On determination of sample size in hierarchical binomial models

We consider a two- and a three-stage hierarchical design containing the eff ects of k clusters with n units per cluster. In the two-stage model, the co nditional distribution of the discrete response Y-i is assumed to be indepe ndent binomial with mean n theta (i) (i=1,...,k). The success probabilities , theta (i)'s, are assumed exchangeable across the k clusters, each arising from a beta distribution. In the three-stage model, the parameters in the beta distribution are assumed to have independent gamma distributions. The size of each cluster, n, is determined for functions of theta (i). Lengths of central posterior intervals are computed for various functions of the th eta (i)'s using Markov chain Monte Carlo and Monte Carlo simulations. Sever al prior distributions are characterized and tables are provided for n with given k. Methods for sample size calculations under the two- and three-sta ge models are illustrated and compared for the design of a multi-institutio nal study to evaluate the appropriateness of discharge planning rates for a cohort of patients with congestive heart failure. Copyright (C) 2001 John Wiley & Sons, Ltd.