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Applied and Environmental Microbiology, October 2008, p. 6481-6482, Vol. 74, No. 20
0099-2240/08/$08.00+0     doi:10.1128/AEM.01217-08
Copyright © 2008, American Society for Microbiology. All Rights Reserved.

LETTER TO THE EDITOR

Models with Insignificant Parameters

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A recent article published in Applied and Environmental Microbiology by Buckow et al. (1) describes the inactivation of feline calicivirus (FCV) in cell culture medium and in mineral water by heat and high hydrostatic pressure. These authors used a primary model (nth-order reaction scheme) to define the isobaric-isothermal inactivation of the virus.

What I have found bothersome in the paper of Buckow et al. (1) is the secondary model and its parameter estimation step. They used the following empirical polynomial equation to define the specific rate constant (k') that was previously obtained from their primary model fit to the survival curves of the virus:

(1)

where P is pressure and T is temperature. First of all, this model, equation 1, lacks parsimony (i.e., simplicity) since it has 10 parameters. Therefore, Buckow et al. (1) removed some variables which did not significantly contribute for both cell culture medium (parameters A₆, A₇, and A₉ were removed for cell culture medium) and mineral water (parameters A₆ and A₈ were removed for mineral water) (see Table 3 in the article by Buckow et al. [1]). Specific-rate-constant (k') values presented by Buckow et al. (1) were used to show the results of the fitting of equation 1. The parameters removed in equation 1 were the same as those removed by Buckow et al. (1). These results are presented in Table 1 of this letter.

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TABLE 1. Model parameter valuesa

Looking at Table 1 (see the P values), it could be seen that there are still insignificant parameters in the model used by Buckow et al. (1). The P value is the probability of being wrong in concluding that there is an association between the dependent and independent variables. The smaller the P value, the greater the probability that there is an association. Traditionally, it can be concluded that the independent variable can be used to describe the dependent variable when P is <0.05. P values exceeding 0.05 are shown in boldface type. In the paper by Buckow et al. (1), it was said that the significance of the model parameters used in equation 1 was assessed by determining the mean square errors (MSEs); however, it should be done by using P values since MSEs are an informative measure of goodness-of-fit for regression models, not an indicator to understand the significance of the model parameters.

Here, I proposed to remove some more variables from equation 1 to have models with "significant parameters" (Table 2) for both cell culture medium and mineral water.

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TABLE 2. Second trial for estimation of model parameter values ± standard errora

Table 2 shows that equation 1 can be used to define the specific-rate-constant (k') values with only four and six parameters in cell culture medium and mineral water, respectively, although a very slight loss of goodness of fit occurred for cell culture medium (see MSE values in Tables 1 and 2). Moreover, F-test was used to compare the reduced model with the model of Buckow et al. (1) to see whether the removal of the model parameters significantly improves the fit or not. The more complex equations (the ones used by Buckow et al. [1]) did not provide a significantly better fit (data not shown).

Finally, this comment should be made: isorate lines used to present the combined effects of heat and pressure (see Fig. 5 and 6 of Buckow et al. [1]) were plotted by using models with "insignificant parameters" (secondary models with "insignificant parameters" were incorporated in the primary model to plot the isorate lines); hence, they need to be corrected.

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1
1. Buckow, R., S. Isbarn, D. Knorr, V. Heinz, and A. Lehmacher. 2008. Predictive model for inactivation of feline calicivirus, a norovirus surrogate, by heat and high hydrostatic pressure. Appl. Environ. Microbiol. 74:1030-1038.[Abstract/Free Full Text]

						Sencer Buzrul Food Engineering Department Middle East Technical University 06531 Ankara, Turkey Phone: 90-321-210-5638 Fax: 90-312-210-2767 E-mail: sbuzrul{at}metu.edu.tr

Authors' Reply

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The reduced mathematical models suggested by Dr. Buzrul are interesting and, from a purely statistical point of view, may provide a satisfactory description of the functional relation of feline calicivirus inactivation rate, pressure, and temperature published by Buckow, Isbarn, et al. (1). However, we do not agree with Dr. Buzrul that the parameters of the published models for FCV inactivation should be removed, because of the following reasons.

We used a 3-order polynomial equation in secondary modeling due to its relation to the thermodynamic function of Gibbs free energy (see references 2, 3, and 4). This allows at least some conclusions on the thermodynamic background of protein denaturation (the most likely mechanism of virus inactivation under pressure). Deprivation of secondary order terms in the equation used would revoke this relationship.

MSE is a powerful tool for determining the minimum number of equation parameters required during regression analysis. P values provide a good understanding of the significance of a single parameter in an equation, but not of the equation as a whole. It is not surprising that the significance of a single parameter increases with the decrease of equation parameter values.

The models for calicivirus inactivation proposed by Dr. Buzrul do not provide a better goodness of fit. In contrast to Dr. Buzrul's statement, we could not find R² or MSE values in Buzrul's models better than those published by Buckow et al. (using the k' values published in our paper) (1).

Therefore, we do not see the need to revise the models published and/or to correct the isolines presented in the pressure-temperature diagrams in our paper.

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1
1. Buckow, R., S. Isbarn, et al. 2008. Predictive model for inactivation of feline calicivirus, a norovirus surrogate, by heat and high hydrostatic pressure. Appl. Environ. Microbiol. 74:1030-1038.[Abstract/Free Full Text]
2
2. Knorr, D., V. Heinz, et al. 2006. High pressure application for food biopolymers. Biochim. Biophys. Acta 1764:619-631.[Medline]
3
3. Meersman, F., L. Smeller, et al. 2006. Protein stability and dynamics in the pressure-temperature plane. Biochim. Biophys. Acta 1764:346-354.[Medline]
4
4. Smeller, L. 2002. Pressure-temperature phase diagram of biomolecules. Biochim. Biophys. Acta 1595:11-29.[CrossRef][Medline]

						Roman Buckow Food Science Australia Private Bag 16 Werribee 3030, VIC, Australia Anselm Lehmacher* Institut für Hygiene und Umwelt Abteilung Mikrobiologischer Verbraucherschutz Marckmannstrasse 129a D-20539 Hamburg, Germany
						* Phone: 49-40-42845-7270 Fax: 49-40-42845-7274 E-mail: anselm.lehmacher{at}hu.hamburg.de

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Applied and Environmental Microbiology, October 2008, p. 6481-6482, Vol. 74, No. 20
0099-2240/08/$08.00+0     doi:10.1128/AEM.01217-08
Copyright © 2008, American Society for Microbiology. All Rights Reserved.

This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Reprints and Permissions Copyright Information Books from ASM Press MicrobeWorld Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Buzrul, S. Articles by Lehmacher, A. Search for Related Content PubMed PubMed Citation Articles by Buzrul, S. Articles by Lehmacher, A. Agricola Articles by Buzrul, S. Articles by Lehmacher, A.