A two-stage hierarchical regression model for meta-analysis of epidemiologic nonlinear dose-response data

To estimate a summarized dose-response relation across different exposure levels from epidemiologic data, meta-analysis often needs to take into account heterogeneity across studies beyond the variation associated with fixed effects. We extended a generalized-least-squares method and a multivariate maximum likelihood method to estimate the summarized nonlinear dose-response relation taking into account random effects. These methods are readily suited to fitting and testing models with covariates and curvilinear dose-response relations.