title: Prior Effective Sample Size in Conditionally Independent Hierarchical Models.
abstract: Prior effective sample size (ESS) of a Bayesian parametric model was defined by Morita, et al. (2008,Biometrics,64, 595-602). Starting with anε-information prior defined to have the same means and correlations as the prior but to be vague in a suitable sense, the ESS is the required sample size to obtain a hypothetical posterior very close to the prior. In this paper, we present two alternative definitions for the prior ESS that are suitable for a conditionally independent hierarchical model. The two definitions focus on either the first level prior or second level prior. The proposed methods are applied to important examples to verify that each of the two types of prior ESS matches the intuitively obvious answer where it exists. We illustrate the method with applications to several motivating examples, including a single-arm clinical trial to evaluate treatment response probabilities across different disease subtypes, a dose-finding trial based on toxicity in this setting, and a multicenter randomized trial of treatments for affective disorders.
authors.affiliation: Department of Biostatistics and Epidemiology, Yokohama City University Medical Center, Yokohama 232-0024, Japan.
authors.forename: Satoshi
authors.initials: S
authors.lastname: Morita
authors.forename: Peter F
authors.initials: PF
authors.lastname: Thall
authors.forename: Peter
authors.initials: P
authors.lastname: Müller
keywords: Bayesian hierarchical model; Computationally intensive methods; Conditionally independent hierarchical model; Effective sample size; Epsilon-information prior