Addressing extrema and censoring in pollutant and exposure data using mixture of normal distributions

Atmospheric Environment

Volumn 77, Issue , 2013, Pages 464-473

  Li, Shi ^a   Batterman, Stuart ^a   Su, Feng Chiao ^a   Mukherjee, Bhramar ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Air pollution; Density estimation; Dirichlet process mixture; Limits of detection; Mixture of normal; Volatile organic compounds

Indexed keywords

DENSITY ESTIMATION; DENSITY ESTIMATION METHODS; DIRICHLET PROCESS MIXTURE; DIRICHLET PROCESS MIXTURES (DPM); LIMITS OF DETECTION; MIXTURE OF NORMAL DISTRIBUTIONS; PARAMETRIC DISTRIBUTIONS; VOLATILE ORGANIC COMPOUND (VOC);

AIR POLLUTION; ESTIMATION; NORMAL DISTRIBUTION; VARIATIONAL TECHNIQUES; VOLATILE ORGANIC COMPOUNDS;

MIXTURES;

1,4 DICHLOROBENZENE; CHLOROFORM; STYRENE;

ATMOSPHERIC POLLUTION; PERFORMANCE ASSESSMENT; POLLUTION EXPOSURE; VOLATILE ORGANIC COMPOUND;

AIR POLLUTANT; AIR POLLUTION; AMBIENT AIR; ARTICLE; CONCENTRATION (PARAMETERS); CONTROLLED STUDY; ENVIRONMENTAL EXPOSURE; PRIORITY JOURNAL;

EID: 84879337321     PISSN: 13522310     EISSN: 18732844     Source Type: Journal    
DOI: 10.1016/j.atmosenv.2013.05.004     Document Type: Article

References (59)

