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Bayesian Nonparametric Meta‐Analysis Using Polya Tree Mixture Models

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  • Adam J. Branscum
  • Timothy E. Hanson

Abstract

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.

Suggested Citation

  • Adam J. Branscum & Timothy E. Hanson, 2008. "Bayesian Nonparametric Meta‐Analysis Using Polya Tree Mixture Models," Biometrics, The International Biometric Society, vol. 64(3), pages 825-833, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:825-833
    DOI: 10.1111/j.1541-0420.2007.00946.x
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    References listed on IDEAS

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    1. Deborah Burr & Hani Doss, 2005. "A Bayesian Semiparametric Model for Random-Effects Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 242-251, March.
    2. Susan M. Paddock, 2002. "Bayesian nonparametric multiple imputation of partially observed data with ignorable nonresponse," Biometrika, Biometrika Trust, vol. 89(3), pages 529-538, August.
    3. Stephen Walker & Bani K. Mallick, 1999. "A Bayesian Semiparametric Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 55(2), pages 477-483, June.
    4. Hanson, Timothy E., 2006. "Inference for Mixtures of Finite Polya Tree Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1548-1565, December.
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    1. Chen, Yuhui & Hanson, Timothy E., 2014. "Bayesian nonparametric k-sample tests for censored and uncensored data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 335-346.
    2. Ma, Zichen & Hanson, Timothy E., 2020. "Bayesian nonparametric test for independence between random vectors," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    3. Burr, Deborah, 2012. "bspmma: An R Package for Bayesian Semiparametric Models for Meta-Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i04).
    4. Angela Schörgendorfer & Adam J. Branscum & Timothy E. Hanson, 2013. "A Bayesian Goodness of Fit Test and Semiparametric Generalization of Logistic Regression with Measurement Data," Biometrics, The International Biometric Society, vol. 69(2), pages 508-519, June.
    5. Saman Muthukumarana & David Martell & Ram Tiwari, 2019. "Meta analysis of binary data with excessive zeros in two-arm trials," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-17, December.

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