# 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 |