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(3) X ijk = (γ 0 + g 1 i + g 2 ij ) + (γ 1 + g 3 i ) Z ijk + γ 2 Season ijk + γ 3 CityVariables i + γ 4 Z ijk CityVariables i + ε ijk Candidate city-specific variables were identified from previous studies showing their importance to the personal-ambient relationship, including air conditioning use, unemployment, race, public transport [ 53- 55] and traffic [ 54] (Additional file 1: Table S4).
The ambient concentration response relationship for O3 shows evidence of nonlinearity.
To investigate the shape of the ambient concentration response relationship, we used the same models with the pollutant effects represented by natural splines with 6 df.
Smith et al. (2009) fit a piece-wise linear ambient concentration response relationship with breaks at 40 ppb and 60 ppb, and they showed that a hockey-stick shaped curve withockey-stick shaped is curvestent with the data.
This limits our ability to examine personal characteristics that may impact the personal and ambient exposure relationships.
Among various approaches evaluating ambient concentration response relationships, Bell et al. (2006) used natural splines followed by a hierarchical Bayes procedure to obtain a national estimate.
Bootstrap means for flexible ambient concentration response relationships, using 6 df natural splines, between pollutant concentrations and deaths on the following day estimated from single-pollutant models suggest nonlinearity and threshold-like behavior for NO2, PM10, and O3.
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The relationship of ambient criteria pollutant concentrations to ambient and personal PM2.5 was explored.
For example, mortality typically exhibits a curvilinear relationship with ambient temperature, with mortality rates increasing with increasing ambient temperature (above the temperature at which mortality is at a minimum) (Kovats and Koppe, in press).
The impact of home ventilation status on the relationship between ambient and personal gas concentrations, however, is untested, leaving open the possibility that ambient gas concentrations may better reflect corresponding personal exposures under certain conditions or for some segments of the population.
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