IDEAS home Printed from https://ideas.repec.org/a/gam/jijerp/v16y2019i5p746-d210226.html
   My bibliography  Save this article

Comparison of Frequentist and Bayesian Generalized Additive Models for Assessing the Association between Daily Exposure to Fine Particles and Respiratory Mortality: A Simulation Study

Author

Listed:
  • Xin Fang

    (Unit of Biostatistics, Institute of Environmental Medicine, Karolinska Institutet, Stockholm 17177, Sweden)

  • Bo Fang

    (Division of Vital Statistics, Shanghai Municipal Center for Disease Control and Prevention, Shanghai 200336, China)

  • Chunfang Wang

    (Division of Vital Statistics, Shanghai Municipal Center for Disease Control and Prevention, Shanghai 200336, China)

  • Tian Xia

    (Institute of Health Information, Shanghai Municipal Center for Disease Control and Prevention, Shanghai 200336, China)

  • Matteo Bottai

    (Unit of Biostatistics, Institute of Environmental Medicine, Karolinska Institutet, Stockholm 17177, Sweden)

  • Fang Fang

    (Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm 17177, Sweden)

  • Yang Cao

    (Clinical Epidemiology and Biostatistics, School of Medical Sciences, Örebro University, Örebro 70182, Sweden)

Abstract

Objective: To compare the performance of frequentist and Bayesian generalized additive models (GAMs) in terms of accuracy and precision for assessing the association between daily exposure to fine particles and respiratory mortality using simulated data based on a real time-series study. Methods : In our study, we examined the estimates from a fully Bayesian GAM using simulated data based on a genuine time-series study on fine particles with a diameter of 2.5 μm or less (PM 2.5 ) and respiratory deaths conducted in Shanghai, China. The simulation was performed by multiplying the observed daily death with a random error. The underlying priors for Bayesian analysis are estimated using the real world time-series data. We also examined the sensitivity of Bayesian GAM to the choice of priors and to true parameter. Results : The frequentist GAM and Bayesian GAM show similar means and variances of the estimates of the parameters of interest. However, the estimates from Bayesian GAM show relatively more fluctuation, which to some extent reflects the uncertainty inherent in Bayesian estimation. Conclusions : Although computationally intensive, Bayesian GAM would be a better solution to avoid potentially over-confident inferences. With the increasing computing power of computers and statistical packages available, fully Bayesian methods for decision making may become more widely applied in the future.

