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Bayesian Inference for Multivariate Meta-Regression With a Partially Observed Within-Study Sample Covariance Matrix

Author

Listed:
  • Hui Yao
  • Sungduk Kim
  • Ming-Hui Chen
  • Joseph G. Ibrahim
  • Arvind K. Shah
  • Jianxin Lin

Abstract

Multivariate meta-regression models are commonly used in settings where the response variable is naturally multidimensional. Such settings are common in cardiovascular and diabetes studies where the goal is to study cholesterol levels once a certain medication is given. In this setting, the natural multivariate endpoint is low density lipoprotein cholesterol (LDL-C), high density lipoprotein cholesterol (HDL-C), and triglycerides (TG) (LDL-C, HDL-C, TG). In this article, we examine study level (aggregate) multivariate meta-data from 26 Merck sponsored double-blind, randomized, active, or placebo-controlled clinical trials on adult patients with primary hypercholesterolemia. Our goal is to develop a methodology for carrying out Bayesian inference for multivariate meta-regression models with study level data when the within-study sample covariance matrix S for the multivariate response data is partially observed. Specifically, the proposed methodology is based on postulating a multivariate random effects regression model with an unknown within-study covariance matrix Σ in which we treat the within-study sample correlations as missing data, the standard deviations of the within-study sample covariance matrix S are assumed observed, and given Σ, S follows a Wishart distribution. Thus, we treat the off-diagonal elements of S as missing data, and these missing elements are sampled from the appropriate full conditional distribution in a Markov chain Monte Carlo (MCMC) sampling scheme via a novel transformation based on partial correlations. We further propose several structures (models) for Σ, which allow for borrowing strength across different treatment arms and trials. The proposed methodology is assessed using simulated as well as real data, and the results are shown to be quite promising. Supplementary materials for this article are available online.

Suggested Citation

  • Hui Yao & Sungduk Kim & Ming-Hui Chen & Joseph G. Ibrahim & Arvind K. Shah & Jianxin Lin, 2015. "Bayesian Inference for Multivariate Meta-Regression With a Partially Observed Within-Study Sample Covariance Matrix," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 528-544, June.
  • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:510:p:528-544
    DOI: 10.1080/01621459.2015.1006065
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    References listed on IDEAS

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    1. Richard D. Riley, 2009. "Multivariate meta‐analysis: the effect of ignoring within‐study correlation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(4), pages 789-811, October.
    2. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
    3. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    4. Wang, Y. & Daniels, M.J., 2013. "Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 130-140.
    5. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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