Bayesian Borrowing Methods for Count Data: Analysis of Incontinence Episodes in Patients with Overactive Bladder

Abstract

We examine the performance of the power prior and the meta-analytic-predictive (MAP) prior for the analysis of (overdispersed) count data when multiple historical control data are incorporated into the analysis of the current data. To this end, we explore the Poisson and the negative binomial distribution. We propose a computational approach based on path sampling for the calculation of the scaling constant of the Modified Power Prior (MPP). We illustrate the methods through a motivating example of a clinical trial evaluating the effect of an experimental treatment to reduce the number of incontinence events for patients with an overactive bladder. Furthermore, we assess the performance of these methods via a simulation study in case of heterogeneity of the control arms. For similar current and historical control arms, the MPP approach offers greater statistical power than the MAP prior approach. When the means are different across the control arms, the MPP yields a slightly inflated Type I error rate, whereas the MAP prior does not. When the dispersion parameters are different across the control arms, the results are reversed. In conclusion, the MPP approach outperforms the MAP prior approach for count data.

KEYWORDS:

• Meta-analytic predictive prior
• Negative binomial
• Overdispersion
• Poisson
• Power prior

Disclosure Statement

The authors declare that they have no competing interests.

Funding

Hercules Foundation; EWI Department of the Flemish Government; BOF-BILA of UHasselt;

Additional information

Funding

For the simulations we used the infrastructure of the VSC—Flemish Supercomputer Center, funded by the Hercules foundation and the Flemish Government—department EWI. The unreserved support of BOF bilateral cooperation of UHasselt for the financial support to the first author for his research visits is duly acknowledged.