A graphical model approach to systematically missing data in meta-analysis of observational studies

When studies in meta-analysis include different sets of confounders, simple analyses can cause a bias (omitting confounders that are missing in certain studies) or precision loss (omitting studies with incomplete confounders, i.e. a complete-case meta-analysis). To overcome these types of issues, a previous study proposed modelling the high correlation between partially and fully adjusted regression coefficient estimates in a bivariate meta-analysis. When multiple differently adjusted regression coefficient estimates are available, we propose exploiting such correlations in a graphical model. Compared with a previously suggested bivariate meta-analysis method, such a graphical model approach is likely to reduce the number of parameters in complex missing data settings by omitting the direct relationships between some of the estimates. We propose a structure-learning rule whose justification relies on the missingness pattern being monotone. This rule was tested using epidemiological data from a multi-centre survey. In the analysis of risk factors for early retirement, the method showed a smaller difference from a complete data odds ratio and greater precision than a commonly used complete-case meta-analysis. Three real-world applications with monotone missing patterns are provided, namely, the association between (1) the fibrinogen level and coronary heart disease, (2) the intima media thickness and vascular risk and (3) allergic asthma and depressive episodes. The proposed method allows for the inclusion of published summary data, which makes it particularly suitable for applications involving both microdata and summary data. Copyright © 2016 John Wiley & Sons, Ltd.