Suggested Citation

  • Xin Fang & Bo Fang & Chunfang Wang & Tian Xia & Matteo Bottai & Fang Fang & Yang Cao, 2019. "Comparison of Frequentist and Bayesian Generalized Additive Models for Assessing the Association between Daily Exposure to Fine Particles and Respiratory Mortality: A Simulation Study," IJERPH, MDPI, vol. 16(5), pages 1-20, March.
    • Handle: RePEc:gam:jijerp:v:16:y:2019:i:5:p:746-:d:210226
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1660-4601/16/5/746/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1660-4601/16/5/746/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xin Fang & Bo Fang & Chunfang Wang & Tian Xia & Matteo Bottai & Fang Fang & Yang Cao, 2017. "Relationship between fine particulate matter, weather condition and daily non-accidental mortality in Shanghai, China: A Bayesian approach," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-23, November.
    2. Schmid, Matthias & Hothorn, Torsten, 2008. "Boosting additive models using component-wise P-Splines," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 298-311, December.
    3. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    4. Scheipl, Fabian, 2011. "spikeSlabGAM: Bayesian Variable Selection, Model Choice and Regularization for Generalized Additive Mixed Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i14).
    5. Young‐Ju Kim & Chong Gu, 2004. "Smoothing spline Gaussian regression: more scalable computation via efficient approximation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 337-356, May.
    6. Juliana B. de Souza & Valdério A. Reisen & Glaura C. Franco & Márton Ispány & Pascal Bondon & Jane Meri Santos, 2018. "Generalized additive models with principal component analysis: an application to time series of respiratory disease and air pollution data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(2), pages 453-480, February.
    7. Andreas Mayr & Nora Fenske & Benjamin Hofner & Thomas Kneib & Matthias Schmid, 2012. "Generalized additive models for location, scale and shape for high dimensional data—a flexible approach based on boosting," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(3), pages 403-427, May.
    8. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
    9. Duncan Lee & Gavin Shaddick, 2010. "Spatial Modeling of Air Pollution in Studies of Its Short-Term Health Effects," Biometrics, The International Biometric Society, vol. 66(4), pages 1238-1246, December.
    10. Nadja Klein & Thomas Kneib & Stefan Lang, 2015. "Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 405-419, March.
    11. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    12. Martin, Andrew D. & Quinn, Kevin M. & Park, Jong Hee, 2011. "MCMCpack: Markov Chain Monte Carlo in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i09).
    13. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    14. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 11-30, March.
    15. Francesca Dominici & Aidan M.C. Dermott & Trevor J. Hastie, 2004. "Improved Semiparametric Time Series Models of Air Pollution and Mortality," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 938-948, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hyungkyoo Kim, 2020. "Seasonal Impacts of Particulate Matter Levels on Bike Sharing in Seoul, South Korea," IJERPH, MDPI, vol. 17(11), pages 1-17, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Umlauf, Nikolaus & Adler, Daniel & Kneib, Thomas & Lang, Stefan & Zeileis, Achim, 2015. "Structured Additive Regression Models: An R Interface to BayesX," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i21).
    2. Simon N. Wood, 2020. "Inference and computation with generalized additive models and their extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 307-339, June.
    3. Simon N. Wood & Natalya Pya & Benjamin Säfken, 2016. "Smoothing Parameter and Model Selection for General Smooth Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1548-1563, October.
    4. Stefan Lang & Nikolaus Umlauf & Peter Wechselberger & Kenneth Harttgen & Thomas Kneib, 2012. "Multilevel structured additive regression," Working Papers 2012-07, Faculty of Economics and Statistics, Universität Innsbruck.
    5. Yue, Yu Ryan & Rue, Håvard, 2011. "Bayesian inference for additive mixed quantile regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 84-96, January.
    6. Nadja Klein & Michel Denuit & Stefan Lang & Thomas Kneib, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," Working Papers 2013-24, Faculty of Economics and Statistics, Universität Innsbruck.
    7. Nicole H. Augustin & Stefan Lang & Monica Musio & Klaus Von Wilpert, 2007. "A spatial model for the needle losses of pine‐trees in the forests of Baden‐Württemberg: an application of Bayesian structured additive regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(1), pages 29-50, January.
    8. Klein, Nadja & Denuit, Michel & Lang, Stefan & Kneib, Thomas, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," LIDAM Discussion Papers ISBA 2013045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Schmidt, Paul & Mühlau, Mark & Schmid, Volker, 2017. "Fitting large-scale structured additive regression models using Krylov subspace methods," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 59-75.
    10. Belitz, Christiane & Lang, Stefan, 2008. "Simultaneous selection of variables and smoothing parameters in structured additive regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 61-81, September.
    11. Birgit Schrödle & Leonhard Held, 2011. "A primer on disease mapping and ecological regression using $${\texttt{INLA}}$$," Computational Statistics, Springer, vol. 26(2), pages 241-258, June.
    12. Groll Andreas & Kneib Thomas & Mayr Andreas & Schauberger Gunther, 2018. "On the dependency of soccer scores – a sparse bivariate Poisson model for the UEFA European football championship 2016," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 14(2), pages 65-79, June.
    13. Klein, Nadja & Herwartz, Helmut & Kneib, Thomas, 2020. "Modelling regional patterns of inefficiency: A Bayesian approach to geoadditive panel stochastic frontier analysis with an application to cereal production in England and Wales," Journal of Econometrics, Elsevier, vol. 214(2), pages 513-539.
    14. Kneib, Thomas & Silbersdorff, Alexander & Säfken, Benjamin, 2023. "Rage Against the Mean – A Review of Distributional Regression Approaches," Econometrics and Statistics, Elsevier, vol. 26(C), pages 99-123.
    15. Riccardo Borgoni & Francesco Billari, 2003. "Bayesian spatial analysis of demographic survey data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 8(3), pages 61-92.
    16. Tamvada, Jagannadha Pawan, 2010. "The Dynamics of Self-employment in a Developing Country: Evidence from India," MPRA Paper 20042, University Library of Munich, Germany.
    17. Simon N. Wood & Zheyuan Li & Gavin Shaddick & Nicole H. Augustin, 2017. "Generalized Additive Models for Gigadata: Modeling the U.K. Black Smoke Network Daily Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1199-1210, July.
    18. David L. Miller & Richard Glennie & Andrew E. Seaton, 2020. "Understanding the Stochastic Partial Differential Equation Approach to Smoothing," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 1-16, March.
    19. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    20. Ezra Gayawan & Samson B. Adebayo, 2013. "A Bayesian semiparametric multilevel survival modelling of age at first birth in Nigeria," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(45), pages 1339-1372.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jijerp:v:16:y:2019:i:5:p:746-:d:210226. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.