Systematically missing confounders in individual participant data meta-analysis of observational cohort studies

One difficulty in performing meta- analysesof observational cohortstudies is that the availability of confoundersmay vary between cohorts, so that some cohortsprovide fully adjusted analyseswhile others only provide partially adjusted analyses. Commonly, analysesof the association between an exposure and disease either are restricted to cohortswith full confounderinformation, or use all cohortsbut do not fully adjust for confounding. We propose using a bivariate random-effects meta-analysis model to use information from all available cohortswhile still adjusting for all the potential confounders. Our method uses both the fully adjusted and the partially adjusted estimated effects in the cohortswith full confounderinformation, together with an estimate of their within- cohortcorrelation. The method is applied to estimate the association between fibrinogen level and coronary heart disease