Table 1.

Risk coefficients of all-cause mortality for ${\mathrm{PM}}_{2.5}$ concentrations applied to the health impact function.

Study	Study population	$\mathrm{\beta }\left(\mathrm{\sigma }\right)$	Likelihood weightc	${\mathrm{\mu }\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$ (percentile)d	$\mathrm{\tau }$e
Krewski et al. (2009)a	American Cancer Society Population ages $\ge 30\mathrm{y}$	0.005826 (0.000962)	–	–	–
Nasari et al. (2016)b	American Cancer Society Cancer Prevention Study $\text{II}\ge \text{Population}$ ages $\ge 30\mathrm{y}$	0.0930 (0.00984)f	0.036	−5.43 (−5%)	0.1
		0.0802 (0.00843)	0.080	1.38 (0%)	0.1
		0.0433 (0.00446)	0.460	8.19 (5%)	0.1
		0.0398 (0.00412)	0.324	9.04 (10%)	0.1
		0.0351 (0.00369)	0.056	10.55 (25%)	0.1
		0.0666 (0.00704)	0.044	1.38 (0%)	0.2

^aLong-term hazard ratio for all-cause ${\mathrm{PM}}_{2.5}-\text{related}$ mortality reported in the most recent extended analysis of the American Cancer Society Cancer Prevention Study II (ages 30 and older) [hazard ratio 1.06; 95% confidence interval (CI): 1.04, 1.08 per $10{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$ increase in average ${\mathrm{PM}}_{2.5}$ concentrations in 1999–2000, adjusted for all individual-level and ecologic covariates).

^bThis is the effect coefficient (per $1{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$) and standard error for each of the six log-linear concentration–response functions within a specific concentration range. Adjusted for individual-level and ecologic covariates.

^cWe weighted the average of the six results using these likelihood weights.

^dThis term determines the air quality level at which the c-r function curves.

^eParameter $\mathrm{\tau }$ controls the curvature of the weighting function, with larger values yielding shapes with less curvature.

^fThis function would be specified in the BenMAP-CE tool as: $(1-(1/\text{EXP(Beta}\ast \text{(LOG(Q1)/(1+EXP(-(Q1-(-5}\text{.43))/2}\text{.66))-LOG(Q0)/1+EXP(-(Q0-(-5}\text{.43))/2}\text{.66))))))}\ast \text{Incidence}\ast \text{POP}$.