Synthesizing regression results: a factored likelihood method

Wu, Meng-Jia; Becker, Betsy Jane

doi:10.1002/jrsm.1063

Cited by 13 publications

(11 citation statements)

References 23 publications

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“…Thus, the estimate proposed here, coupled with the advances in multivariate meta-analysis software, can facilitate further the use of the method. Some other, more advanced techniques have also been proposed for synthesizing regression coefficients, especially when the studies are included in the meta-analysis evaluate different set of explanatory variables [46] [47]. However, these techniques require spe-cialised software or user-written code, whereas the traditional approach mentioned here can be fitted using standard software for multivariate meta-analysis.…”

Section: Resultsmentioning

confidence: 99%

On the Covariance of Regression Coefficients

Bagos¹,

Αδάμ²

2015

OJS

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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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Section: Resultsmentioning

confidence: 99%

On the Covariance of Regression Coefficients

Bagos¹,

Αδάμ²

2015

OJS

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“…We did not include such data in Table because of the inconsistent adjustments. How to incorporate such data with different adjustments is of great interest to enrich the MVMA‐MF and enhance the robustness and precision of the results . We leave this to future studies.…”

Section: Discussionmentioning

confidence: 99%

Bayesian multivariate meta‐analysis of multiple factors

Lin

Chu

2018

Research Synthesis Methods

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In medical sciences, a disease condition is typically associated with multiple risk and protective factors. Although many studies report results of multiple factors, nearly all meta-analyses separately synthesize the association between each factor and the disease condition of interest. The collected studies usually report different subsets of factors, and the results from separate analyses on multiple factors may not be comparable because each analysis may use different subpopulation. This may impact on selecting most important factors to design a multifactor intervention program. This article proposes a new concept, multivariate meta-analysis of multiple factors (MVMA-MF), to synthesize all available factors simultaneously. By borrowing information across factors, MVMA-MF can improve statistical efficiency and reduce biases compared with separate analyses when factors were missing not at random. As within-study correlations between factors are commonly unavailable from published articles, we use a Bayesian hybrid model to perform MVMA-MF, which effectively accounts for both within- and between-study correlations. The performance of MVMA-MF and the conventional methods are compared using simulations and an application to a pterygium dataset consisting of 29 studies on 8 risk factors.

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“…These approaches can be organized into three methodological groups. The first group focuses on methods that combine full regression models (e.g., Wu & Becker, 2013), the second group focuses on attempting to approximate the bivariate correlation when it is not directly reported (e.g., Peterson & Brown, 2005), and the third group focuses on methods that combine partial effect sizes that have been extracted from regression models (e.g., Aloe & Becker, 2012;Keef & Roberts, 2004). …”

Section: Abstract: Meta-analysis Research Synthesis Partial Effectmentioning

confidence: 99%

“…Almost two decades ago researchers argued that results from regression models can be treated as effect-size indices (e.g., Becker & Schram, 1994;Cooper & Hedges, 1994;Greenwald, Hedges, & Laine, 1996;Valentine, DuBois, & Cooper, 2004). More recently, different approaches have been proposed to synthesize regression models (Aloe & Becker, 2012;Becker & Wu, 2007;Peterson & Brown, 2005;Wu & Becker, 2013). These approaches can be organized into three methodological groups.…”

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confidence: 99%

The Synthesis of Partial Effect Sizes

Aloe¹,

Thompson²

2013

Journal of the Society for Social Work and Research

114

121

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In this article we focus on three partial effect sizes for the correlation ( family of effects: the standardized slope , the partial correlation , and the semi-partial correlation . These partial effect sizes are useful for meta-analyses in two common situations: when primary studies reporting regression models do not report bivariate correlations, and when it is of specific interest to partial out the effects of other variables. We clarify the use of these three indices in the context of meta-analysis and describe how the indices can be estimated and analyzed. We provide examples of syntheses of these partial effect sizes using a published social work meta-analysis. Finally, we share practical recommendations for meta-analysts wanting to use such indices. Key words: meta-analysis, research synthesis, partial effect sizes, regression analysisMeta-analysis is the statistical analysis of empirical results of a series of studies (Glass, 1977). Quantitative procedures in meta-analysis typically begin by transforming study results to a common metric, which often represents results as effect sizes. An effect size is a scale-free index that assesses the magnitude and direction of some relationship between variables. Almost two decades ago researchers argued that results from regression models can be treated as effect-size indices (e.g., Becker & Schram, 1994;Cooper & Hedges, 1994;Greenwald, Hedges, & Laine, 1996;Valentine, DuBois, & Cooper, 2004). More recently, different approaches have been proposed to synthesize regression models (Aloe & Becker, 2012;Becker & Wu, 2007;Peterson & Brown, 2005;Wu & Becker, 2013). These approaches can be organized into three methodological groups. The first group focuses on methods that combine full regression models (e.g., Wu & Becker, 2013), the second group focuses on attempting to approximate the bivariate correlation when it is not directly reported (e.g., Peterson & Brown, 2005), and the third group focuses on methods that combine partial effect sizes that have been extracted from regression models (e.g., Aloe & Becker, 2012;Keef & Roberts, 2004).This article focuses on the estimation and use of the partial effect sizes for the family of effects, which can be computed when multiple predictor variables are included in a primary study. A partial effect size is an index that describes the magnitude of an effect after controlling for the influence of other variables in a model. Part of our rationale for focusing on partial effect sizes is that they are quantities that researchers typically find familiar. Furthermore, partial effect sizes are often directly reported or easily estimated from results found in primary studies. Finally, typical meta-analysis techniques can be used once partial effects are extracted or computed from primary studies.We begin by briefly introducing the meta-analysis of correlational data. Next we introduce required notation for effects and meta-analytic models, including three partial effect sizes (partial correlation, semi-partial correlation, and standardiz...

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Synthesizing regression results: a factored likelihood method

Cited by 13 publications

References 23 publications

On the Covariance of Regression Coefficients

On the Covariance of Regression Coefficients

Bayesian multivariate meta‐analysis of multiple factors

The Synthesis of Partial Effect Sizes

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