Study Design

The time series approach was adopted in this study. This design specifically caters for matched daily series of exposure and outcome data (Schwartz et al., 1996). It aims to quantify adverse short term effects of the current levels of air pollutants on health. The "health outcome" time series data were daily counts of hospital admissions from certain causes (total respiratory and cardiovascular diseases and individual diseases, namely, bronchial asthma and acute myocardial infarction). The "exposure" time series data were daily measurements of the following "criteria pollutants": nitrogen dioxide, respirable suspended particulates (with aerodynamic diameter less than 10 µm), sulphur dioxide and ozone. Statistical modelling was then performed, taking into consideration the characteristic (approximately Poisson) distribution, overdispersion and positive autocorrelation of the outcome data. Daily meteorological variables (temperature and humidity) and others (seasonal changes, holidays, day of the week, time trends) were included as confounding variables in the statistical model. The health effects of individual pollutants were then examined.

The time series approach allows the best use to be made of routinely collected air quality and hospital data currently available in Hong Kong to address questions concerning the short-term health effects of ambient pollution levels. It addresses the question of whether variations in measured levels of ambient air pollution are statistically associated with variations in health outcomes (in the context of this study, acute hospital admissions for selected diseases).

The general approach of the study is modelled after the protocol of the APHEA project (a European approach using epidemiological time series data), developed within the framework of the EC Environment 1991 - 94 Programme (Katsouyanni et al., 1996). The rationale of using this standard approach is that it represents the best compromise between rigour and feasibility. It caters for the use of aggregated time series data on air quality and health outcomes that were not originally collected for the purpose of epidemiological investigation. It also allows the specific methods to be adapted to suit local data and conditions, within a standardized framework that has established guidelines and quality control criteria. Finally, it allows the results to be compared to other epidemiological time series studies within a meta-analysis framework (Briggs et al., 1996).

The databases and statistical methods employed will be elaborated further in the following section.

Databases

Statistical Modelling

The statistical modelling followed the guidelines proposed by the APHEA protocol, which established that hospital admissions data are generally best represented by a Poisson distribution (Schwartz, Spix, Touloumi, et al., 1996). This is because, on any given day, only a small proportion of the population is admitted to hospital and large numbers of admissions are relatively rare. Also, the numbers of admissions represent counts which are non-negative integers. It has also been observed that admissions data are usually overdispersed (that is, the variance is larger than the mean), and positively auto-correlated. This is in contrast to the characteristics of a Poisson distribution, in which the variance is equal to the mean.

In a Poisson process, which is a relative risk model, a homogeneous risk to the underlying population on a given day is assumed (Schwartz et al., 1996). Given that underlying risk, the expected number of admissions on any day is . The probability of y admissions occurring on a given day is given by:

Prob (y) =	e- y
	y!

The Poisson regression model assumes that varies with time varying predictor variables X₁, X₂ ..... Xn,

log = b0 + 1X1 + .... + nXn

where X1 .... Xn are the predictors of daily admissions / mortalities and 1 .... n are the regression coefficients for these predictors. The relative risk of the ith predictor is given by e i .

The presence of overdispersion and serial correlation necessitates some statistical adjustment to the Poisson model. To address these problems, a number of methods have been reported in the literature. An iterative method called Generalized Estimating Equations (GEE), which is an extension of the Poisson regression, was used by Zeger (1988). In this method, the vector of residuals was weighted by an estimate of the inverse of the covariance matrix, and the weighted residuals were filtered with an autoregressive filter.

Brannas and Johansson (1994) extended the Poisson regression model by correcting the covariance matrix. The significance of the predictors was then assessed by the X² test using the corrected estimates of the variances, allowing valid inferences to be made from the regression coefficients. This is a much simpler procedure than the computer intensive method by Zeger.

