Leitte et al. In the first step, a base model without of the trend function was manually adjusted with each modeled according to the same lag pollutants was built for identifying pollutant- based on the absolute value of the sum of the (e.g., same-day total particle number concen- independent variability. Long-term trends and partial autocorrelation function (Touloumi tration and same-day NO2 concentration). seasonality were represented by a smooth func- et al. 2006). To explore the robustness of the models, tion of calendar time, and a categorical vari- The final base model consisted of the cat- we performed several sensitivity analyses for able for day of the week was forced into the egorical variables holiday, weekend, and sea- associations with particle number concentra- model as hospital emergency room admissions son, the linear influence of same-day relative tions from 100 to 300 nm (PNC100–300) that showed weekly and yearly patterns. As fur- air humidity, and the smooth functions of varied the lag pattern of temperature, relative ther potential confounders, we considered the calendar time, air temperature, represented humidity, and air pressure, and used differ- meteorologic parameters air temperature, air by the mean of the present and two previous ent degrees of smoothness for the time trend pressure, and relative humidity. We accounted days, and same-day air pressure. function. Additionally, for PDL models we for time-delayed effects of these variables using The base model was extended by including varied the number of the maximum lag and arithmetic means for days up to 7 days before air pollutants. Delayed effects up to a maxi- the degree of the polynomial order. the visit. Additional influences of the year, mum of 5 days were estimated by polynomial All statistical analyses were done using the season (December–February, March–May, distributed lag (PDL) models (Zanobetti et al. mgcv package in the R software (R Development June–August, September–November), month, 2003), cumulative effects models that repre- Core Team 2003), version 2.90. day of the month and holiday, represented sented the delayed effect as a moving average, Results by categorical variables were investigated as and single lag models that incorporated the well. The base model was selected according to delayed effect as a lagged variable into the In total, we identified 15,981 cases of respira- Akaike’s information criterion (Akaike 1974) model. We constrained the lag coefficients in tory ERV in the study period, including 12,798 and statistical significance of the covariates PDL models to follow a third-degree polyno- (80%) due to acute upper respiratory infec- (p < 0.05). Nonlinear effects were modeled by mial of the lag number. Two-pollutant cumu- tions followed by 1,954 (12%) due to lower regression splines with an automatic smooth- lative effects models included PM10 or NO2 respiratory diseases. The daily mean of respira- ness selection (Wood 2006). The smoothness in addition to another air pollution variable, tory ERV was 15, with a minimum of 0 and a maximum of 88 patients per day (Table 1). Table 1. Descriptive statistics for daily mean values of respiratory ERV, meteorologic variables, and air Because of technical difficulties and mainte- pollution variables. nance, 218 days of particle size–segregated No. of measurements were missing. Consequently, Variable valid days Mean ± SD Minimum Maximum IQR effect estimates for particulate air pollutants Respiratory ERV 1,036 15 ± 10 0 88 12 other than PM10 are based on 818 days of data Air temperature (°C) 1,036 13 ± 11 –10 31 18 (13,055 respiratory ERV were recorded in this Relative humidity (%) 1,036 58 ± 22 9 100 37 period). Particle number concentrations were Air pressure (hPa) 1,036 1,017 ± 10 992 1,048 16 dominated by particles < 300 nm and particle SO2 (µg/m3) 1,036 87 ± 88 6 600 100 surface area concentrations by particles in the NO2 (µg/m3) 1,036 63 ± 38 5 290 40 range of 50–1,000 nm (Table 1). The time PM10 (µg/m3) 1,036 120 ± 83 10 570 90 series of respiratory ERV showed a seasonal UFP (1/cm3) 818 22,000 ± 9,800 5,600 76,000 11,000 and weekly pattern, with more cases during the PNCtotal (1/cm3) 818 29,000 ± 10,000 7,400 87,000 12,600 cold season and a peak on the weekend and on PNC3–10 (1/cm3) 818 3,600 ± 4,400 85 41,000 3,880 holidays (data not shown). PNC10–30 (1/cm3) 818 6,900 ± 3,800 1,200 30,000 4,300 Size-segregated particle number and sur- PNC30–50 (1/cm3) 818 4,900 ± 1,800 890 14,000 2,300 face area concentrations were correlated with PNC50–100 (1/cm3) 818 6,700 ± 2,800 630 19,000 3,600 PNC100–300 (1/cm3) 818 6,300 ± 3,500 340 21,000 4,400 meteorologic and other air pollution variables PNC300–1,000 (1/cm3) 818 870 ± 710 28 4,800 830 [Table 2; see also Supplemental Material, PSCtotal (µm2/cm3) 818 1,300 ± 800 78 5,100 960 Table 1 (doi:10.1289/ehp.1002203)]. Particle PSC50–100 (µm2/cm3) 818 110 ± 49 10 330 60 number concentrations of smaller particles PSC100–300 (µm2/cm3) 818 580 ± 350 29 2,100 440 (< 50 nm) and UFP were negatively correlated PSC300–1,000 (µm2/cm3) 818 510 ± 430 17 2,700 490 with air temperature, relative air humidity, Abbreviations: PNCx, particle number concentration in the given (x nm) or total size range (3 nm–1 µm); PSCx, particle and SO2. UFP and NO2 concentrations were surface area concentration in the given (x nm) or total size range (3 nm–1 µm). not correlated when all days were included in the analysis (Table 2) but were moder- Table 2. Correlation coefficients for daily mean values of meteorologic and air pollution variables. ately correlated when restricted to summer Air temperature Relative Air pressure SO2 NO2 PM10 (r = 0.45), winter (r = –0.33), or transitional Particle fraction (°C) humidity (%) (hPa) (µg/m3) (µg/m3) (µg/m3) months (r = 0.16). There were small nega- UFP (1/cm3) –0.22 –0.39 0.18 –0.26 0.06 0.05 tive correlations between NO2 and PNC3–10 PNCtotal (1/cm3) –0.25 –0.21 0.18 –0.18 0.27 0.23 (–0.16) and PNC10–30 (–0.09) and a moder- PNC3–10 (1/cm3) –0.22 –0.51 0.19 –0.19 –0.16 –0.09 ate positive correlation between NO2 and PNC10–30 (1/cm3) –0.02 –0.40 0.02 –0.32 –0.09 0.01 PNC30–50 (0.22) and PNC50–100 (r = 0.43). PNC30–50 (1/cm3) –0.17 –0.15 0.16 –0.23 0.22 0.12 PNC50–100 (1/cm3) –0.26 0.08 0.19 –0.03 0.43 0.23 Particle number and surface area concentra- PNC100–300 (1/cm3) –0.13 0.36 0.05 0.15 0.55 0.44 tions of larger particles (> 100 nm) as well as PNC300–1,000 (1/cm3) –0.02 0.47 –0.04 0.25 0.56 0.55 PSCtotal were moderately correlated with rela- PSCtotal (µm2/cm3) –0.06 0.44 –0.02 0.23 0.58 0.55 tive air humidity, NO2, and PM10. PNCtotal PSC50–100 (µm2/cm3) –0.26 0.12 0.18 –0.01 0.45 0.24 was moderately correlated with all meteo- PSC100–300 (µm2/cm3) –0.10 0.39 0.02 0.18 0.55 0.47 rologic (air temperature, relative air humid- PSC300–1,000 (µm2/cm3) –0.01 0.48 –0.05 0.25 0.56 0.56 ity, and air pressure) and air pollutant (SO2, 510 119 | number 4 | April 2011 • Environmental Health Perspectives ovlume