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摘要:
In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients’ data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.
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篇名 On the Covariance of Regression Coefficients
来源期刊 统计学期刊(英文) 学科 医学
关键词 META-ANALYSIS LINEAR Regression COVARIANCE MATRIX Regression COEFFICIENTS SYNTHESIS Analysis
年,卷(期) 2015,(7) 所属期刊栏目
研究方向 页码范围 680-701
页数 22页 分类号 R73
字数 语种
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META-ANALYSIS
LINEAR
Regression
COVARIANCE
MATRIX
Regression
COEFFICIENTS
SYNTHESIS
Analysis
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统计学期刊(英文)
半月刊
2161-718X
武汉市江夏区汤逊湖北路38号光谷总部空间
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584
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