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Air Qual Atmos Health. 2016;9(8):961-972. Epub 2016 Mar 2.

A class of non-linear exposure-response models suitable for health impact assessment applicable to large cohort studies of ambient air pollution.

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Environmental Health Science and Research Bureau, Health Canada, 200 Eglantine Driveway, Ottawa, Ontario K1A 0K9 Canada.
Public Health Ontario, Oakville, Ontario Canada.
McLaughlin Centre for Population Health Risk Assessment, Institute of Population Health, University of Ottawa, Ottawa, Ontario Canada ; Centre for Research in Environmental Epidemiology (CREAL), Madrid, Spain ; Universitat Pompeu Fabra (UPF), Barcelona, Spain ; CIBER Epidemiología y Salud Pública (CIBERESP), Barcelona, Spain.
Department of Environmental Health Sciences, University of California at Los Angeles, Los Angeles, CA USA.
Department of Economics, Brigham Young University, Provo, UT USA.
United States Environmental Protection Agency, Research Triangle Park, Durham, NC USA.
Health Effects Institute, Boston, MA USA.
Epidemiology Research Program, American Cancer Society, Atlanta, GA USA.
Institute of Health Metrics and Evaluation, Seattle, WA USA.
Institute of Health and Environment, Seoul National University, Seoul, South Korea.
Department of Environmental and Occupational Health Sciences, University of Washington, Seattle, WA USA.
McLaughlin Centre for Population Health Risk Assessment, Institute of Population Health, University of Ottawa, Ottawa, Ontario Canada.


The effectiveness of regulatory actions designed to improve air quality is often assessed by predicting changes in public health resulting from their implementation. Risk of premature mortality from long-term exposure to ambient air pollution is the single most important contributor to such assessments and is estimated from observational studies generally assuming a log-linear, no-threshold association between ambient concentrations and death. There has been only limited assessment of this assumption in part because of a lack of methods to estimate the shape of the exposure-response function in very large study populations. In this paper, we propose a new class of variable coefficient risk functions capable of capturing a variety of potentially non-linear associations which are suitable for health impact assessment. We construct the class by defining transformations of concentration as the product of either a linear or log-linear function of concentration multiplied by a logistic weighting function. These risk functions can be estimated using hazard regression survival models with currently available computer software and can accommodate large population-based cohorts which are increasingly being used for this purpose. We illustrate our modeling approach with two large cohort studies of long-term concentrations of ambient air pollution and mortality: the American Cancer Society Cancer Prevention Study II (CPS II) cohort and the Canadian Census Health and Environment Cohort (CanCHEC). We then estimate the number of deaths attributable to changes in fine particulate matter concentrations over the 2000 to 2010 time period in both Canada and the USA using both linear and non-linear hazard function models.


Air pollution; Cohort; Exposure; Mortality; Particulate matter

Conflict of interest statement

The authors declare that they have no competing financial interests.

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