Statistics and Its Interface

Volume 13 (2020)

Number 4

Bayesian flexible hierarchical skew heavy-tailed multivariate meta regression models for individual patient data with applications

Pages: 485 – 500



Sungduk Kim (Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Rockville, Maryland, U.S.A.)

Ming-Hui Chen (Department of Statistics, University of Connecticut, Storrs, CT, U.S.A.)

Joseph Ibrahim (Department of Biostatistics, University of North Carolina, Chapel Hill, N.C., U.S.A.)

Arvind Shah (Clinical Biostatistics, Merck & Co., Inc., Rahway, New Jersey, U.S.A.)

Jianxin Lin (Clinical Biostatistics, Merck & Co., Inc., Rahway, New Jersey, U.S.A.)


A flexible class of multivariate meta-regression models are proposed for Individual Patient Data (IPD). The methodology is well motivated from 26 pivotal Merck clinical trials that compare statins (cholesterol lowering drugs) in combination with ezetimibe and statins alone on treatment-naïve patients and those continuing on statins at baseline. The research goal is to jointly analyze the multivariate outcomes, Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Triglycerides (TG). These three continuous outcome measures are correlated and shed much light on a subject’s lipid status. The proposed multivariate meta-regression models allow for different skewness parameters and different degrees of freedom for the multivariate outcomes from different trials under a general class of skew $t$-distributions. The theoretical properties of the proposed models are examined and an efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for carrying out Bayesian inference under the proposed multivariate meta-regression model. In addition, the Conditional Predictive Ordinates (CPOs) are computed via an efficient Monte Carlo method. Consequently, the logarithm of the pseudo marginal likelihood and Bayesian residuals are obtained for model comparison and assessment, respectively. A detailed analysis of the IPD meta data from the 26 Merck clinical trials is carried out to demonstrate the usefulness of the proposed methodology.


collapsed Gibbs, CPO identity II, heterogeneity, multi-dimensional random effects, multiple trials, outlying trials

The research of Drs. Chen and Ibrahim was partially supported by NIH grants #GM70335 and #P01CA142538. Dr. Kim’s research was supported by the Intramural Research Program of National Institutes of Health, National Cancer Institute.

Received 3 January 2020

Accepted 1 April 2020

Published 31 July 2020