title: 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 multi-dimensional. 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 paper, 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 matrixSfor 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 matrixSare assumed observed, and given Σ,Sfollows a Wishart distribution. Thus, we treat the off-diagonal elements ofSas 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.
authors.affiliation: Financial Services Office, Ernst & Young, New York, NY, USA.
authors.forename: Hui
authors.initials: H
authors.lastname: Yao
authors.affiliation: Division of Intramural Population Health Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, NIH, Rockville, MD, USA.
authors.forename: Sungduk
authors.initials: S
authors.lastname: Kim
authors.affiliation: Department of Statistics, University of Connecticut, Storrs, CT, USA.
authors.forename: Ming-Hui
authors.initials: MH
authors.lastname: Chen
authors.affiliation: Department of Biostatistics, University of North Carolina, Chapel Hill, NC, USA.
authors.forename: Joseph G
authors.initials: JG
authors.lastname: Ibrahim
authors.affiliation: Clinical Biostatistics, Merck Research Laboratories, Rahway, NJ, USA.
authors.forename: Arvind K
authors.initials: AK
authors.lastname: Shah
authors.affiliation: Clinical Biostatistics, Merck Research Laboratories, Rahway, NJ, USA.
authors.forename: Jianxin
authors.initials: J
authors.lastname: Lin
keywords: Aggregate covariates; Heterogeneity; Multiple trials; Normal regression models; Random effects; variable selection