title: Imputation method for lifetime exposure assessment in air pollution epidemiologic studies.
abstract: BACKGROUND
  Environmental epidemiology, when focused on the life course of exposure to a specific pollutant, requires historical exposure estimates that are difficult to obtain for the full time period due to gaps in the historical record, especially in earlier years. We show that these gaps can be filled by applying multiple imputation methods to a formal risk equation that incorporates lifetime exposure. We also address challenges that arise, including choice of imputation method, potential bias in regression coefficients, and uncertainty in age-at-exposure sensitivities.
  
  
  METHODS
  During time periods when parameters needed in the risk equation are missing for an individual, the parameters are filled by an imputation model using group level information or interpolation. A random component is added to match the variance found in the estimates for study subjects not needing imputation. The process is repeated to obtain multiple data sets, whose regressions against health data can be combined statistically to develop confidence limits using Rubin's rules to account for the uncertainty introduced by the imputations. To test for possible recall bias between cases and controls, which can occur when historical residence location is obtained by interview, and which can lead to misclassification of imputed exposure by disease status, we introduce an "incompleteness index," equal to the percentage of dose imputed (PDI) for a subject. "Effective doses" can be computed using different functional dependencies of relative risk on age of exposure, allowing intercomparison of different risk models. To illustrate our approach, we quantify lifetime exposure (dose) from traffic air pollution in an established case-control study on Long Island, New York, where considerable in-migration occurred over a period of many decades.
  
  
  RESULTS
  The major result is the described approach to imputation. The illustrative example revealed potential recall bias, suggesting that regressions against health data should be done as a function of PDI to check for consistency of results. The 1% of study subjects who lived for long durations near heavily trafficked intersections, had very high cumulative exposures. Thus, imputation methods must be designed to reproduce non-standard distributions.
  
  
  CONCLUSIONS
  Our approach meets a number of methodological challenges to extending historical exposure reconstruction over a lifetime and shows promise for environmental epidemiology. Application to assessment of breast cancer risks will be reported in a subsequent manuscript.
authors.affiliation: Consulting in the Public Interest (CIPI), Lambertville, NJ, USA. jbeyea@cipi.com
authors.forename: Jan
authors.initials: J
authors.lastname: Beyea
authors.forename: Steven D
authors.initials: SD
authors.lastname: Stellman
authors.forename: Susan
authors.initials: S
authors.lastname: Teitelbaum
authors.forename: Irina
authors.initials: I
authors.lastname: Mordukhovich
authors.forename: Marilie D
authors.initials: MD
authors.lastname: Gammon
mesh_terms: D000368:Aged; D000393:Air Pollutants / Q000633:toxicity*; D001943:Breast Neoplasms / Q000139:chemically induced* / Q000453:epidemiology; D016022:Case-Control Studies; D005260:Female; D006801:Humans; D008875:Middle Aged; D008962:Models, Theoretical; D009518:New York / Q000453:epidemiology; D013997:Time Factors
chemical_list: D000393:Air Pollutants
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