|
Exposure Model
|
\( {\hat{\boldsymbol{\beta}}}_{\mathbf{1}} \)
|
(SEW)/(SEB)a
|
Bias (%)b
|
Change (%)c
|
\( {\hat{\boldsymbol{\beta}}}_{\mathbf{2}} \)
|
(SEW)/(SEB)a
|
Bias (%)b
|
Change (%)c
|
|---|
|
True:
|
|
Multi-Pollutant
|
5.40
|
(1.77)/(4.18)
|
–
|
+ 32.6
|
5.99
|
(1.55)/(3.66)
|
–
|
+ 20.5
|
|
Single-Pollutant
|
7.16
|
(1.71)/(4.06)
|
–
|
7.22
|
(1.50)/(3.55)
|
–
|
|
Classical:
|
|
Multi-Pollutant
|
4.65
|
(1.57)/(3.84)
|
−13.8
|
+ 24.7
|
4.77
|
(1.35)/(3.40)
|
−20.5
|
+ 17.2
|
|
Single-Pollutant
|
5.80
|
(1.54)/(3.80)
|
+ 7.3
|
5.59
|
(1.32)/(3.38)
|
−6.9
|
|
Berkson:
|
|
Multi-Pollutant
|
5.75
|
(2.41)/(6.32)
|
+ 6.4
|
+ 24.7
|
5.93
|
(2.17)/(5.49)
|
−1.2
|
+ 18.0
|
|
Single-Pollutant
|
7.17
|
(2.36)/(6.10)
|
+ 32.8
|
7.00
|
(2.13)/(5.37)
|
+ 16.7
|
|
Mixture:
|
|
Multi-Pollutant
|
5.03
|
(1.80)/(4.37)
|
−6.9
|
+ 22.5
|
4.97
|
(1.68)/(4.25)
|
−17.1
|
+ 17.7
|
|
Single-Pollutant
|
6.16
|
(1.76)/(4.28)
|
+ 14.1
|
5.85
|
(1.62)/(4.21)
|
−2.4
|
- a SEW: Within-simulations (or model-based) standard error, SEB: Between-simulations (or empirical) standard error
- b Relative bias = \( \frac{\left({\hat{\boldsymbol{\beta}}}_{\boldsymbol{\iota}}-{\boldsymbol{\beta}}_{\boldsymbol{\iota}}\right)}{{\boldsymbol{\beta}}_{\boldsymbol{\iota}}} \)
- c Percentage change from multi- to single-pollutant estimate = \( \frac{\left({\hat{\boldsymbol{\beta}}}_{\boldsymbol{S}}-{\hat{\boldsymbol{\beta}}}_{\boldsymbol{M}}\right)}{{\hat{\boldsymbol{\beta}}}_{\boldsymbol{M}}} \)
- (Classical, Berkson) percentages: (43,57%) for PM2.5, (33,67%) for NO2
