The use of chained two-point clusters for the examination of associations of air pollution with health conditions
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Health Canada, Ottawa, Canada (Population Studies Division)
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Mieczysław Szyszkowicz   

Health Canada, Population Studies Division, 200 Eglantine Driveway, Ottawa, ON, K1A 0K9, Canada
Int J Occup Med Environ Health. 2016;29(4):613-22
Objectives: There are a few accepted and intensively applied statistical methods used to study associations of ambient air pollution with health conditions. Among the most popular methods applied to assess short term air health effects are case-crossover (using events) and time-series methodologies (using counts). A few other techniques for studying counts of events have been proposed, including the Generalized Linear Mixed Models (GLMM). One suggested GLMM technique uses cluster structures based on natural embedded hierarchies: days are nested in the days of a week (dow), which, in turn, are nested in months and months in years (< dow, month, years >). Material and Methods: In this study the authors considered clusters with hierarchical structures in a form of < dow, 14-days, year >, where the 14-days hierarchy determines 7 clusters composed of 2 days (the same days) of a week (2 Mondays, 2 Tuesdays, etc.), in 1 year. In this work the authors proposed hierarchical chained clusters in which 2 days of a week are grouped as follows: (first, second), (second, third), (third, fourth) and so on. Such an approach allows determination of an additional series of the slopes on the clusters (second, third), (fourth, fifth), etc., i.e., estimation of the coefficients for other configurations of air pollutant levels. The authors considered a series of 2 point chained clusters covering a year. In such a construction each cluster has one common data point (day) with another one. Results: The authors estimated coefficients (slopes) related to the ambient ozone exposure (mortality) and to 3 selected air pollutants (particulate matter, nitrogen dioxide and ozone) combined into index and considered as health risk exposure (emergency department (ED) visits). The generated results were compared to the estimations obtained from the time-series method and the time-stratified case-crossover method applied to the same data. Conclusions: The proposed statistical method, based on the chained hierarchical clusters (< dow, 14-days, year >), generated results with shorter confidence intervals than the other methods.
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