Nonparametric Bayesian Functional Meta-Regression: Applications in Environmental Epidemiology


Two-stage meta-analysis has been popularly used in epidemiological studies to investigate an association between environmental exposure and health response by analyzing time-series data collected from multiple locations. The first stage estimates the location-specific association, while 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 and is called meta-regression. The existing second-stage meta-regression relies on parametric assumptions and does not accommodate functional meta-predictors and spatial dependency. Motivated by these limitations, our research proposes a nonparametric Bayesian meta-regression which relaxes parametric assumptions and incorporates functional meta-predictors and spatial dependency. The proposed meta-regression is formulated by jointly modeling the association parameters and the functional meta-predictors using Dirichlet process (DP) or local DP mixtures. In doing so, the functional meta-predictors are represented parsimoniously by the coefficients of the orthonormal basis. The proposed models were applied to (1) a temperature–mortality association study and (2) suicide seasonality study, and validated through a simulation study.

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Data Availability Statement

Data used in the simulation study are available in Supplementary Material. Data used in the application are available upon request to the authors.


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We would like to thank the editor, associate editor and two reviewers for their conscientious reading and constructive comments, which improved the quality of this manuscript. This research was supported by the Senior Research grant (2019R1A2C1086194) from the National Research Foundation of Korea, funded by the Ministry of Science, Information and Communication Technologies, the Government-wide R & D Fund project for Infectious Disease (HG18C0025), the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant (JP19K17104), and the Environment Research and Technology Development Fund (S-14) of the Environmental Restoration and Conservation Agency of Japan.

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Correspondence to Yeonseung Chung.

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Yu, J., Park, J., Choi, T. et al. Nonparametric Bayesian Functional Meta-Regression: Applications in Environmental Epidemiology. JABES 26, 45–70 (2021).

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  • Dirichlet process mixture
  • Functional predictor
  • Local Dirichlet process
  • Meta-regression
  • Spatial dependency