Table 2.

Estimated percentage change in daily mortality with an increase in the mean value of the instrumental variable ($10{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$), ${\mathrm{PM}}_{2.5}$ ($10{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$), or ${\text{NO}}_2$ ($10\text{ppb}$), respectively, on the day of and day before death (pooled city-specific estimates derived by random effects meta-analysis).

Regression Model	% Change	95% CI
Instrumental Variable ($10{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$)a	1.54%	1.12%, 1.97%
Instrumental Variable ($10{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$) With Negative Controla,b	1.54%	1.12%, 1.97%
Marginal Structural Modelsc
${\mathrm{PM}}_{2.5}$ ($10{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$)	0.75%	0.35%, 1.15%
${\mathrm{PM}}_{2.5}$ with Negative Control ($10{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$)b	0.79%	0.36%, 1.23%
${\mathrm{PM}}_{2.5}<25{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$d	0.83%	0.39%, 1.27%
${\text{NO}}_2$ ($10\text{ppb}$)	2.59%	1.78%, 3.40%
${\text{NO}}_2$ with Negative Control ($10\text{ppb}$)b	2.62%	1.81%, 3.43%
Conventional Time Seriese
${\mathrm{PM}}_{2.5}\left(10{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3\right)$	0.60%	0.34%, 0.85%
${\text{NO}}_2$ ($10\text{ppb}$)	0.38%	0.08%, 0.69%
${\mathrm{PM}}_{2.5}<25{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$	0.62%	0.32%, 0.93%

^aInstrumental Variable models: quasi-Poisson regression models stratified on month-by-year.

^bNegative Controls: Models with negative controls are adjusted for mean IV, ${\mathrm{PM}}_{2.5}$, or ${\text{NO}}_2$, respectively, on the second and third day after death, in addition to the exposure on the day of and day before death.

^cMarginal Structural Models: Fit with city-specific inverse probability weights based on month, day-of-the-week, temperature, previous day’s temperature, and, for each pollutant, the other pollutant.

^d${\mathrm{PM}}_{2.5}<25{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$: Percentage change in daily mortality with a $10{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$ increase in ${\mathrm{PM}}_{2.5}$ on the day of and day before death, restricted to days with ${\mathrm{PM}}_{2.5}$ below the $25{\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$.

^eConventional Time Series: Models of ${\mathrm{PM}}_{2.5}$ or ${\text{NO}}_2$ with penalized splines for temperature (same day and previous day) and indicator variables for the month-of-year and day-of-week.