{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T06:11:16Z","timestamp":1791612676037,"version":"4.3.4"},"reference-count":39,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,3,20]],"date-time":"2023-03-20T00:00:00Z","timestamp":1679270400000},"content-version":"vor","delay-in-days":3632,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000066","name":"National Institute of Environmental Health Sciences","doi-asserted-by":"publisher","award":["T32ES012871"],"award-info":[{"award-number":["T32ES012871"]}],"id":[{"id":"10.13039\/100000066","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000066","name":"National Institute of Environmental Health Sciences","doi-asserted-by":"publisher","award":["R01ES012054"],"award-info":[{"award-number":["R01ES012054"]}],"id":[{"id":"10.13039\/100000066","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000066","name":"National Institute of Environmental Health Sciences","doi-asserted-by":"publisher","award":["R01ES019560"],"award-info":[{"award-number":["R01ES019560"]}],"id":[{"id":"10.13039\/100000066","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000139","name":"US Environmental Protection Agency","doi-asserted-by":"publisher","award":["RD-83479801"],"award-info":[{"award-number":["RD-83479801"]}],"id":[{"id":"10.13039\/100000139","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000139","name":"US Environmental Protection Agency","doi-asserted-by":"publisher","award":["RD-83241701"],"award-info":[{"award-number":["RD-83241701"]}],"id":[{"id":"10.13039\/100000139","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,5,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Hierarchical models (HMs) have been used extensively in multisite time series studies of air pollution and health to estimate health effects of a single pollutant adjusted for other pollutants and other time varying factors. Recently, the US Environmental Protection Agency has called for research quantifying health effects of simultaneous exposure to many air pollutants. However, straightforward application of HMs in this context is challenged by the need to specify a random-effect distribution on a high dimensional vector of nuisance parameters. Here we introduce the reduced HM as a general statistical approach for analysing correlated data with many nuisance parameters. For reduced HMs we first calculate the integrated likelihood of the parameter of interest (e.g. the excess number of deaths attributed to simultaneous exposure to high levels of many pollutants), and we then specify a flexible random-effect distribution directly on this parameter. Simulation studies show that the reduced HM performs comparably with the full HM in many scenarios and even performs better in some cases, particularly when the multivariate random-effect distribution of the full HM is misspecified. Methods are applied to estimate relative risks of cardio-vascular hospital admissions associated with simultaneous exposure to elevated levels of particulate matter and ozone in 51 US counties during 1999\u20132005.<\/jats:p>","DOI":"10.1111\/rssc.12006","type":"journal-article","created":{"date-parts":[[2013,9,5]],"date-time":"2013-09-05T09:36:34Z","timestamp":1378373794000},"page":"451-472","source":"Crossref","is-referenced-by-count":6,"title":["Reduced Hierarchical Models with Application to Estimating Health Effects of Simultaneous Exposure to Multiple Pollutants"],"prefix":"10.1093","volume":"62","author":[{"given":"Jennifer F.","family":"Bobb","sequence":"first","affiliation":[{"name":"Harvard School of Public Health , Boston , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesca","family":"Dominici","sequence":"additional","affiliation":[{"name":"Harvard School of Public Health , Boston , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roger D.","family":"Peng","sequence":"additional","affiliation":[{"name":"Johns Hopkins School of Public Health , Baltimore , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2013,4,9]]},"reference":[{"key":"2023032100061527800_","first-page":"639","article-title":"Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies","volume":"47","author":"Agresti","year":"2004","journal-title":"Computnl Statist. Data Anal."},{"key":"2023032100061527800_","first-page":"2372","article-title":"Ozone and short-term mortality in 95 US urban communities, 1987-2000","volume":"292","author":"Bell","year":"2004","journal-title":"J. Am. Med. Ass."},{"key":"2023032100061527800_","first-page":"1","article-title":"Integrated likelihood methods for eliminating nuisance parameters","volume":"14","author":"Berger","year":"1999","journal-title":"Statist. Sci."