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U.S. Department of Health and Human Services

Animal & Veterinary

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Presentation: Mathematical Validity of CVM Risk Assessment

Slide 1

Mathematical Validity of CVM Risk Assessment

Tony Cox

Slide 2

Is the CVM RA sound and useful?

  • Sound:

    • Predicted risks are calculated correctly by the model, given its assumptions
    • Model can be calibrated by simulation
  • Useful:

    • Model assumptions approximate reality well enough to support effective risk management decisions

Slide 3

Explicit assumptions

  • A strength of the model is its listing and discussion of formulas, assumptions, and their limitations (e.g., Appendix C)
  • Examples: Attribution of fluoroquinolone resistance to chicken, stability of risk estimates over time, care-seeking behavior.
  • Implicit assumptions are also important.

Slide 4

Other Key Modeling Assumptions

  • Independence of uncertain quantities
  • Extrapolation between populations
  • Aggregation of event sequences
  • Modeling of input uncertainties and formula uncertainties (e.g., beta and gamma distributions, productsand ratios of uncertain quantities)

Slide 5

Independence Assumptions

  • Example: Should inputs be modeled as statistically independent (e.g., pbm and pnm)?

    • Alternative: Estimate conditional distribution (pnm | pbm). Then joint distribution: Pr(pnm, pnm) = Pr(pbm )Pr(pnm | pbm)
  • Generalization: Condition each uncertain quantity on its relevant causal predecessors.

    • pm*(pbc | pm)*(pt | pm, pbc)*(p+ | pm, pbc, pt)
  • Expected impact: Small when independence is a reasonable approximation.

Slide 6


  • Example: Scaling estimates up by nUS/nEN.
  • "Expected observed cases" is a different (simulation-oriented) conceptual approach from typical Bayesian conditioning of a prior on observations.
  • As stated in the report, different populations may have different distributions of relevant factors.

Slide 7

Aggregation of Events

  • Example: p = pmpbcptp+ = (pmpbc)(ptp+)
  • Estimating all components and combining allows detailed information in outputs
  • Estimating p directly and by different "factorings" might slightly increase precision of estimates.

    • Exact PDF of product of beta distributions is known

Slide 8

Modeling Input Uncertainties

  • Specific parametric distributions (gamma and beta) are reasonable, but strongest conclusions come from sensitivity analysis.
  • Uncertainties about joint distributions and dependencies among uncertainties could be analyzed further -- Minor refinements
  • Trying other technical options for estimating joint distribution of inputs could add to confidence from current sensitivity analyses.

Slide 9

Model Formula Uncertainties

  • Most of the model's formulas are intended as simple logical identities based on sums, products, and ratios.
  • Even simple non-linear formulas (ratios) can introduce some biases (but often < 1%).
  • Potential bias for whole model should ideally be estimated (e.g., via simulation calibration.)

Slide 10

Potential Extensions

  • Calibrate by simulation.

    • "True" values -- simulated sample values -- model estimates of values
  • Additional sensitivity analyses

    • Initial sensitivity analyses are encouraging, i.e., main results not very sensitive to input or model uncertainties
    • Sensitivity to population heterogeneity

Slide 11


  • Model structure and calculations are well-documented and logical. ("Face validity")
  • Model-based risk predictions are credible.

    • Calibration and extensions could quantify credibility
  • Uncertainties in input quantities are explicitly and, in general, appropriately modeled.

    • Could model dependencies among variables
    • Could do further sensitivity analyses to assumed distributions of inputs and/or estimate them differently
    • High value from going beyond point estimates

Slide 12

Potential Workshop Issues

  • Discussion of model

    • What do you see are limitations of model?
    • Do you feel there are significant data gaps?
    • What are positive aspects of model?
    • What aspects would you consider changing?
    • How can this model be used to help industry reduce the level of risk?
  • Mathematics of model
  • Use of the model for other antimicrobial-foodborne pathogen combinations