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Meta analysis of binary data with excessive zeros in two-arm trials

Author

Listed:
  • Saman Muthukumarana

    (Department of Statistics, University of Manitoba)

  • David Martell

    (ITAM)

  • Ram Tiwari

    (Office of Biostatistics, Center for Drug Evaluation and Research, Food and Drug Administration)

Abstract

We present a novel Bayesian approach to random effects meta analysis of binary data with excessive zeros in two-arm trials. We discuss the development of likelihood accounting for excessive zeros, the prior, and the posterior distributions of parameters of interest. Dirichlet process prior is used to account for the heterogeneity among studies. A zero inflated binomial model with excessive zero parameters were used to account for excessive zeros in treatment and control arms. We then define a modified unconditional odds ratio accounting for excessive zeros in two arms. The Bayesian inference is carried out using Markov chain Monte Carlo (MCMC) sampling techniques. We illustrate the approach using data available in published literature on myocardial infarction and death from cardiovascular causes. Bayesian approaches presented here use all the data, including the studies with zero events and capture heterogeneity among study effects, and produce interpretable estimates of overall and study-level odds-ratios, over the commonly used frequentist’s approaches. Results from the data analysis and the model selection also indicate that the proposed Bayesian method, while accounting for zero events, adjusts for excessive zeros and provides better fit to the data resulting in the estimates of overall odds-ratio and study-level odds-ratios that are based on the totality of the information.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jstada:v:6:y:2019:i:1:d:10.1186_s40488-019-0099-x
    DOI: 10.1186/s40488-019-0099-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. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
    3. 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.
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