title: The use of chained two-point clusters for the examination of associations of air pollution with health conditions.
abstract: OBJECTIVE
  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 >).
  
  
  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.
authors.affiliation: Health Canada, Ottawa, Canada (Population Studies Division). mietek.szyszkowicz@hc-sc.gc.ca.
authors.forename: Mieczysław
authors.initials: M
authors.lastname: Szyszkowicz
authors.affiliation: Health Canada, Ottawa, Canada (Population Studies Division). wesley.burr@hc-sc.gc.ca.
authors.forename: Wesley S
authors.initials: WS
authors.lastname: Burr
mesh_terms: D000393:Air Pollutants / Q000032:analysis; D000397:Air Pollution / Q000009:adverse effects / Q000706:statistics & numerical data*; D016000:Cluster Analysis; D004636:Emergency Service, Hospital / Q000706:statistics & numerical data*; D004781:Environmental Exposure / Q000009:adverse effects / Q000706:statistics & numerical data; D006801:Humans; D016014:Linear Models; D009026:Mortality; D009585:Nitrogen Dioxide / Q000009:adverse effects; D009864:Ontario / Q000453:epidemiology; D010126:Ozone / Q000009:adverse effects; D052638:Particulate Matter / Q000009:adverse effects
chemical_list: D000393:Air Pollutants; D052638:Particulate Matter; D010126:Ozone; D009585:Nitrogen Dioxide
keywords: ambient air pollution; case-crossover; cluster; mortality; odds ratio; relative risk