When applying Brannas and Johannson's method in this study, we have found that the deviance remained quite large despite using different transformations of the independent variables specified in the APHEA protocol. Williams (1982) suggested that a large residual variation might be due either to the intrinsic (overdispersed) nature of the data or to some overlooked explanatory variables. He proposed a method for correcting overdispersion by multiplying the variance by an estimate of the dispersion parameter.* This method was adapted to the Poisson model by Breslow (1984) by taking appropriate limits in Williams' formulae. After testing all the potential confounding variables recommended by the APHEA protocol, we accepted that the data was overdispersed and adopted Williams' method of correction. Williams' method is supported by the SAS statistical software (SAS, 1996).#

*	Suppose that the data consist of n binomial observations.  The variance of the response probability is given by: V(Pi) = ØØ pi(1-pi)   An estimate of Ø  , a non-negative but otherwise unknown dispersion parameter, was made by equating the value of Pearson's chi-square statistic for the full model to its approximate expected value. After a weighted fit of the model, and X2 were recalculated, and a revised estimate of Ø was calculated. The iterative procedure was repeated until  c2 is very close to its degree of freedom.
#	We used PROC LOGISTIC of SAS to run the Poison regression model.  The option scale=Williams in PROC LOGISTIC was then chosen.

The APHEA guidelines (Katsouyanni et al., 1996) were also followed in the construction of the models. This procedure started with the construction of a "core" model in which the potential confounders of the short term relationship of air pollutants and daily hospital admissions for respiratory and cardiovascular diseases in 1994 and 1995 were investigated. In a time series model, the response variables (hospital admissions and deaths) show both a long term trend and shorter term periodic variations. These have to be adjusted for in order to identify the effects attributable to the pollutants. The APHEA guidelines specify that the core model (without pollutant variables) should include variables to account for the following - long term trends (time trend), medium term variations (season, using sine and cosine terms to control for seasonal and other cyclical patterns), short term systematic (day of the week, holidays, day after holiday) and short term, less systematic (meteorological) variations. The inclusion of these variables removes much of the "noise" in the model. Based on the APHEA protocol and the goodness-of-fit of the models, the following variables were included:

Time lags for temperature and humidity, and the interaction between temperature and relative humidity were found to be insignificant when entered in a stepwise multiple linear regression model. These were excluded from the core model on this basis.

Verhoeff, Hoek, Schwartz & van Wijnen (1995) observed in the Amsterdam study of air pollution and daily mortalities that, after controlling for season and trend, the magnitude of the serial correlation in hospital admission data was low and the estimates were only slightly changed by incorporating serial correlation. However, considerable overdispersion was noted in Hong Kong's hospital admissions dataset for 1994 and 1995. Accordingly, adjustments for the overdispersion of the daily hospital admissions were made using Williams' method (1982), described above, and the results compared with the simple Poisson model.

Delayed effects of air pollutants were explored using single day lags and cumulative lags up to five days for ozone and three days for the other air pollutants. Owing to the high correlation coefficients between individual pollutants, the 'single pollutant model' was used to determine the effect of each individual pollutant on hospital admissions. In this approach, each air pollutant was separately entered into the "core model" to obtain its respective partial regression coefficient. It is recognized that adverse health outcomes may be due to the combined exposure to more than one pollutant. However, certain pollutant variables were highly correlated and the APHEA protocol recommends the construction of single-pollutant models as a starting point. Based on the partial regression coefficients (b) of the individual pollutants in the single pollutant model, relative risks of hospital admissions and deaths due to respiratory and cardiovascular diseases associated with a 100 ug.m-3 increase in air pollutant concentrations were derived.

The effects of more than one pollutant (including their interactions) were then explored using a 'multiple pollutant model'. In this multiple pollutant model*, relative risks of individual pollutants adjusted for the effects of the others, were obtained. The final model was constructed by the following steps:

1. Initially, all 4 pollutants (main effects) and all 2-way interactions were included. Stepwise selection was employed to select the significant interaction(s).
   
   
2. Insignificant pollutants (except those involved in the significant interactions) were then removed from the model.
   
   
3. William? method was applied to the model obtained in Step 2.
   
   
4. Any insignificant interaction(s) and main effect(s) was (were) removed.
   
   
5. The final model consisted of significant main effect(s) and significant interaction(s) as well as the corresponding main effect(s) in those significant interaction terms (even though the main effects by themselves were insignificant).

In the choice of pollutant parameters, the 'best' lags or cumulative lags which had been selected in the single pollutant models were used in the construction of the multiple pollutants model. When significant interactions were observed, the relative risks of one pollutant at different levels of the interacting pollutant were calculated. The effect of multi-collinearity was compared with and without using Ridge regression (Schaefer, 1986).

Validation of Model

The model based on data from 1994 to 1995 was then validated using data for the first half-year of 1996. Fitness of the model was assessed by plotting the observed and predicted daily admissions on the same graph for each pollutant to look for discrepancies visually.