Animal & Veterinary
Presentation: Mathematical Validity of CVM Risk Assessment
Mathematical Validity of CVM Risk Assessment
Is the CVM RA sound and useful?
- Predicted risks are calculated correctly by the model, given its assumptions
- Model can be calibrated by simulation
- Model assumptions approximate reality well enough to support effective risk management decisions
- 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.
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)
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.
- 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.
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
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.
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.)
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
- 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
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