Non‐parametric Bayesian multivariate metaregression: an application in environmental epidemiology

In biomedical research, meta‐analysis is a popular tool to combine evidence from multiple studies to investigate an exposure–response association. A two‐stage analytical approach is used in meta‐analysis for its computational convenience and flexibility. The first stage estimates the association for each study whereas the second stage combines the study‐specific estimates correcting for the study‐specific error. The second stage often incorporates study‐specific covariates (metapredictors) and is called metaregression. One application where the two‐stage meta‐analysis is useful is an epidemiological study for the health effects of environmental exposure, which often analyses time series data of exposure and health outcome collected from multiple locations. The first stage models location‐specific association, which is often represented by multiple parameters as the association is non‐linear or delayed, and the second stage conducts a multivariate metaregression with location‐specific characteristics as metapredictors. The currently used multivariate metaregression is a form of normal linear regression, which may be limited as it assumes linearity in metapredictors, residual normality and homoscedasticity. In the paper, we propose a flexible multivariate metaregression in a non‐parametric Bayesian modelling framework incorporating a residual spatial dependence. The proposed metaregression was evaluated through a simulation study and applied to investigate a temperature–mortality association in the 135 US cities.