title: Indirect adjustment for multiple missing variables applicable to environmental epidemiology.
abstract: OBJECTIVE
  Develop statistical methods for survival models to indirectly adjust hazard ratios of environmental exposures for missing risk factors.
  
  
  METHODS
  A partitioned regression approach for linear models is applied to time to event survival analyses of cohort study data. Information on the correlation between observed and missing risk factors is obtained from ancillary data sources such as national health surveys. The relationship between the missing risk factors and survival is obtained from previously published studies. We first evaluated the methodology using simulations, by considering the Weibull survival distribution for a proportional hazards regression model with varied baseline functions, correlations between an adjusted variable and an adjustment variable as well as selected censoring rates. Then we illustrate the method in a large, representative Canadian cohort of the association between concentrations of ambient fine particulate matter and mortality from ischemic heart disease.
  
  
  RESULTS
  Indirect adjustment for cigarette smoking habits and obesity increased the fine particulate matter-ischemic heart disease association by 3%-123%, depending on the number of variables considered in the adjustment model due to the negative correlation between these two risk factors and ambient air pollution concentrations in Canada. The simulations suggested that the method yielded small relative bias (<40%) for most cohort designs encountered in environmental epidemiology.
  
  
  CONCLUSIONS
  This method can accommodate adjustment for multiple missing risk factors simultaneously while accounting for the associations between observed and missing risk factors and between missing risk factors and health endpoints.
authors: Population Studies Division, Health Canada, Ottawa, Canada; Department of Mathematics and Statistics, Queen's University, Kingston, Canada.
authors: Hwashin H
authors: HH
authors: Shin
authors: Population Studies Division, Health Canada, Ottawa, Canada.
authors: Sabit
authors: S
authors: Cakmak
authors: Population Studies Division, Health Canada, Ottawa, Canada.
authors: Orly
authors: O
authors: Brion
authors: Population Studies Division, Health Canada, Ottawa, Canada; Division of Occupational and Environmental Health, Dalla Lama School of Public Health, University of Toronto, Toronto, Canada.
authors: Paul
authors: P
authors: Villeneuve
authors: Institute of Population Health, University of Ottawa, Ottawa, Canada.
authors: Michelle C
authors: MC
authors: Turner
authors: Department of Medicine, McGill University, Montreal, Canada.
authors: Mark S
authors: MS
authors: Goldberg
authors: School of Public Health, University of California, Berkeley, CA, USA.
authors: Michael
authors: M
authors: Jerrett
authors: Public Health Ontario, Toronto, Ontario, Canada.
authors: Hong
authors: H
authors: Chen
authors: Population Studies Division, Health Canada, Ottawa, Canada.
authors: Dan
authors: D
authors: Crouse
authors: Statistics Canada, Ottawa, Canada.
authors: Paul
authors: P
authors: Peters
authors: Department of Economics, Brigham Young University, Provo, USA.
authors: C Arden
authors: CA
authors: Pope
authors: Population Studies Division, Health Canada, Ottawa, Canada. Electronic address: rick.burnett@hc-sc.gc.ca.
authors: Richard T
authors: RT
authors: Burnett
mesh_terms: D015331:Cohort Studies; D004781:Environmental Exposure; D016021:Epidemiologic Studies; D006801:Humans; D008962:Models, Theoretical; D016019:Survival Analysis
keywords: Air pollution; Cohort study; Indirect adjustment; Simulation; Survival analysis