Roadside monitors were excluded from MEK inhibitor drugs the main analysis. We averaged the raw data in monitor records over short-term periods

of 1 h for NO2, 24 h for PM and SO2, and daily maximum consecutive of 8 h for O3. We converted all short-term average concentrations recorded in units of ppb/ppm to μg/m3 using the conversion factors at 25 °C according to the US Environmental Protection Agency data coding manual (USEPA, 2010). In each short-term averaging period, we used the maximum average concentration among all monitor records to establish a mass concentration-frequency distribution of the highest air pollution exposure in a year, that is the maximum aggregation approach which reflects the precautionary principle. We excluded extreme concentration values on days when there were accidents or natural events (WHO, 2000b), R428 purchase such as huge fires or dust storms, documented from news reports. We examined the air pollutant concentration data by considering the mean and variance of the number of monitors within and between years to reduce potential biases due to systematic missing patterns of monitoring records. The first stage obtained the distribution properties, such as the variance and the percentile differences between the maximums and the means in the observed distribution of pollutant concentration data. This allowed a generalized

approach for modeling data from different places without setting arbitrary value. The second stage applied the extracted distribution properties in the first stage to calculate an annual limit value corresponding to the WHO short-term AQG value so that the underlying factors of the pollution distribution in individual cities remain unchanged except the compliance of the short-term AQG. (i) Obtaining the distribution properties from observed data: We defined any concentration enough value X under the lognormal probability distribution is a function of geometric mean (μg), geometric standard deviation (σg) and cumulative probability (ΣP) ( Limpert et al., 2001), with X = ∞ when ΣP = 1 and X = μg when ΣP = 0.5. We assumed X ≠ ∞ so

that the cumulative probability of the observed maximum concentration value ΣPm < 1. When putting μg, σg and the observed maximum concentration value m (as X) of real data in the function to compute ΣPm, we obtained dm as the difference from 1. We assumed that the arithmetic mean μa is greater than μg due to skewness and hence the cumulative probability of the observed arithmetic mean ΣPa > 0.5. When putting μg, σg and the observed value of μa (as X) of real data in the function to compute ΣPa, we obtained dμ as the difference from 0.5 ( Fig. 1). Fig. 1.  Statistical parameters in a lognormal distribution. We obtained the mean estimates of limit values for PM10, PM2.5, NO2, SO2 and O3 from 2004 to 2010 in individual cities and then pooled them by both fixed and random effect methods.