Using full probability models to compute probabilities of actual interest to decision makers

The objective of this paper is to illustrate the advantages of the Bayesian approach in quantifying, presenting, and reporting scientific evidence and in assisting decision making. Th ree basic components in the Bayesian fram ework are the prior distribution, likelihood function, and posterior distri bution. The prior distribution describes analysts' belief a priori; the lik elihood function captures how data modify the prior knowledge; and the post erior distribution synthesizes both prior and likelihood information. The B ayesian approach treats the parameters of interest as random variables, use s the entire posterior distribution to quantify the evidence, and reports e vidence in a "probabilistic" manner, Two clinical examples are used to demo nstrate the value of the Bayesian approach to decision makers. Using either an uninformative or a skeptical prior distribution, these examples show th at the Bayesian methods allow calculations of probabilities that are usuall y of more interest to decision makers, e.g., the probability that treatment A is similar to treatment B, the probability that treatment A is at least 5% better than treatment B, and the probability that treatment A is not wit hin the "similarity region" of treatment B, etc. In addition, the Bayesian approach can deal with multiple endpoints more easily than the classic appr oach. For example, if decision makers wish to examine mortality and cost jo intly, the Bayesian method can report the probability that a treatment achi eves at least 2% mortality reduction and less than $20,000 increase in cost s. In conclusion, probabilities computed from the Bayesian approach provide more relevant information to decision makers and are easier to interpret.