Methods for meta-analysis of individual participant data from Mendelian randomisation studies with binary outcomes

Mendelian randomisation is an epidemiological method for estimating causal associations from observational data by using genetic variants as instrumental variables. Typically the genetic variants explain only a small proportion of the variation in the risk factor of interest, and so large sample sizes are required, necessitating data from multiple sources. Meta-analysis based on individual patient data requires synthesis of studies which differ in many aspects. A proposed Bayesian framework is able to estimate a causal effect from each study, and combine these using a hierarchical model. The method is illustrated for data on C-reactive protein and coronary heart disease (CHD) from the C-reactive protein CHD Genetics Collaboration (CCGC). Studies from the CCGC differ in terms of the genetic variants measured, the study design (prospective or retrospective, population-based or case-control), whether C-reactive protein was measured, the time of C-reactive protein measurement (pre- or post-disease), and whether full or tabular data were shared. We show how these data can be combined in an efficient way to give a single estimate of causal association based on the totality of the data available. Compared to a two-stage analysis, the Bayesian method is able to incorporate data on 23% additional participants and 51% more events, leading to a 23-26% gain in efficiency.