Using Copulas to Measure Association between Air Pollution and Respiratory Diseases

Air pollution is still considered as one of the major environmental and health issues. There is enough research evidence to show a strong relationship between exposure to air contaminants and respiratory illnesses among children and adults. In this paper we used the Copula approach to study a potential relationship between selected air pollutants (PM10 and NO2) and hospital admissions for respiratory diseases. Kendall-s tau and Spearman-s rho rank correlation coefficients are calculated and used in Copula method. This paper demonstrates that copulas can be used to provide additional information as a measure of an association when compared to the standard correlation coefficients. The results find a significant correlation between the selected air pollutants and hospital admissions for most of the selected respiratory illnesses.




References:
[1] Al-Harthy, M., S. Begg, et al., 2007. Copulas: A new technique to model
dependence in petroleum decision making, Journal of Petroleum Science
and Engineering 57: 195-208.
[2] Barnett A. G et al. Air pollution and child respiratory health: a case
crossover study in Australia and New Zealand. American Journal of
Respiratory and Critical Care Medicine, 2005, 171:1272-1278.
[3] Barnett Jack, Rodney E. Kreps, John A. Major, and Gary G. Venter,
"Multivariate Copulas for Financial Modeling," Variance 1:1, 2007, pp.
103-119.
[4] Bateson T.F. and Schwartz J, 2001. Selection bias and confounding in
case-crossoveranalyses of environmental time series data. Epidemiology
12, p.654 - 661.
[5] Bouyé, E. and M. Salmon, 2008. Measuring the Dependence between
Non-Gaussian Financial Assets Using Copula: Risk Management,
Option Pricing and Default Risk, available at SSRN:
http://ssrn.com/abstract=1272345.
[6] Brook, R., Franklin, B., Cascio, W., Hong, Y., Howard, G., Lipsett, M.
et al. 2004.ÔÇÿAir pollution and cardiovascular disease: A statement for
healthcare professionals from the Expert Panel on Population and
Prevention Science of the American Heart Association-, Circulation, vol.
109, no. 21, pp. 2655-71.
[7] Chan-Yeung, M.N. 2000, ÔÇÿAir pollution and health-, Hong Kong
Medical Journal, vol. 6, no. 4, pp. 390-8.
[8] Deheuvels, P., 1978. Caracterisation complete des lois extremes
multivariees et de la convergence des types extremes, Publ. Inst. Statist.
Univ. Paris 23, p. 1-37.
[9] Dominici F. and all, 2002. On the Use of Generalized Additive Models
in Time-Series Studies of Air Pollution,and Health. Am J Epidemiol,
Vol. 156, N 3.
[10] Embrechts, P., A. J. McNeil, and R. Frey, 2001. Quantitative Risk
Management: Concepts, Techniques and Tools, Princeton University
Press.
[11] Galambos, J., 1978. The Asymptotic Theory of Extreme Order Statistics,
Wiley, New York.
[12] Joe, H., 1997. Multivariate Models and Dependence Concepts. Chapman
and Hall, London.
[13] Hinwood, A., De Klerk, N., Rodriguez, C., Jacoby, P, Runnion, T, Rye,
P, Landau, L, Murray, F, Feldwick, M. and Spickett, J. 2006.'The
relationship between changes in daily air pollution and hospitalizations
in Perth, Australia 1992-1998: A case-crossover study', International
Journal of Environmental Health Research, 16: 1, 27 ÔÇö 46.
[14] Kumar P. and Shoukri M., 2008. Evaluating Aortic Stenosis Using the
Archimedean Copula Methodology. Journal of Data Science 6(2008),
173-187.
[15] Kumar P. and Shoukri M., 2007. Copula based prediction models: an
application to an aortic regurgitation study. BMC Medical Research
Methodology 2007, 7:21
[16] Lancaster, H.O., 1982. Dependence, measures and indices of. In
Encyclopedia of Statistical Sciences, 2, S. Kotz and N.L. Johnson,
editors, John Wiley & Sons, New York, pp. 334-339.
[17] Lin M et al. Effect of short-term exposure to gaseous pollution on
asthma hospitalization in children: a bi-directional case-crossover
analysis. Journal of Epidemiology and Community Health, 2003, 57:50-
55.
[18] Linn et al., 2000. Air pollution and daily hospital admissions in
metropolitan Los Angeles. Environmental Health Perspectives, 108, p.
427-434.
[19] Marshall, A. W. and Olkin, I. (1988). Families of multivariate
distributions. Journal of the American Statistical Association 83, 834-
841.
[20] Mclure M. 1991. The case-crossover design: A method for studying the
transient effects on the risk of acute events. Am. J. Epidemiol. 133,
p.144 - 153.
[21] Nelsen, R. B., 1999, An introduction to copulas, Springer.
[22] Scarsini, M., 1984. On measures of concordance, Stochastica, N 8, p.
201-218.
[23] Schwartz, J., 1994. Air pollution and hospital admissions for the elderly
in Detroit, Michigan. American Journal of Respiratory and Critical Care
Medicine, 150, p. 648-655.
[24] Sheppard L., 2003. Ambient air pollution and nonelderly asthma
hospital admissions in Seattle, Washington, 1987-1994. In: Revised
analyses of time-series studies of air pollution and health. Boston, MA,
Health Effects Institute, p.227-230 (HEI Special report)
(http://www.healtheffects.org/Pubs/TimeSeries.pdf, accessed 12
December 2006).
[25] Sklar, A. (1959), "Fonctions de r'epartition `a n dimensions et leurs
marges," Publ.Inst. Statist. Univ. Paris 8, 229-231.
[26] Sunyer J et al. Urban air pollution and emergency room admissions
forasthma in four European cities: the APHEA Project. Thorax, 1997,
52:760-765.
[27] World Health Organization 2005, WHO Air Quality Guidelines for
Europe, 2nd edn, WHO Regional Office or Europe,
http://www.euro.who.int/air/activities/20050223_4.