These histograms will represent the overall (or clinical) and skeptical (or cautious) prior distributions associated with the stakeholders’ views of the problem. A skeptical prior distribution corresponds to the beliefs of individuals who are reluctant to accept alternative hypotheses of interest to the investigators. The resulting histograms can be transformed to the scale on which research data have been collected (Tan et al., 2003).
Steps 4–7. Determination of multivariate prior distributions from multiple stakeholders, estimation of summary likelihoods from multiple datasets, resulting in a derivation of a summary posterior distribution: Such a procedure is based on Bayes’ rule and entails intractable integration resulting in simulation-based integration (e.g., Markov Chain Monte Carlo), which many commercially available software packages now offer (Spiegelhalter et al., 1994).
Steps 8. Choosing a utility function to incorporate costs and stakeholders’ sensitivity to such costs: Such functions involve determining costs from implementing mitigation strategies and reduced costs from preventing problem outcomes (Pliskin et al., 1980; Berger, 1985; Lindley, 1985; Gold et al., 1996). Sensitivity analysis of the overall procedure outlined here includes varying such cost estimates (Matchar and Samsa, 1999; Matchar et al., 1997).
Step 9. Decisions based on regrets or opportunity costs from weighing information on outcomes under mitigation strategies against outcomes under the absence of mitigation strategies: Regrets are based on loss functions as contrasts between decisions that lead to optimal utility benefits and the utility benefits based on observed or predicted data. The expected loss functions allow the incorporation of research data and previous opinions of stakeholders by integrating utility functions for the optimal and observed decisions with respect to the summary posterior distributions (Berger, 1985: Lindley, 1985). For complex sequences of branching decisions based on outcomes of previous decisions, backward induction algorithms may be used (Bellman, 1957).
Overall, such decision processes present a complex web of different statistical procedures, research datasets, and opinions by stakeholders. This complex web is sensitive to selected procedures and corresponding assumptions; thus, this sensitivity is assessed by varying assumptions and operational procedures (Matchar and Samsa, 1999). Varying assumptions, procedures, and information used for forming utility functions and prior distribution may be done formally with quantified ranges of possible values