title: Synthesis of linear regression coefficients by recovering the within-study covariance matrix from summary statistics.
abstract: Recently, the number of regression models has dramatically increased in several academic fields. However, within the context of meta-analysis, synthesis methods for such models have not been developed in a commensurate trend. One of the difficulties hindering the development is the disparity in sets of covariates among literature models. If the sets of covariates differ across models, interpretation of coefficients will differ, thereby making it difficult to synthesize them. Moreover, previous synthesis methods for regression models, such as multivariate meta-analysis, often have problems because covariance matrix of coefficients (i.e. within-study correlations) or individual patient data are not necessarily available. This study, therefore, proposes a brief explanation regarding a method to synthesize linear regression models under different covariate sets by using a generalized least squares method involving bias correction terms. Especially, we also propose an approach to recover (at most) threecorrelations of covariates, which is required for the calculation of the bias term without individual patient data. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Department of Global Health Policy, The University of Tokyo, Tokyo, Japan.|Department of Epidemiology & Cancer Control Memphis, St. Jude Children's Research Hospital, United States.
authors.forename: Daisuke
authors.initials: D
authors.lastname: Yoneoka
authors.affiliation: Department of Data Science, The Institute of Statistical Mathematics, Tokyo, Japan.|Department of Statistical Sceince, SOKENDAI (The Graduate University for Advanced Studies), Tokyo, Japan.
authors.forename: Masayuki
authors.initials: M
authors.lastname: Henmi
mesh_terms: D015982:Bias; D003627:Data Interpretation, Statistical; D016018:Least-Squares Analysis; D016014:Linear Models; D015201:Meta-Analysis as Topic; D015999:Multivariate Analysis; D012044:Regression Analysis
keywords: correlation of covariates; imbalance of covariates; linear regression; model misspecification; synthesis of regression