6  Posterior Probabilities in Decision Making

• Optimum Bayes decision optimizes expected utility/loss/cost

  • is a function of the posterior distribution

• Difficult to specify utility function

  • different stakeholders, monetary + non-monetary costs, public health

• Decision makers have an informal way of accounting for their utilities

  • may consider death vs. “soft” endpoints, other options for patients

• Since expected utility uses PP, PP logical for final result of analysis

• Cutoffs on PPs: similar problems as p-value cutoffs

• Can informally factor utilities into cutoffs

• Examples of how PPs may be used in decision making

  • λ : true B:A hazard ratio for death
  • LVEF: left ventricular ejection fraction
  • Δ : true reduction in mean LVEF

Indication or Harm	Posterior Probability
Mortality reduction	P(λ < 1) ≥ 0.95 or P(λ < 0.8) ≥ 0.8
Any mortality reduction or large improvement in LVEF	P(λ < 1) ≥ 0.9 or P(Δ > 0.15) ≥ 0.95
Mortality Increase	P(λ > 1) ≥ 0.9
Mortality reduction in a Phase 2 trial	P(λ < 1) ≥ 0.8
Major improvement in one target or improvement in any 3 of 5 targets	P(specific target ↓20%) ≥ 0.95 or P(≥ 3 targets improved any) ≥ 0.95