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Lin and colleagues have published an interesting paper on asthma hospitalisation in children.1 They concluded that the study showed positive relations between gaseous pollutants and asthma hospitalisation in children and that the effects of certain specific gaseous pollutants were found to vary in boys and girls. There are several issues that should be discussed before these conclusions can be confidently accepted.
The authors performed separate regression analyses for boys and girls, and compared the sexes by examining the odds ratios. Examination of their figure 1 suggests the possibility that differences between the sexes might be chance fluctuations. It has been recommended that statistical tests for interaction, which directly examine the strength of evidence for the treatment difference varying between subgroups, are the most useful approach for evaluating subgroup analyses.2 The most simple hypothesis is that there is no difference in susceptibility between boys and girls. It would thus be helpful to know if these apparent differences are statistically significant.
A consideration in performing hypothesis tests is the standard error of the coefficients. The authors have treated all hospitalisation events as independent. It is probable, however, that some children were admitted to hospital more than once during the course of the study. I have compiled a cohort of some 108 000 people from primary care and respiratory practices in the cities of Hamilton and Toronto, Ontario (Toronto was the setting for the study by Lin et al). Hospitalisations for asthma, 1992–1999, were ascertained by linkage to the Provincial Hospital Discharge database. Ninety four children, aged 6–12, were hospitalised a total of 145 times, with a mean admission frequency of 1.5 times. Twenty two per cent of children were admitted more than once. Table 1 displays the distribution of numbers of asthma hospitalisations. The study of Lin et al is thus, in a sense, a repeated measures longitudinal study. Failure to take account of the non-independence of events will lead to underestimation of the standard errors and the possibility of inappropriate rejection of the null hypotheses of no effect of pollutants or no difference between the sexes.
We appreciate Dr Finkelstein’s comments on our paper1 regarding sex differences in effects of air pollution on asthma hospitalisation and the possible impact that autocorrelations in the data would have on our risk estimates. In our study, the effects of certain gaseous pollutants on asthma hospitalisation were found to differ between boys and girls 6 to 12 years of age. Some of these differences were “statistically significant”, for example, the regression coefficient for six to seven day SO2 effect was significantly greater for girls than for boys (p<0.01). Although individual results can be examined for statistical significance in this manner, we prefer to base conclusions on the broad risk patterns in the data that emerge after our analysis of a number of gaseous pollutants and exposure periods. Collectively, these results suggest a differential effect of gaseous air pollutants on asthma hospitalisation in girls as compared with boys.
We agree that it is probable that some children would be admitted to hospital for asthma more than once during the study period, and consequently, some autocorrelation may exist in our admission series. Generalised estimation equations (GEE) can be used to address this issue if readmissions can be identified. Unfortunately, our data do not include personal identifiers needed to identify readmissions. However, the residuals of asthma hospitalisation count data did not display notable “intraclass” type correlation, and then it is not obvious that the repeated asthma hospital admissions have induced sizable additional variation. In addition, in a separate analysis using a different dataset from Vancouver in which asthma readmissions were identifiable, the results based on all admissions were similar to those based on first admission. This second analysis suggests that the effect of autocorrelation on our presented risk estimates within our asthma admission series is small.