Modeling the Frequency and Duration of Microbial Contamination Events: Considering Uncertainty and V

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Modeling the Frequency and Duration of Microbial
Contamination Events Considering Uncertainty and
Variability in Censored Data

• Mark Powell, USDA, Wash., DC
• Greg Paoli, Decisionalysis, Ottawa, CA
• IAFP 2004
• 8-11 August, Phoenix, AZ

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Overview

• Frequency and duration of Listeria contamination
  event data for RTE products are censored.
• Statistical methods specifically designed for
  analyzing censored data are available.
• The analysis considers natural variability in
  the frequency and duration of contamination
  events parameter uncertainty (within model)
  model uncertainty (between models).

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Duration of Listeria spp. contamination events
Source Tompkin (2002)
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Frequency of Listeria spp. Contamination Events
Source FSIS (2003)
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Exponential Variability Distribution

• Assumes random event occurs with a constant
  probability over time.
• ß mean time until occurrence.

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Weibull Variability Distribution

• Probability of occurrence varies with time
• prob. inc
• a gt 1
• prob. dec.
• a lt 1

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Maximum Likelihood Estimation for Censored Data
where DL detection limit f prob.
density F cum. prob. x uncensored data
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Parameter Uncertainty Large Sample Size

• Empirical bootstrap for large sample sizes -
  duration of contamination events
• Advantage relax statistical assumptions about
  parameter distributions
• Repeatedly sample with replacement from the data
  and apply MLE procedure each time.
• Do this separately for the parameters of the
  exponential and Weibull distributions.

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Parameter Uncertainty Small Sample Size

• Parametric bootstrap for small samples - duration
  of contamination events.
• Bootstrap sample distributions represent
  parameter uncertainty for each time-to-event
  model.

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Model Uncertainty Model Weights
Bayesian Information Criterion (BIC)
Bayes Factor (BF)
Model Weight
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Results Duration of Contamination
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Duration of Contamination Events Weibull Model
Median 4 d 95 CL -95th ile 40 d
Large variability, little parameter or model
uncertainty.
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Results Frequency of Contamination
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Frequency of Contamination Events
Large variability and parameter uncertainty, some
model uncertainty.
Median 14 d 5 CL, 5th ile 0.7 d
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Cautionary Example of Large Model Uncertainty
Source Salin et al. 2002. Survival Analysis of
U.S. Meat and Poultry Recalls, 1994-200, Fig. 10
(Time Until Class 1 Recall, Pre-HACCP)
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Next Steps

• Some data we talk about as censored, like
  microbial concentrations, really aren't.
• Zero counts for discrete microorganisms are not
  censored data below an analytical detection
  limit, as assumed by models for continuously
  distributed chemical concentrations.
• Zero microbial counts arise from variation in
  sampling and detection processes.
• Methods (e.g., Poisson regression) are available
  for microbial concentration data including zero
  counts, non-detects, and MPN, but well save
  those for another day.