The Distribution of the Difference of Two Proportions: An Application of Sample Size Calculations Using Bayesian Approach

• Activity Number: 547
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Mohammad Sahtout*+ and Wijith Munasinghe
• Companies: and AbbVie
• Keywords: truncated beta-binomial distribution ; posterior mean ; credible interval ; estimation ; sample size

Abstract

Some drug related adverse events may depend on frequency of dose administration and it would be interesting to compare the adverse events rates across different dosing regimens. The challenge is that to come up with sample size which would give reasonable estimate for that difference as well as variability in such estimate. The options to investigate the difference in incidence rates are; a study with altered frequency of dose administration compared to historical data or a randomized study with an active control group. In either case, two independent Binomial distributions will be observed with unknown incidence rates. It will be better if possible range for incidence rate and its uncertainty can be incorporated into the estimation process. These unknown incidence rates may follow truncated Beta prior distributions with unity shape parameters which lead to truncated Beta-Binomial posterior distributions. This comes down to the distribution of difference between two independent truncated Beta-Binomial distributions and its properties. Posterior mean and credible interval of such distribution was used to guide the selection of reasonable sample size for this estimation problem.