},{"key":"2023032100061527800_","first-page":"1605","article-title":"A Bayesian model averaging approach for estimating the relative risk of mortality associated with heat waves in 105 U.S. cities","volume":"67","author":"Bobb","year":"2011","journal-title":"Biometrics"},{"key":"2023032100061527800_","first-page":"347","article-title":"A Monte Carlo EM algorithm for generalized linear mixed models with flexible random effects distribution","volume":"3","author":"Chen","year":"2002","journal-title":"Biostatistics"},{"key":"2023032100061527800_","first-page":"187","article-title":"Protecting human health from air pollution: shifting from a single-pollutant to a multipollutant approach","volume":"21","author":"Dominici","year":"2010","journal-title":"Epidemiology"},{"key":"2023032100061527800_","first-page":"1127","article-title":"Fine particulate air pollution and hospital admission for cardiovascular and respiratory diseases","volume":"295","author":"Dominici","year":"2006","journal-title":"J. Am. Med. Ass."},{"key":"2023032100061527800_","first-page":"263","article-title":"Combining evidence on air pollution and daily mortality from the 20 largest US cities: a hierarchical modelling strategy (with discussion)","volume":"163","author":"Dominici","year":"2000","journal-title":"J. R. Statist. Soc. A"},{"key":"2023032100061527800_","volume-title":"Likelihood","author":"Edwards","year":"1992"},{"key":"2023032100061527800_","first-page":"538","article-title":"Empirical Bayes methods for combining likelihoods","volume":"91","author":"Efron","year":"1996","journal-title":"J. Am. Statist. Ass."},{"key":"2023032100061527800_","volume-title":"The benefits and costs of the Clean Air Act from 1990 to 2020","author":"Environmental Protection Agency","year":"2011"},{"key":"2023032100061527800_","first-page":"209","article-title":"A Bayesian analysis of some nonparametric problems","volume":"1","author":"Ferguson","year":"1973","journal-title":"Ann. Statist."},{"key":"2023032100061527800_","first-page":"363","article-title":"Semi-nonparametric maximum likelihood estimation","volume":"55","author":"Gallant","year":"1987","journal-title":"Econometrica"},{"key":"2023032100061527800_","volume-title":"Markov Chain Monte Carlo in Practice","author":"Gilks","year":"1995"},{"key":"2023032100061527800_","first-page":"973","article-title":"Misspecified maximum likelihood estimates and generalised linear mixed models","volume":"88","author":"Heagerty","year":"2001","journal-title":"Biometrika"},{"key":"2023032100061527800_","first-page":"521","article-title":"Confounding and effect modification in the short-term effects of ambient particles on total mortality: results from 29 European cities within the aphea2 project","volume":"12","author":"Katsouyanni","year":"2001","journal-title":"Epidemiology"},{"key":"2023032100061527800_","first-page":"3441","article-title":"Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution","volume":"52","author":"Kom\u00e1rek","year":"2008","journal-title":"Computnl Statist. Data Anal."},{"key":"2023032100061527800_","first-page":"805","article-title":"Nonparametric maximum likelihood estimation of a mixing distribution","volume":"73","author":"Laird","year":"1978","journal-title":"J. Am. Statist. Ass."},{"key":"2023032100061527800_","first-page":"551","article-title":"Data cloning: easy maximum likelihood estimation for complex ecological models using bayesian markov chain monte carlo methods","volume":"10","author":"Lele","year":"2007","journal-title":"Ecol. Lett."},{"key":"2023032100061527800_","first-page":"268","article-title":"A hierarchical Bayesian model for combining multiple 2 \u00d7 2 tables using conditional likelihoods","volume":"55","author":"Liao","year":"1999","journal-title":"Biometrics"},{"key":"2023032100061527800_","first-page":"3125","article-title":"The impact of a misspecified random-effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models","volume":"27","author":"Liti\u00e8re","year":"2008","journal-title":"Statist. Med."},{"key":"2023032100061527800_","first-page":"656","article-title":"Rejoinder to \u2018\u2018A note on type II error under random effects misspecification in generalized linear mixed models\u2019\u2019","volume":"66","author":"Liti\u00e8re","year":"2010","journal-title":"Biometrics"},{"key":"2023032100061527800_","first-page":"1141","article-title":"A smooth nonparametric estimate of a mixing distribution using mixtures of Gaussians","volume":"91","author":"Magder","year":"1996","journal-title":"J. Am. Statist. Ass."