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Nonparametric Bayesian Functional Meta-Regression: Applications in Environmental Epidemiology

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Abstract

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.

References

  • Ajdacic-Gross, V., Lauber, C., Sansossio, R., Bopp, M., Eich, D., Gostynski, M., ... and Rössler, W. (2007). Seasonal associations between weather conditions and suicide–evidence against a classic hypothesis. American journal of epidemiology, 165(5), 561-569.

  • Arbuthnott, K., Hajat, S., Heaviside, C. and Vardoulakis, S. (2016). Changes in population susceptibility to heat and cold over time: assessing adaptation to climate change. Environmental Health, 15(1), S33.

    Article  Google Scholar 

  • Armstrong B.G., Gasparrini A., Tobias A., and Sera F. (2020). Sample size issues in time series regressions of counts on environmental exposures. BMC medical research methodology, 20(1), 1-9.

    Article  Google Scholar 

  • Bhaskaran, K., Gasparrini, A., Hajat, S., Smeeth, L. and Armstrong, B. (2013). Time series regression studies in environmental epidemiology. International Journal of Epidemiology, 42(4), 1187-1195.

    Article  Google Scholar 

  • Bigelow, J. L. and Dunson, D. B. (2009). Bayesian semiparametric joint models for functional predictors. Journal of the American Statistical Association, 104(485), 26-36.

    Article  MathSciNet  Google Scholar 

  • Bobb, J. F., Peng, R. D., Bell, M. L. and Dominici, F. (2014). Heat-related mortality and adaptation to heat in the United States. Environmental Health Perspectives, 122(8), 811-816.

    Article  Google Scholar 

  • Cardot, H., Ferraty, F. and Sarda, P. (2003). Spline estimators for the functional linear model. Statistica Sinica, 571-591.

  • Chew, K. S. and McCleary, R. (1995). The spring peak in suicides: a cross-national analysis. Social science & medicine, 40(2), 223-230.

    Article  Google Scholar 

  • Christodoulou, C., Douzenis, A., Papadopoulos, F. C., Papadopoulou, A., Bouras, G., Gournellis, R. and Lykouras, L. (2012). Suicide and seasonality. Acta Psychiatrica Scandinavica, 125(2), 127-146.

    Article  Google Scholar 

  • Chung, Y. and Dunson, D. B. (2009). Nonparametric Bayes conditional distribution modeling with variable selection. Journal of the American Statistical Association, 104(488), 1646-1660.

    Article  MathSciNet  Google Scholar 

  • ——– (2011). The local Dirichlet process. Annals of the Institute of Statistical Mathematics, 63(1), 59-80.

  • Chung, Y., Noh, H., Honda, Y., Hashizume, M., Bell, M. L., Guo, Y. L. L. and Kim, H. (2017). Temporal changes in mortality related to extreme temperatures for 15 cities in Northeast Asia: adaptation to heat and maladaptation to cold. American Journal of Epidemiology, 185(10), 907-913.

    Article  Google Scholar 

  • Chung, Y., Yang, D., Gasparrini, A., Vicedo-Cabrera, A. M., Fook Sheng Ng, C., Kim, Y., ... and Hashizume, M. (2018). Changing susceptibility to non-optimum temperatures in Japan, 1972–2012: The role of climate, demographic, and socioeconomic factors. Environmental Health Perspectives, 126(5), 057002.

  • Crainiceanu, C. M., Staicu, A. M. and Di, C. Z. (2009). Generalized multilevel functional regression. Journal of the American Statistical Association, 104(488), 1550-1561.

    Article  MathSciNet  Google Scholar 

  • Dominici, F., Daniels, M., Zeger, S. L., and Samet, J. M. (2002). Air pollution and mortality: estimating regional and national relationships. Journal of the American Statistical Association, 97(457), 100-111.

    Article  MathSciNet  Google Scholar 

  • Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. The Annals of Statistics, 209-230.

  • Gasparrini, A., Armstrong, B. and Kenward, M. G. (2012). Multivariate meta analysis for non-linear and other multi parameter associations. Statistics in Medicine, 31(29), 3821-3839.

    Article  MathSciNet  Google Scholar 

  • Gasparrini, A. (2014). Modeling exposure lag response associations with distributed lag non-linear models. Statistics in Medicine, 33(5), 881-899.

    Article  MathSciNet  Google Scholar 

  • Gasparrini, A., Guo, Y., Hashizume, M., Lavigne, E., Zanobetti, A., Schwartz, J., ... and Armstrong, B. (2015). Mortality risk attributable to high and low ambient temperature: a multicountry observational study. The Lancet, 386(9991), 369-375.

  • Goldsmith, J., Bobb, J., Crainiceanu, C. M., Caffo, B. and Reich, D. (2011). Penalized functional regression. Journal of Computational and Graphical Statistics, 20(4), 830-851.

    Article  MathSciNet  Google Scholar 

  • Görür, D. and Rasmussen, C. E. (2010). Dirichlet process gaussian mixture models: Choice of the base distribution. Journal of Computer Science and Technology, 25(4), 653-664.

    Article  MathSciNet  Google Scholar 

  • Griffin, J. E. and Steel, M. F. (2010). Bayesian nonparametric modelling with the Dirichlet process regression smoother. Statistica Sinica, 1507-1527.

  • Ibrahim, J. G., Chen, M. H. and Sinha, D. (2014). Bayesian Survival Analysis. Wiley StatsRef: Statistics Reference Online.

  • Ishwaran, H. and James, L. F. (2001). Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association, 96(453), 161-173.

    Article  MathSciNet  Google Scholar 

  • ——– (2002). Approximate Dirichlet process computing in finite normal mixtures: smoothing and prior information. Journal of Computational and Graphical statistics, 11(3), 508-532.