1. Antoniak C.E. Mixtures of Dirichlet processes with applications to nonparametric problems. Annals of Statistics 1974, 2:1152-1174.
2. Antweiler R., Taylor H. Evaluation of statistical treatments of left-censored environmental data using coincident uncensored data sets: I. Summary statistics. Environmental Science & Technology 2008, 42:3732-3738.
3. ATSDR Toxicological Profile for Chloroform 1997, Agency for Toxic Substances and Disease Registry, Atlanta, GA, Available from:. http://www.atsdr.cdc.gov/ToxProfiles/tp.asp%3fid%3d53%26tid%3d16.
4. ATSDR Toxicological Profile for Dichlorobenzenes 2006, Agency for Toxic Substances and Disease Registry, Atlanta, GA, Available from:. http://www.atsdr.cdc.gov/toxprofiles/tp.asp%3fid%3d704%26tid%3d126.
5. ATSDR Toxicological Profile for Styrene 2010, Agency for Toxic Substances and Disease Registry, Atlanta, GA, Available from:. http://www.atsdr.cdc.gov/PHS/PHS.asp%3fid%3d419%26tid%3d74.
6. Batterman S., Jia C., Godwin C., Hatzivasilis G. Adominant source of VOC exposure: attached garages. Epidemiology 2006, 17:S350.
7. Batterman S., Su F.C., Jia C., Naidoo R.N., Robins T., Naik I. Manganese and lead in children's blood and airborne particulate matter in Durban, South Africa. Science of the Total Environment 2011, 409:1058-1068.
8. Benaglia T., Chauveau D., Hunter D.R., Young D.S. mixtools: an R package for analyzing mixture models. Journal of Statistical Software 2009, 32.
9. Biernacki C., Celeux C., Govaert G. Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence 2000, 22:719-725.
10. Blackwell D., MacQueen J.B. Ferguson distributions via Polya Urn schemes. Annals of Statistics 1973, 1:353-355.
11. Burmaster D.E., Wilson A.M. Fitting second-order finite mixture models to data with many censored values using maximum likelihood estimation. Risk Analysis: An Official Publication of the Society for Risk Analysis 2000, 20:261-272.
12. Caldwell J.C., Woodruff T.J., Morello-Frosch R., Axelrad D.A. Application of health information to hazardous air pollutants modeled in EPA's cumulative exposure project. Toxicology and Industrial Health 1998, 14:429-454.
13. CDC NHANES 1999-2000 Laboratory Files 2012, Centers for Disease Control and Prevention, Atlanta, GA, Available from:. http://www.cdc.gov/nchs/nhanes/nhanes1999-2000/lab99_00.htm.
14. Charnigo R., Sun J. Testing homogeneity in a mixture distribution via the L2 distance between competing models. Journal of the American Statistical Association 2004, 99:488-498.
15. Chen H., Chen J., Kalbfleisch J.D. Amodified likelihood ratio test for homogeneity in finite mixture models. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 2001, 63:19-29.
16. Chin J.Y., Godwin C., Jia C., Robins T., Lewis T., Parker E., Max P., Batterman S. Concentrations and risks of p-dichlorobenzene in indoor and outdoor air. Indoor Air 2012, 10.1111/j.1600-0668.2012.00796.x.
17. Chu H., Kensler T.W., Muñoz A. Assessing the effect of interventions in the context of mixture distributions with detection limits. Statistics in Medicine 2005, 24:2053-2067.
18. D'Souza J.C., Jia C., Mukherjee B., Batterman S. Ethnicity, housing and personal factors as determinants of VOC exposures. Atmospheric Environment 2009, 43:2884-2892.
19. Dempster A.P., Laird N.M., Rubin D.B. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 1977, 39:1-38.
20. Dey D., Liu J. Aquantitative study of quantile based direct prior elicitation from expert opinion. Bayesian Analysis 2007, 2:137-166.
21. Escobar M.D. Estimating normal means with a dirichlet process prior. Journal of the American Statistical Association 1994, 89:268-277.
22. Escobar M.D., West M. Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association 1995, 90:577-588.
23. Ferguson T.S. ABayesian analysis of some nonparametric problems. The Annals of Statistics 1973, 1:209-230.
24. Ferguson T.S. Bayesian density estimation by mixtures of normal distributions. Recent Advances in Statistics 1983, 287-302. Academic Press, New York, US. M. Rizvi, J. Rustagi, D. Siegmund (Eds.).
25. Fraley C., Raftery A.E. How many clusters? Which clustering method? Answers via model-based cluster analysis. The Computer Journal 1998, 41:578-588.
26. Hammonds J.S., Hoffman F.O., Bartell S.M. An Introductory Guide to Uncertainty Analysis in Environmental and Health Risk Assessment, ES/ER/TM-35 1994, US Environmental Protection Agency, Washington, DC.
27. Hurvich C.M., Tsai C.L. Regression and time series model selection in small samples. Biometrika 1989, 76:297-307.
28. IARC Agents Classified by the IARC Monographs 2012, World Health Organization, International Agency for Research on Cancer, Lyon, France, Available from:. http://monographs.iarc.fr/ENG/Classification/index.php.
29. Jara A. Applied Bayesian non- and semi-parametric inference using DPpackage. RNews 2007, 7:17-26.
30. Jara A., Hanson T., Quintana F.A., Müller P., Rosner G.L. DPpackage: Bayesian semi- and nonparametric modeling in R. Journal of Statistical Software 2011, 40:1-30.
31. Jia C., Batterman S. Acritical review of naphthalene sources and exposures relevant to indoor and outdoor air. International Journal of Environmental Research and Public Health 2010, 7:2903-2939.
