title: Case studies in Bayesian microbial risk assessments.
abstract: BACKGROUND
  The quantification of uncertainty and variability is a key component of quantitative risk analysis. Recent advances in Bayesian statistics make it ideal for integrating multiple sources of information, of different types and quality, and providing a realistic estimate of the combined uncertainty in the final risk estimates.
  
  
  METHODS
  We present two case studies related to foodborne microbial risks. In the first, we combine models to describe the sequence of events resulting in illness from consumption of milk contaminated with VTEC O157. We used Monte Carlo simulation to propagate uncertainty in some of the inputs to computer models describing the farm and pasteurisation process. Resulting simulated contamination levels were then assigned to consumption events from a dietary survey. Finally we accounted for uncertainty in the dose-response relationship and uncertainty due to limited incidence data to derive uncertainty about yearly incidences of illness in young children. Options for altering the risk were considered by running the model with different hypothetical policy-driven exposure scenarios. In the second case study we illustrate an efficient Bayesian sensitivity analysis for identifying the most important parameters of a complex computer code that simulated VTEC O157 prevalence within a managed dairy herd. This was carried out in 2 stages, first to screen out the unimportant inputs, then to perform a more detailed analysis on the remaining inputs. The method works by building a Bayesian statistical approximation to the computer code using a number of known code input/output pairs (training runs).
  
  
  RESULTS
  We estimated that the expected total number of children aged 1.5-4.5 who become ill due to VTEC O157 in milk is 8.6 per year, with 95% uncertainty interval (0,11.5). The most extreme policy we considered was banning on-farm pasteurisation of milk, which reduced the estimate to 6.4 with 95% interval (0,11). In the second case study the effective number of inputs was reduced from 30 to 7 in the screening stage, and just 2 inputs were found to explain 82.8% of the output variance. A combined total of 500 runs of the computer code were used.
  
  
  CONCLUSIONS
  These case studies illustrate the use of Bayesian statistics to perform detailed uncertainty and sensitivity analyses, integrating multiple information sources in a way that is both rigorous and efficient.
authors.affiliation: Food and Environment Research Agency, Sand Hutton, York, UK. marc.kennedy@fera.gsi.gov.uk
authors.forename: Marc C
authors.initials: MC
authors.lastname: Kennedy
authors.forename: Helen E
authors.initials: HE
authors.lastname: Clough
authors.forename: Joanne
authors.initials: J
authors.lastname: Turner
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D016022:Case-Control Studies; D002417:Cattle; D015331:Cohort Studies; D003198:Computer Simulation; D004927:Escherichia coli Infections / Q000453:epidemiology*; D005517:Foodborne Diseases / Q000453:epidemiology*; D006801:Humans; D008892:Milk / Q000382:microbiology / Q000506:poisoning; D009010:Monte Carlo Method; D018570:Risk Assessment / Q000379:methods; D054323:Shiga-Toxigenic Escherichia coli / Q000302:isolation & purification; D006113:United Kingdom / Q000453:epidemiology