  • Kim, Y., Kim, H., Gasparrini, A., Armstrong, B., Honda, Y., Chung, Y., Ng, C.F., Hashizume, M. (2019) Suicide and ambient temperature: a multi-city multi-country study, Environ Health Perspectives, 127, 117007.

    Article  Google Scholar 

  • Lau, J. W. and Green, P. J. (2007). Bayesian model-based clustering procedures. Journal of Computational and Graphical Statistics, 16(3), 526-558.

    Article  MathSciNet  Google Scholar 

  • Montagna, S., Tokdar, S. T., Neelon, B. and Dunson, D. B. (2012). Bayesian latent factor regression for functional and longitudinal data. Biometrics, 68(4), 1064-1073.

    Article  MathSciNet  Google Scholar 

  • Müller, H. G. and Stadtmüller, U. (2005). Generalized functional linear models. The Annals of Statistics, 33(2), 774-805.

    Article  MathSciNet  Google Scholar 

  • Müller, P., Erkanli, A. and West, M. (1996). Bayesian curve fitting using multivariate normal mixtures. Biometrika, 83(1), 67-79.

    Article  MathSciNet  Google Scholar 

  • Müller, P. and Quintana, F. A. (2004). Nonparametric Bayesian data analysis. Statistical Science, 95-110.

  • Müller, P., Quintana, F. A., Jara, A. and Hanson, T. (2015). Bayesian nonparametric data analysis (Vol. 18). New York: Springer.

    Book  Google Scholar 

  • Papadopoulos, F. C., Frangakis, C. E., Skalkidou, A., Petridou, E., Stevens, R. G., and Trichopoulos, D. (2005). Exploring lag and duration effect of sunshine in triggering suicide. Journal of affective disorders, 88(3), 287-297.

    Article  Google Scholar 

  • Papastamoulis, P. and Iliopoulos, G. (2010). An artificial allocations based solution to the label switching problem in Bayesian analysis of mixtures of distributions. Journal of Computational and Graphical Statistics, 19(2), 313-331.

    Article  MathSciNet  Google Scholar 

  • Petridou, E., Papadopoulos, F. C., Frangakis, C. E., Skalkidou, A., and Trichopoulos, D. (2002). A role of sunshine in the triggering of suicide. Epidemiology, 13(1), 106-109.

    Article  Google Scholar 

  • Ramsay, J. and Silverman, B. W. (2005). Functional Data Analysis. Springer Science & Business Media.

    Book  Google Scholar 

  • Rodriguez, A., Dunson, D. B. and Gelfand, A. E. (2009). Bayesian nonparametric functional data analysis through density estimation. Biometrika, 96(1), 149-162.

    Article  MathSciNet  Google Scholar 

  • Sera, F., Armstrong, B., Blangiardo, M. and Gasparrini, A. (2019). An extended mixed-effects framework for meta-analysis. Statistics in Medicine, 38(29), 5429-5444.

    Article  MathSciNet  Google Scholar 

  • Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statistica Sinica, 639-650.

  • Sim, G., Kim, H., Zanobetti, A., Schwartz, J. and Chung, Y. (2018). Non-parametric Bayesian multivariate metaregression: an application in environmental epidemiology. Journal of the Royal Statistical Society: Series C (Applied Statistics), 67(4), 881-896.

    MathSciNet  Google Scholar 

  • Sim, K., Kim, Y., Hashizume, M., Gasparrini, A., Armstrong, B., Sera, F., Ng, C., Honda, Y., Chung, Y. (2020) Nonlinear temperature-suicide association in Japan from 1972 to 2015: its heterogeneity and the role of climate, demographic, and socioeconomic factors. Environment International, 142, 105829.

    Article  Google Scholar 

  • Vicedo-Cabrera, A. M., Sera, F., Guo, Y., Chung, Y., Arbuthnott, K., Tong, S., ... and Gasparrini, A. (2018). A multi-country analysis on potential adaptive mechanisms to cold and heat in a changing climate. Environment International, 111, 239-246.

  • Vyssoki, B., Kapusta, N. D., Praschak-Rieder, N., Dorffner, G., and Willeit, M. (2014). Direct effect of sunshine on suicide. JAMA psychiatry, 71(11), 1231-1237.

    Article  Google Scholar 

  • Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research, 11(Dec), 3571-3594.

    MathSciNet  MATH  Google Scholar 

  • Welty, L. J., Peng, R. D., Zeger, S. L., Dominici, F. (2009). Bayesian distributed lag models: estimating effects of particulate matter air pollution on daily mortality. Biometrics, 65(1), 282-291.

    Article  MathSciNet  Google Scholar 

  • Wilson, A., Rappold, A. G., Neas, L. M., Reich, B. J. (2014). Modeling the effect of temperature on ozone-related mortality. The Annals of Applied Statistics, 1, 1728-1749.

    Article  MathSciNet  Google Scholar 

  • Yao, F., Müller, H. G., Clifford, A. J., Dueker, S. R., Follett, J., Lin, Y., ... and Vogel, J. S. (2003). Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate. Biometrics, 59(3), 676-685.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, South Korea

    Jaeeun Yu, Jinsu Park & Yeonseung Chung

  2. Department of Statistics, Korea University, Seoul, South Korea

    Taeryon Choi

  3. Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo, Tokyo, Japan

    Masahiro Hashizume

  4. Department of Global Environmental Health, Graduate School of Medicine, The University of Tokyo, Tokyo, Japan

    Yoonhee Kim

  5. Faculty of Health and Sport Sciences, University of Tsukuba, Tsukuba, Japan

    Yasushi Honda

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  1. Jaeeun Yu
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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). https://doi.org/10.1007/s13253-020-00409-z

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