32. Jia C., Batterman S., Godwin C. VOCs in industrial, urban and suburban neighborhoods - Part 2: Factors affecting indoor and outdoor concentrations. Atmospheric Environment 2008, 42:2101-2116.
33. Jia C., D'Souza J., Batterman S. Distributions of personal VOC exposures: a population-based analysis. Environment International 2008, 34:922-931.
34. Kim H., Bernstein J. Air pollution and allergic disease. Current Allergy and Asthma Reports 2009, 9:128-133.
35. Krishnamoorthy K., Mallick A., Mathew T. Model-based imputation approach for data analysis in the presence of non-detects. Annals of Occupational Hygiene 2009, 53:249-263.
36. Ling Z., Guo H., Cheng H., Yu Y. Sources of ambient volatile organic compounds and their contributions to photochemical ozone formation at a site in the Pearl River Delta, southern China. Environmental Pollution 2011, 159:2310-2319.
37. Lubin J., Colt J., Camann D., Davis S., Cerhan J., Severson R., Bernstein L., Hartge P. Epidemiologic evaluation of measurement data in the presence of detection limits. Environmental Health Perspectives 2004, 112:1691-1696.
38. McLachlan G.J. On bootstrapping the likelihood ratio test statistics for the number of components in a normal mixture. Journal of the Royal Statistical Society. Series C (Applied Statistics) 1987, 36:318-324.
39. McLachlan G.J., Basford K.E. Mixture Models: Inference and Applications to Clustering 1988, Dekker, M, New York.
40. McLachlan G.J., Krishnan T. The EM Algorithm and Extensions 1997, Wiley & Sons, New York, US.
41. McLachlan G.J., Peel D. Finite Mixture Models 2000, Wiley and Sons, New York,US.
42. MDE Top Ten Sources of Volatile Organic Compound in the Baltimore Area 2002 2010, Maryland Department of the Environment, Available from:. http://www.mde.state.md.us/Air/air_information/TopTenVOC.asp.
43. Mendell N.R., Thode H.C., Finch S.J. The likelihood ratio test for the two-component normal mixture problems: power and sample size analysis. Biometrics 1991, 47:1143-1148.
44. Meng X.L., Pedlow S. EM: a bibliographic review with missing articles. The Proceedings of the Statistical Computing Section of the American Statistical Association 1992, 24-27.
45. Mueller P., Quintana F. Nonparametric Bayesian data analysis. Statistical Science 2004, 19:95-110.
46. OEHHA Air Toxics Hot Spots Program Risk Assessment Guidelines Part II: Technical Support Document for Describing Available Cancer Potency Factors 2005, California Environmental Protection Agency, Office of Environmental Health Hazard Assessment, Air Toxicology and Epidemiology Section, Sacramento, CA.
47. Rappaport S.M., Kupper L.L. Variability of environmental exposures to volatile organic compounds. Journal of Exposure Analysis and Environmental Epidemiology 2004, 14:92-107.
48. Razzaghi M., Kodell R.L. Risk assessment for quantitative responses using a mixture model. Biometrics 2000, 56:519-527.
49. Redner R., Walker H. Mixture densities, maximum likelihood and the EM algorithm. SIAM Review 1984, 26:195-239.
50. Richardson S., Green P.J. On Bayesian analysis of mixtures with an unknown number of components. Journal of the Royal Statistical Society. Series B (Methodological) 1997, 59:731-792.
51. Su F.-C., Jia C., Batterman S. Extreme value analyses of VOC exposures and risks: a comparison of RIOPA and NHANES datasets. Atmospheric Environment 2012, 62:97-106.
52. Taylor D.J., Kupper L.L., Rappaport S.M., Lyles R.H. Amixture model for occupational exposure mean testing with a limit of detection. Biometrics 2001, 57:681-688.
53. Titterington D.M., Smith A.F.M., Makov U.E. Statistical Analysis of Finite Mixture Distributions 1985, John Wiley and Sons, Chichester, UK.
54. USEPA Integrated Risk Information System (IRIS) 2012, US Environmental Protection Agency, Washington, DC, Available from:. http://www.epa.gov/IRIS/index.html.
55. USEPA An Introduction to Indoor Air Quality: Volatile Organic Compounds (VOCs) 2012, US Environmental Protection Agency, Washington, DC, Available from:. http://www.epa.gov/iaq/voc.html.
56. Weisel C.P., Zhang J., Turpin B.J., Morandi M.T., Colome S., Stock T.H., Spektor D.M., Korn L., Winer A., Alimokhtari S., Kwon J., Mohan K., Harrington R., Giovanetti R., Cui W., Afshar M., Maberti S., Shendell D. Relationship of Indoor, Outdoor and Personal Air (RIOPA) study: study design, methods and quality assurance/control results. Journal of Exposure Analysis and Environmental Epidemiology 2005, 15:123-137.
57. Weisel C.P., Zhang J., Turpin B.J., Morandi M.T., Colome S., Stock T.H., Spektor D.M., Korn L., Winer A.M., Kwon J., Meng Q.Y., Zhang L., Harrington R., Liu W., Reff A., Lee J.H., Alimokhtari S., Mohan K., Shendell D., Jones J., Farrar L., Maberti S., Fan T. Relationships of Indoor, Outdoor, and Personal Air (RIOPA). Part I. Collection Methods and Descriptive Analyses 2005, Health Effects Institute Research Report 1-127.
58. Weschler C.J. Chemistry in indoor environments: 20 years of research. Indoor Air 2011, 21:205-218.
59. Zheng J., Frey H.C. Quantification of variability and uncertainty using mixture distributions: evaluation of sample size, mixing weights, and separation between components. Risk Analysis 2004, 24:553-571.