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Bayesian Nonparametric Meta‐Analysis Using Polya Tree Mixture Models
Author(s) -
Branscum Adam J.,
Hanson Timothy E.
Publication year - 2008
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2007.00946.x
Subject(s) - nonparametric statistics , random effects model , econometrics , latent class model , statistics , parametric statistics , mixture model , bayesian probability , computer science , normality , parametric model , mathematics , meta analysis , medicine
Summary A common goal in meta‐analysis is estimation of a single effect measure using data from several studies that are each designed to address the same scientific inquiry. Because studies are typically conducted in geographically disperse locations, recent developments in the statistical analysis of meta‐analytic data involve the use of random effects models that account for study‐to‐study variability attributable to differences in environments, demographics, genetics, and other sources that lead to heterogeneity in populations. Stemming from asymptotic theory, study‐specific summary statistics are modeled according to normal distributions with means representing latent true effect measures. A parametric approach subsequently models these latent measures using a normal distribution, which is strictly a convenient modeling assumption absent of theoretical justification. To eliminate the influence of overly restrictive parametric models on inferences, we consider a broader class of random effects distributions. We develop a novel hierarchical Bayesian nonparametric Polya tree mixture (PTM) model. We present methodology for testing the PTM versus a normal random effects model. These methods provide researchers a straightforward approach for conducting a sensitivity analysis of the normality assumption for random effects. An application involving meta‐analysis of epidemiologic studies designed to characterize the association between alcohol consumption and breast cancer is presented, which together with results from simulated data highlight the performance of PTMs in the presence of nonnormality of effect measures in the source population.