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.