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

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.

• Aggregate covariates
• Heterogeneity
• Multiple trials
• Normal regression models
• Random effects
• Variable selection

Additional information

Notes on contributors

Hui Yao

Hui Yao is Statistician, Financial Services Office, Ernst & Young, New York, NY 10036 (E-mail: [email protected]).

Sungduk Kim

Ming-Hui Chen is Professor, Department of Statistics, University of Connecticut, Storrs, CT 06269 (E-mail: [email protected]).

Ming-Hui Chen

Sungduk Kim is Staff Scientist, Biostatistics and Bioinformatics Branch, Division of Intramural Population Health Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, 6100 Executive Blvd, Rockville, MD 20852 (E-mail: [email protected]).

Joseph G. Ibrahim

Joseph Ibrahim is Professor, Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599 (E-mail: [email protected]).

Arvind K. Shah

Arvind Shah is Senior Principal Scientist (E-mail: [email protected]).

Jianxin Lin

Jianxin Lin is Senior Scientist (E-mail: [email protected]) Clinical Biostatistics, Merck Research Laboratories, Rahway, NJ 07065.