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HIERARCHICAL SELECTION MODELS WITH APPLICATIONS IN META-ANALYSIS
Nancy L. Paul
Abstract:
This paper introduces hierarchical selection models and illustrates
how they may be used in meta-analysis. Our approach combines the use
of hierarchical models, which allow one to investigate variability
both within and between units (e.g., studies), and weight functions,
which allow one to model non-randomly selected data. We show how
Markov Chain Monte Carlo methods may be used to estimate the
hierarchical selection model. This approach is illustrated first for
known weight functions, and then extended to allow for estimation of
the weight function. Hierarchical selection models are shown to be
especially useful in meta-analysis, where one often needs to account
for both between-study variability and bias involved in the collection
of the studies. However, the methods presented are very general and
can be used in a variety of other situations, e.g., in a multi-center
clinical trial where there is bias involved in the selection of
centers.
Weight functions provide an approach for examining sensitivity of
results to bias in the way studies are obtained. However, this is
shown to be different from examining sensitivity to unobserved studies
directly. In order to investigate sensitivity of results to unobserved
studies, while still accounting for between-study variability and bias
in the collection of the observed studies, the hierarchical selection
model approach is combined with data augmentation to account for
unobserved studies. Again, Markov Chain Monte Carlo methods may be
used to estimate the model. This is illustrated for both known and
unknown (i.e., estimated) weight functions.
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