wageningen, the Netherlands – sequence: 3 givenname: Martinus A.J.S. surname: van Boekel fullname: van Boekel, Martinus A.J.S. email: tiny.vanboekel@wur.nl organization: Food Quality & Design, Wageningen University & Research, P.O. Box 17, 6700 AA Wageningen, the Netherlands
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Keywords	Robust statistics Bayesian statistics Predictive microbiology Kinetic modelling Pasteurization Gamma-Poisson regression Microbial inactivation Poisson regression
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Snippet	A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model...
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SubjectTerms	Bayesian statistics food microbiology Gamma-Poisson regression Kinetic modelling kinetics liquids Listeria monocytogenes Microbial inactivation Pasteurization plate count Poisson distribution Poisson regression Predictive microbiology regression analysis Robust statistics stress tolerance uncertainty
Title	The Most Probable Curve method - A robust approach to estimate kinetic models from low plate count data resulting in reduced uncertainty
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