Two-stage meta-analysis with nonparametric Bayesian functional regression

Abstract

Two-stage meta-analysis has been popularly used in epidemiological studies in which an association between environmental exposure and health response is investigated analyzing time-series data collected for multiple locations. The first stage estimates the location-specific association between exposure and response controlling for various confounders, whereas the second stage pools the associations across locations. The second stage often incorporates location-specific predictors (i.e., meta-predictors) to explain the between-location heterogeneity in the association, and is called meta-regression. The existing meta-regression typically relies on parametric assumptions and does not accommodate functional meta-predictors and spatial dependency. Motivated by this limitation, our research proposes a nonparametric Bayesian multivariate meta-regression which incorporates functional meta-predictors and spatial dependency. A flexible functional meta-regression is formulated by jointly modeling the association parameters and the functional meta-predictors using Dirichlet process (DP) or local DP mixtures. The functional meta-predictors, while being jointly modeled with the association parameters, are represented parsimoniously by orthonormal basis coefficients obtained through the functional principal component analysis. The proposed models are applied to two motivating data: temperature-mortality study and study of suicide seasonality. A simulation study is conducted to compare the performances of the two proposed models and a parametric functional meta-regression.