A GEE moving average analysis of the relationship between air pollution and mortality for asthma in Barcelona, Spain

Several studies have assessed the association between air pollution and hos pital admissions or emergency room visits for asthma. Because of both the p resence of missing data and the small number of observations, the relations hip between air pollution and mortality for respiratory causes has been rar ely analysed, and when it has, the results are very inconclusive or even in consistent. The objective of this study is to assess the relation between l evels of air pollutants (black smoke, sulphur dioxide, nitrogen dioxide and ozone), meteorological variables (24th average temperature and relative hu midity) and daily mortality for asthma (ICD-9 493, 2 to 45 years old) in Ba rcelona, Spain, during the period 1986-1989. Since the range of daily morta lity for asthma (2 to 45 years old) during the period 1986-1989 was 0-1), w e have preferred to consider this variable as dichotomous. First, the relat ionship between air pollutants, meteorological variables and daily mortalit y (controlled for the occurrence of asthma epidemics) was estimated using l ogistic regression models. As was expected, the residuals from this regress ion were autocorrelated, showing a complex moving average (MA) structure. I f covariates were not time dependent the so-called generalized linear mixed models, could be applied. In our case the covariates vary. As a consequenc e the likelihood is numerically intractable because it involves the evaluat ion of n-fold integral. An alternative method that avoids these numerical p roblems is the generalized estimating equations method (GEE). It is a multi variate analogue of quasi-likelihood estimation. In the absence of a likeli hood function the parameters can be estimated by solving a multivariate ana logue of the quasi score function. We have modified the GEE method in this paper, allowing for a different structure in the error covariance matrix (M A). Both air pollutants and meteorological variables are related with the o ccurrence of a death for asthma. In this sense, nitrogen dioxide, NO, (beta = 0.037, p < 0.05), ozone, O-3 (beta = 0.021, p < 0.06) and high temperatu re (the beta's were in the range (0.098-0.182), p < 0.05) increased the pro bability of dying for asthma in Barcelona during the period 1986-1989. Copy right (C) 1999 John Wiley & Sons, Ltd.