},{"key":"2023032100061527800_","first-page":"270","article-title":"Prediction of random effects in linear and generalized linear models under model misspecification","volume":"67","author":"McCulloch","year":"2011","journal-title":"Biometrics"},{"key":"2023032100061527800_","first-page":"1087","article-title":"Equation of state calculations by fast computing machines","volume":"21","author":"Metropolis","year":"1953","journal-title":"J. Chem. Phys."},{"key":"2023032100061527800_","volume-title":"Research priorities for airborne particulate matter: IV, Continuing research progress","author":"National Research Council","year":"2004"},{"key":"2023032100061527800_","first-page":"249","article-title":"Markov chain sampling methods for Dirichlet process mixture models","volume":"9","author":"Neal","year":"2000","journal-title":"J. Computnl Graph. Statist."},{"key":"2023032100061527800_","first-page":"755","article-title":"The effects of mixture distribution misspecification when fitting mixed-effects logistic models","volume":"79","author":"Neuhaus","year":"1992","journal-title":"Biometrika"},{"key":"2023032100061527800_","volume-title":"In All Likelihood: Statistical Modelling and Inference using Likelihood","author":"Pawitan","year":"2001"},{"key":"2023032100061527800_","first-page":"957","article-title":"Emergency admissions for cardiovascular and respiratory diseases and the chemical composition of fine particle air pollution","volume":"117","author":"Peng","year":"2009","journal-title":"Environ. Hlth Perspect."},{"key":"2023032100061527800_","first-page":"701","article-title":"Toward a quantitative estimate of future heat wave mortality under global climate change","volume":"119","author":"Peng","year":"2011","journal-title":"Environ. Hlth Perspect."},{"key":"2023032100061527800_","first-page":"2172","article-title":"Coarse particulate matter air pollution and hospital admissions for cardiovascular and respiratory diseases among Medicare patients","volume":"299","author":"Peng","year":"2008","journal-title":"J. Am. Med. Ass."},{"key":"2023032100061527800_","first-page":"179","article-title":"Model choice in time series studies of air pollution and mortality (with comments)","volume":"169","author":"Peng","year":"2006","journal-title":"J. R. Statist. Soc. A"},{"key":"2023032100061527800_","first-page":"539","article-title":"Control for confounding in the presence of measurement error in hierarchical models","volume":"4","author":"Schwartz","year":"2003","journal-title":"Biostatistics"},{"key":"2023032100061527800_","first-page":"2685","article-title":"Bayesian approaches to random effects meta-analysis: a comparative study","volume":"14","author":"Smith","year":"1995","journal-title":"Statist. Med."},{"key":"2023032100061527800_","first-page":"541","article-title":"The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data","volume":"23","author":"Verbeke","year":"1997","journal-title":"Computnl Statist. Data Anal."},{"key":"2023032100061527800_","first-page":"1601","article-title":"Bayesian random effects meta-analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales","volume":"21","author":"Warn","year":"2002","journal-title":"Statist. Med."},{"key":"2023032100061527800_","first-page":"80","article-title":"Are the acute effects of particulate matter on mortality in the national morbidity, mortality, and air pollution study the result of inadequate control for weather and season?: a sensitivity analysis using flexible distributed lag models","volume":"162","author":"Welty","year":"2005","journal-title":"Am. J. Epidem."},{"key":"2023032100061527800_","first-page":"1686","article-title":"Estimating the independent effects of multiple pollutants in the presence of measurement error: an application of a measurement-error-resistant technique","volume":"112","author":"Zeka","year":"2004","journal-title":"Environ. Hlth Perspect."}],"container-title":["Journal of the Royal Statistical Society Series C: Applied Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssc.12006","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssc\/article-pdf\/62\/3\/451\/49562581\/jrsssc_62_3_451.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssc\/article-pdf\/62\/3\/451\/49562581\/jrsssc_62_3_451.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T01:18:22Z","timestamp":1679361502000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssc\/article\/62\/3\/451\/7080765"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,9]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,4,9]]},"published-print":{"date-parts":[[2013,5,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssc.12006","relation":{},"ISSN":["0035-9254","1467-9876"],"issn-type":[{"value":"0035-9254","type":"print"},{"value":"1467-9876","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2013,5]]},"published":{"date-parts":[[2013,4,9]]}}}