Across counties, the median number of PM2.5 monitors in a county was 5; the first quartile (Q1, 25th percentile) was 4; and the third quantile (Q3, 75th percentile) was 8. Similarly, the median number of PM2.5 and PM10 collocated monitor pairs was 3 (Q1 = 2 and Q3 = 5). Therefore, by restricting our analysis to collocated monitor pairs, the standard TM exposure for PM10 − 2.5 was calculated based on a considerably smaller number of monitors compared to PM2.5. In , correlation of daily PM measurements at any pair of monitors in the same county is plotted versus the distance between the monitors. There was considerable larger spatial variability in PM10 − 2.5 measurements compared to PM2.5.
Fig. 2. Correlations of monitor-level daily PM time series calculated between pairs of PM2.5 or PM10 − 2.5 monitoring locations in the same county and plotted versus the distance between monitor pair. For PM2.5, we used all available monitors without (more ...)
Our study included approximately 5 million Medicare enrollees between the period 1999 and 2005. There were about 2.6 million admissions for cardiovascular diseases and 1.0 million admissions for respiratory diseases. Across counties, the median daily admission for cardiovascular diseases was 18.7 per 100 000 people (Q1 = 15.8 and Q3 = 21.4) and the median for respiratory diseases was 7.4 per 100 000 people (Q1 = 6.3 and Q3 = 8.8).
We considered 5 exposure measures of daily county-average PM10 − 2.5 level. For example, shows the marginal posterior distributions of PM10 − 2.5 exposure on July 17, 2000 in Harris County, TX. The 4 posterior distributions were obtained under different ME modeling and estimation approaches: (1) constant ME variances across monitors without using the health data (ME, [X|W,Z]); (2) constant ME variances across monitors using the health data (ME, [X|W,Z,Y]); (3) population-WME variances across monitors without using the health data (WME, [X|W,Z]); and (4) population-WME variances across monitors using the health data (WME, [X|W,Z,Y]). For (2) and (4), the relative risks associated with cardiovascular admissions were simultaneously estimated with PM10 − 2.5 exposure. Also, a vertical line is placed at the 10% TM estimate. The differences in exposure estimates reflect which monitor-level observations were used. On this particular day, there were 4 observations of PM10 − 2.5 concentration: 3 observations 18, 61, and 20 were from Houston and one observation 12 was from Deer Park. The TM PM10 − 2.5 measure excluded 12 and 61 in computing the average; the ME measure considered all values equally; and the WME measure down weighted the measurement from Deer Park which has a considerably smaller population than Houston.
Fig. 3. Posterior distributions of the average exposure to outdoor PM10 − 2.5 concentration on July 17, 2000 in Harris County, TX. The vertical line is placed at the 10% TM estimate. The solid and dotted lines represent 4 different PM10 − 2.5 (more ...)
We calculated the SD of county-level PM2.5 and PM10 − 2.5 levels across days and gives the median, Q1, and Q3 across 59 counties for different exposure measures. First, daily variation of county-average PM10 − 2.5 levels derived from ME and WME were lower compared to TM and this decrease was less significant for PM2.5. PM daily variation decreases when ME is considered because the model assumes that the observed PM concentrations are more noisy than the true exposure. Specifically, a large decrease in time series SD reflects greater disagreement between same-day monitor-level measurements. Moreover, for both PM10 − 2.5 and PM2.5, the decrease in daily variation was more significant for the ME measures compared to the WME measures. If PM levels vary across cities of different population sizes, county-average exposure is determined mainly by measurements in cities with large populations. Since the true exposure represents a population-weighted average exposure, the WME approach can result in smaller ME because disagreement between PM measurements in cities with small populations and the true exposure is down-weighted.
