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. Supplementary materials accompanying this paper appear online.

[1]  F. Dominici,et al.  Heat-Related Mortality and Adaptation to Heat in the United States , 2014, Environmental health perspectives.

[2]  A. Gelfand,et al.  Bayesian Nonparametric Functional Data Analysis Through Density Estimation. , 2009, Biometrika.

[3]  J. Schwartz,et al.  Mortality risk attributable to high and low ambient temperature: a multicountry observational study , 2015, The Lancet.

[4]  L. Lykouras,et al.  Suicide and seasonality , 2012, Acta psychiatrica Scandinavica.

[5]  D. Trichopoulos,et al.  Exploring lag and duration effect of sunshine in triggering suicide. , 2005, Journal of affective disorders.

[6]  James O. Ramsay,et al.  Functional Data Analysis , 2005 .

[7]  Lancelot F. James,et al.  Gibbs Sampling Methods for Stick-Breaking Priors , 2001 .

[8]  B. Reich,et al.  Modeling the effect of temperature on ozone-related mortality , 2013, 1412.1642.

[9]  M. Steel,et al.  Bayesian nonparametric modelling with the Dirichlet process regression smoother , 2010 .

[10]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[11]  Gyuseok Sim,et al.  Non‐parametric Bayesian multivariate metaregression: an application in environmental epidemiology , 2018 .

[12]  D. Dunson,et al.  The local Dirichlet process , 2011, Annals of the Institute of Statistical Mathematics.

[13]  Ana-Maria Staicu,et al.  Generalized Multilevel Functional Regression , 2009, Journal of the American Statistical Association.

[14]  F. Gutzwiller,et al.  Seasonal associations between weather conditions and suicide--evidence against a classic hypothesis. , 2006, American journal of epidemiology.

[15]  Sotiris Vardoulakis,et al.  Changes in population susceptibility to heat and cold over time: assessing adaptation to climate change , 2016, Environmental Health.

[16]  M. Hashizume,et al.  Temporal Changes in Mortality Related to Extreme Temperatures for 15 Cities in Northeast Asia: Adaptation to Heat and Maladaptation to Cold , 2017, American journal of epidemiology.

[17]  Martina S. Ragettli,et al.  Suicide and Ambient Temperature: A Multi-Country Multi-City Study , 2019, Environmental health perspectives.

[18]  Ulrich Stadtmüller,et al.  Generalized functional linear models , 2005 .

[19]  A. Gasparrini,et al.  Suicide and Ambient Temperature: A Multi-City Multi-Country Study , 2018, ISEE Conference Abstracts.

[20]  Antonio Gasparrini,et al.  An extended mixed‐effects framework for meta‐analysis , 2019, Statistics in medicine.

[21]  A. Gasparrini,et al.  Nonlinear temperature-suicide association in Japan from 1972 to 2015: Its heterogeneity and the role of climate, demographic, and socioeconomic factors , 2020, Environment international.

[22]  G. Dorffner,et al.  Direct effect of sunshine on suicide. , 2014, JAMA psychiatry.

[23]  Fernando A. Quintana,et al.  Nonparametric Bayesian data analysis , 2004 .

[24]  R. McCleary,et al.  The spring peak in suicides: a cross-national analysis. , 1995, Social science & medicine.

[25]  S L Zeger,et al.  Bayesian Distributed Lag Models: Estimating Effects of Particulate Matter Air Pollution on Daily Mortality , 2009, Biometrics.

[26]  K. Bhaskaran,et al.  Time series regression studies in environmental epidemiology , 2013, International journal of epidemiology.

[27]  D. Trichopoulos,et al.  A Role of Sunshine in the Triggering of Suicide , 2002, Epidemiology.

[28]  Scott L. Zeger,et al.  Air Pollution and Mortality , 2002 .

[29]  A. Gasparrini,et al.  Changing Susceptibility to Non-Optimum Temperatures in Japan, 1972–2012: The Role of Climate, Demographic, and Socioeconomic Factors , 2018, Environmental health perspectives.

[30]  Dilan Görür,et al.  Dirichlet process Gaussian mixture models: choice of the base distribution , 2010 .

[31]  Sumio Watanabe,et al.  Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory , 2010, J. Mach. Learn. Res..

[32]  J. Sethuraman.  A CONSTRUCTIVE DEFINITION OF DIRICHLET PRIORS , 1991 .

[33]  P. Green,et al.  Bayesian Model-Based Clustering Procedures , 2007 .

[34]  Brian Neelon,et al.  Bayesian Latent Factor Regression for Functional and Longitudinal Data , 2012, Biometrics.

[35]  P. Sarda,et al.  SPLINE ESTIMATORS FOR THE FUNCTIONAL LINEAR MODEL , 2003 .

[36]  Ciprian M Crainiceanu,et al.  Penalized Functional Regression , 2011, Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America.

[37]  Lancelot F. James,et al.  Approximate Dirichlet Process Computing in Finite Normal Mixtures , 2002 .

[38]  H. Müller,et al.  Shrinkage Estimation for Functional Principal Component Scores with Application to the Population Kinetics of Plasma Folate , 2003, Biometrics.

[39]  A Gasparrini,et al.  Multivariate meta-analysis for non-linear and other multi-parameter associations , 2012, Statistics in medicine.

[40]  David B. Dunson,et al.  Bayesian Semiparametric Joint Models for Functional Predictors , 2009, Journal of the American Statistical Association.

[41]  Martina S. Ragettli,et al.  A multi-country analysis on potential adaptive mechanisms to cold and heat in a changing climate. , 2018, Environment international.

[42]  A. Gasparrini,et al.  Sample size issues in time series regressions of counts on environmental exposures , 2020, BMC Medical Research Methodology.

[43]  George Iliopoulos,et al.  An Artificial Allocations Based Solution to the Label Switching Problem in Bayesian Analysis of Mixtures of Distributions , 2010 .

[44]  D. Dunson,et al.  Nonparametric Bayes Conditional Distribution Modeling With Variable Selection , 2009, Journal of the American Statistical Association.

[45]  Fernando A. Quintana,et al.  Bayesian Nonparametric Data Analysis , 2015 .

[46]  Antonio Gasparrini,et al.  Modeling exposure–lag–response associations with distributed lag non-linear models , 2013, Statistics in medicine.

[47]  P. Müller,et al.  Bayesian curve fitting using multivariate normal mixtures , 1996 .