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On determination of sample size in hierarchical binomial models
Author(s) -
Zou Kelly H.,
Normand SharonLise T.
Publication year - 2001
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.855
Subject(s) - statistics , mathematics , monte carlo method , sample size determination , markov chain monte carlo , beta binomial distribution , binomial distribution , negative binomial distribution , cluster (spacecraft) , binomial (polynomial) , statistical physics , computer science , poisson distribution , physics , programming language
We consider a two‐ and a three‐stage hierarchical design containing the effects of k clusters with n units per cluster. In the two‐stage model, the conditional distribution of the discrete response Y i is assumed to be independent binomial with mean n θ i ( I =1,…, k ). The success probabilities, θ 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 θ i . Lengths of central posterior intervals are computed for various functions of the θ i 's using Markov chain Monte Carlo and Monte Carlo simulations. Several prior distributions are characterized and tables are provided for n with given k . Methods for sample size calculations under the two‐ and three‐stage models are illustrated and compared for the design of a multi‐institutional study to evaluate the appropriateness of discharge planning rates for a cohort of patients with congestive heart failure. Copyright © 2001 John Wiley & Sons, Ltd.