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Synthesis of linear regression coefficients by recovering the within‐study covariance matrix from summary statistics
Author(s) -
Yoneoka Daisuke,
Henmi Masayuki
Publication year - 2017
Publication title -
research synthesis methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.376
H-Index - 35
eISSN - 1759-2887
pISSN - 1759-2879
DOI - 10.1002/jrsm.1228
Subject(s) - covariate , statistics , linear regression , regression diagnostic , regression analysis , context (archaeology) , econometrics , linear model , covariance matrix , analysis of covariance , regression , multivariate statistics , design matrix , covariance , computer science , mathematics , bayesian multivariate linear regression , geography , archaeology
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.