Table 1. Quantiles of county-specific SD of PM2.5 and PM10–2.5 time series using either TM, ME modeling with constant error variance (ME), or monitor-specific weighted error variance (WME). The median (25th quantile and 75th quantile) of the SD across (more ...)
gives some pairwise correlations between PM10 − 2.5 and PM2.5 exposure measures obtained using either TM or WME across counties. Comparing rows 1 and 2, higher correlations are observed between different PM2.5 measures compared to PM10 − 2.5. This is expected since PM2.5 level is less heterogeneous spatially and the ME approach results in less calibration when the between-monitor agreement is strong. Comparing rows 3 and 4, we find that deriving PM10 − 2.5 and PM2.5 exposures via ME modeling increases the correlation between the 2 pollutants slightly. We also found very high correlation between the average exposure measures derived from the 2 ME models (ME vs. WME) for PM10 − 2.5 and PM2.5, having minimum correlation of 0.82 and 0.87, respectively, in the 59 counties (not shown in table).
Quantiles of correlations between different measures of county-level daily PM10–2.5 and PM2.5 exposures across 59 counties. Exposure measures for PM2.5 and PM10–2.5 are derived using either TM or WME modeling
The ME variances, σ12,c and σ2c in (2.4) quantify the variability across monitors of the PM values. plots the posterior mean and 95% intervals for the ME SD versus log-transformed county land area (square kilometer). We found greater between-monitor variation for PM10 − 2.5 (black) measurements compared to PM2.5 (gray) measurements, even though the 2 pollutants had similar average concentration over the study period. The median ME SD across counties for PM10 − 2.5 is 5.6 (Q1 = 4.4 and Q3 = 8.8) and for PM2.5 is 2.3 (Q1 = 1.7 and Q3 = 3.2). In , it also appears that larger counties were associated with greater between-monitor variation in PM measurements. We also found evidence of a weak positive association between PM2.5 and PM10 − 2.5 measurement errors at collocated monitors for some counties. The posterior means of ρc across 59 counties have a median of 0.10 (min = − 0.23, Q1 = − 0.1, Q3 = 0.4, max = 0.6) .
Fig. 4. County-specific ME SD (σ12,c and σ22,c in (2.4) for PM10 − 2.5 (black) and PM2.5 (gray) plotted versus log county land area (cubic kilometer) for 59 counties. Each bullet denotes the posterior mean and the vertical line indicates (more ...)
The 2 upper panels in plot the county-specific standardized coefficients,
to examine the strength and direction of the health effect of PM10 − 2.5
on cardiovascular and respiratory admissions estimated using different exposure measures. Comparing estimates derived from standard TM exposure and WME with the Bayesian risk estimation, we did not observe large changes in the health effects' direction. However, there is attenuation for large
possibly due to increased uncertainty in risk estimates when MEs are accounted for. From the 2 bottom panels in , we show that in our application, standard error (SE),
for cardiovascular and respiratory admissions are very similar between those derived from regression calibration and those estimated through the Bayesian approach. For the Poisson health model, regression calibration will result in some bias in the relative risk estimates; however in the analysis of PM10 − 2.5
, the uncertainty in exposure appears to dominate.
Fig. 5. Upper panels: scatter plot of county-specific standardized health effect estimates for PM10 − 2.5, , comparing 2 approaches: (1) including ME modeling with monitor-specific weighted error variance (WME) versus (2) using TM as PM10 − 2.5 (more ...)
gives the pooled estimates of percent increase in cardiovascular and respiratory disease admissions per 10 μg/m3 increase in same-day particulate matter concentration. Exposure measures for PM2.5 and PM10 − 2.5 were derived using either TM, ME, or WME, and we considered both regression calibration and Bayesian risk estimations. The original Peng and others (2008) estimates based on 108 counties using TM exposure are also shown. We found consistent positive effects for PM10 − 2.5 and PM2.5 with different exposure measures and estimation procedures. For cardiovascular admissions, effects of PM2.5 remain statistically significant under different scenarios. The posterior intervals are wider under ME modeling compared to using the standard TM exposure. Also, when ME modeling are used, the confidence intervals are wider for Bayesian risk estimations compared to regression calibration and the bias associated with regression calibration appears negligible.
Fig. 6. Percent increase in emergency hospital admissions rates for cardiovascular and respiratory diseases per 10 μg/m3 increase in same-day particulate matter concentration. Exposure measures for PM2.5 and PM10 − 2.5 are derived using either (more ...)