Use of a Posterior Beta Distribution with Recurrent Event Data

• Activity Number: 31
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Jerry Weaver*+
• Companies: Novartis
• Keywords: posterior beta distribution ; Poisson-gamma mixture ; Berhens-Fisher ; over-dispersion parameter

Abstract

The negative binomial is a very flexible model which naturally arises out of a Poisson-gamma mixture of distributions, and is often preferable to use with recurrent events than the more restrictive Poisson model. A common over-dispersion parameter among the treatment groups is usually taken at face value when designing clinical trials. However, violation of this assumption leads to a Berhens-Fisher like problem which may result in loss of power for which the study is originally designed. As a possible solution to this problem, a closed form posterior beta distribution will be derived and discussed. This closed form posterior distribution and its operating characteristics will be evaluated in relationship to frequentist approaches and alternative Bayesian ones when designing trials with and without a common overdispersion parameter.