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Int J Epidemiol. 2011 Jun;40(3):765-77. doi: 10.1093/ije/dyq248. Epub 2010 Dec 23.

A proposed method of bias adjustment for meta-analyses of published observational studies.

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  • 1MRC Biostatistics Unit, Cambridge, UK.



Interpretation of meta-analyses of published observational studies is problematic because of numerous sources of bias. We develop bias assessment, elicitation and adjustment methods, and apply them to a systematic review of longitudinal observational studies of the relationship between objectively measured physical activity and subsequent change in adiposity in children.


We separated internal biases that reflect study quality from external biases that reflect generalizability to a target setting. Since published results were presented in different formats, these were all converted to correlation coefficients. Biases were considered as additive or proportional on the correlation scale. Opinions about the extent of each bias in each study, together with its uncertainty, were elicited in a formal process from quantitatively trained assessors for the internal biases and subject-matter specialists for the external biases. Bias-adjusted results for each study were combined across assessors using median pooling, and results combined across studies by random-effects meta-analysis.


Before adjusting for bias, the pooled correlation is difficult to interpret because the studies varied substantially in quality and design, and there was considerable heterogeneity. After adjusting for both the internal and external biases, the pooled correlation provides a meaningful quantitative summary of all available evidence, and the confidence interval incorporates the elicited uncertainties about the extent of the biases. In the adjusted meta-analysis, there was no apparent heterogeneity.


This approach provides a viable method of bias adjustment for meta-analyses of observational studies, allowing the quantitative synthesis of evidence from otherwise incompatible studies. From the meta-analysis of longitudinal observational studies, we conclude that there is no evidence that physical activity is associated with gain in body fat.

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