Exact Bayesian Inference Comparing Binomial Proportions, With Application to Proof-of-Concept Clinical Trials

Abstract

The authors revisit the problem of exact Bayesian inference comparing two independent binomial proportions. Numerical integration in R is used to compute exact posterior distribution functions, probability densities, and quantiles of the risk difference, relative risk, and odds ratio. An application of the methodology is given in the context of randomized comparative proof-of-concept clinical trials that are driven by evaluation of quantitative criteria combining statistical significance and clinical relevance. A two-stage adaptive design based on predictive probability of success is proposed and its operating characteristics are studied via Monte Carlo simulation. The authors conclude that exact Bayesian methods provide an elegant and efficient way to facilitate design and analysis of proof-of-concept studies.

Estimating Relative Risk When Observing Zero Events—Frequentist Inference and Bayesian Credibility Intervals

“…A weakness of this study is that it had to be limited to the most well-known approaches. Thus, we were not able to compare all the approaches suggested in the literature, such as the exact approaches to the CI [ 21 ] and exact Bayesian inference [ 22 ]. Another limitation is that due to the observation of zero events laying at the border of the parameter space for all frequentist methods, no formal evaluation of coverage for the obtained CIs was feasible.…”

Replicability of studies following a dual‐criterion design

“…The references contain real trial examples in different indications like non-small cell lung cancer, 17 cystic fibrosis and psoriasis, 18 or age-related macular degeneration. 24 An early implementation of a dual-criterion design occurred in a study in acute pain planned to demonstrate superior pain relief of an experimental COX-2 inhibitor over ibuprofen in a post-oral surgery pain model. 25 Primary endpoint was TOTPAR6, the area under the curve of a pain relief score over 6 days, which was supposed to differ by 3 points to be clinically relevant.…”

“…Dual criterion designs were first proposed for POC trials 17,18,24 to explicitly account for relevance in clinical decision making. The references contain real trial examples in different indications like non‐small cell lung cancer, 17 cystic fibrosis and psoriasis, 18 or age‐related macular degeneration 24 …”

bayesint: A Python Package for Calculating Bayesian Credible Intervals of Ratios of Beta Distributions

“…We compare our bayesint Python solution with the two following calculation options for calculating the uncertainty of a ratio of beta distributions. Matsen IV et al [13] uses the same Pham-Gia [17] density that we consider, but does not explicitly calculate the distribution on the basis of this density and Sverdlov et al [19] consider Nurminen and Mutanen [15] which is subsumed in Bekker-Nielsen Dunbar et al [1]. As such, we expect them to contain at least an implementation of the equaltailed credible interval, as it is the easier of the two to program.…”

“…The strength of our approach compared with these implementations is that we have considered use of priors for the proportions p 1 and p 2 that need not be the same. Sverdlov et al [19] mention the use of informative priors…”