Prior and posterior probability distributions. (A) Prior probability distributions for the Prob (CR) with standard treatment (S) and for each of the 4 experimental treatments (E). The mean of all distributions is 0.49, corresponding to the historical CR rate, but the prior on S is informative given previous data in 591 patients, whereas the prior on each E is noninformative given the lack of data. (B) Posterior distributions for Prob (CR) with treatment arms LDT, LDT + Thal, LDA, and LDA + Thal, after observing 0 of 6, 0 of 5, 18 of 40, and 17 of 40 CRs, respectively, compared with the prior Prob (CR) with S. The prior and posterior with S (solid line) are identical because no patients were given S in this trial. The curves for LDT and LDT + Thal (dotted lines) remain relatively uninformative given the small sample sizes, but there is virtually no probability that the CR rates with these arms overlap the (higher) CR rates seen with S. The LDA and LDA + Thal curves are more informative (dashed lines) and most of the probability density is to the left of the lowest plausible CR rate produced by S. Thus, the posterior probability that LDA is 20% better than historical is 0.001, and the posterior probability that it is 10% better is 0.039.The corresponding probabilities for LDA + Thal are 0.0004 and 0.019.