HIERARCHICAL SELECTION MODELS WITH APPLICATIONS IN METAANALYSIS

Hierarchical selection models are introduced and shown to be useful in meta-analysis. These models combine the use of hierarchical models, a llowing investigation of variability both within and between studies, and weight functions, allowing modeling of nonrandomly selected studie s. Markov chain Monte Carlo (MCMC) methods are used to estimate the hi erarchical selection model. This is first illustrated for known weight functions, and then extended to allow for estimation of unknown weigh t fractions. To investigate sensitivity of results to unobserved studi es directly, which is shown to be different from modeling bias in the selection of observed studies, the: hierarchical selection model is us ed in conjunction with data augmentation. Again, MCMC methods may be u sed to estimate the model. This is illustrated for an unknown weight f unction.