Verification of a Tertiary Model for Growth of Salmonella

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Verification of a Tertiary Model for Growth of
Salmonella

• Thomas P. Oscar, Ph.D.
• USDA, Agricultural Research Service
• Microbial Food Safety Research Unit
• University of Maryland Eastern Shore
• Princess Anne, MD

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Stages of Model Development

• Challenge Study
• Primary Modeling
• Secondary Modeling
• Tertiary Modeling
• Performance Evaluation
• Verification
• Interpolation
• Extrapolation

Not verified Not validated
Criteria
Verified Validated
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Performance EvaluationRatio Method of Ross

• Bias factor (Bf)
• Obs/Pred
• Bf 1.0 no bias
• Acceptable Bf
• 0.7 (fail-safe) to 1.15 (fail-dangerous)

• Accuracy factor (Af)
• ?Obs/Pred?
• Af 1.0 perfect agreement
• Acceptable Af
• 1.0 to 1.45 for a model with 3 independent
  variables

Ross, T. 1996. J. Appl. Bacteriol. 81501-508.
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Limitations of Bf and Af

• Unable to detect some forms of prediction bias.
• Mean values subject to bias by outliers.
• No growth prediction cases are excluded.

Ross, T. 1996. J. Appl. Bacteriol. 81501-508.
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Objectives

• Develop a performance evaluation method
• overcomes limitations of Bf and Af
• quantifies performance of all model types
• Develop a tertiary model.
• Verify tertiary model predictions.

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Challenge Study

• Salmonella Typhimurium ATCC 14028
• Stationary phase cells grown at 30C
• Sterilized, cooked chicken breast (1 g)
• Initial density 4.8 log/g.
• 8 to 47C
• Viable cell counts
• BHI agar

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Augustin, J.C., V. Carlier. 2000. Int. J. Food
Microbiol. 5629-51.
P R I M A R Y
Logistic w Delay Best-fit values ID
4.81 LT 4.29 SGR 0.139
MPD 10.46
M O D E L
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Oscar, T. P. 2003. J. Food Prot. 66200-207.
Hyperbola (Plateau) Best-fit values
P 47.6 TMIN 6.62 M 1.44
TOPT 38.9
S E C O N D A R Y
M O D E L
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Oscar (unpublished)
Modified Ratkowsky Best-fit values B
0.0164 TMIN 2.37 TOPT 41.8
C -0.0560
S E C O N D A R Y
M O D E L
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Zwietering, M.H., et al. 1994. Appl. Environ.
Microbiol. 60195-203.
S E C O N D A R Y
Asymptote Model Best-fit values A
2.48 TMIN 7.08
TMAX 52.27 TSUBMIN 6.77 TSUPMAX 53.28
M O D E L
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T E R T I A R Y
M O D E L
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Performance Evaluation Acceptable Prediction
Zone Method

• Rate Models
• LT, SGR
• Bf obs/pred
• pBf proportion of Bf in APZone, which was wider
  in the fail-safe direction.

• Density Models
• PM, MPD, TM
• ? obs pred
• p? proportion of ? in APZone, which was wider
  in the fail-safe direction.

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Fail-dangerous
P R I M A R Y
M O D E L
Fail-safe
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p? or pBf Grade
0.9 to 1.0 Excellent
0.8 to 0.89 Good
0.7 to 0.79 Acceptable
0.6 to 0.69 Poor
lt 0.6 Unacceptable
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Performance Evaluation Acceptable Prediction
Zone Method
APZone Bf LT pBf SGR pBf
0.9 to 1.05 0.40 0.62
0.8 to 1.10 0.67 0.79
0.7 to 1.15 0.77 0.86
0.6 to 1.20 0.87 0.93
0.5 to 1.25 0.90 1.00
0.4 to 1.30 0.93 1.00
M O D E L S
R A T E
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Performance Evaluation Acceptable Prediction
Zone Method
APZone ? PM p? MPD p? TM p?
-0.10 to 0.05 0.45 0.13 0.32
-0.30 to 0.15 0.86 0.73 0.65
-0.50 to 0.25 0.95 0.80 0.79
-0.70 to 0.35 0.97 0.93 0.88
-1.00 to 0.50 0.99 1.00 0.97
-1.50 to 0.75 1.00 1.00 0.99
D E N S I T Y
M O D E L S
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Fail-dangerous
T E R T I A R Y
M O D E L
Fail-safe
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Model Type p? pBf
Primary 0.95
Secondary for LT 0.77
Secondary for SGR 0.86
Secondary for MPD 0.80
Tertiary 0.79
R E S U L T S
A P Z O N E
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Summary and Conclusions

• Tertiary model
• loss of performance (p? of 0.79 vs. 0.95)
• shift towards fail-dangerous predictions
• successfully verified

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Summary and Conclusions

• Acceptable prediction zone method
• for all model types
• overcomes limitations of Bf and Af
• single performance factor (pBf or p?)
• detects global or regional prediction problems

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P R I M A R Y
M O D E L
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The author thanks Jaci Ludwig of ARS and Dwayne
Blakeney of UMES for their excellent
technical assistance on this project.