Generalized Models to Analyze the Relationship between Daily

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1 Generalized Models to Analyze the Relationship between Daily Mortality Rates and Major Air Pollutants Minjae Park 1, Hoang Pham 1 and Ho Kim 2 1 Department of Industrial and Systems Engineering, Rutgers University 2 Biostatistics & Epidemiology, School of Public Health, Seoul National University Abstract In this paper, we present generalized models to evaluate the daily mortality rates considering five major air pollutants affects such as particulate matter < 10 µ m in aerodynamic diameter (PM 10 ), carbon monoxide (CO), nitrogen dioxide (NO 2 ), sulfur dioxide (SO 2 ) and ozone (O 3 ) based on the real data from Seoul, Korea (1999~2003) using generalized additive models. Stepwise function is used to obtain the best fitted generalized additive models using R software. Despite there being many researches on air pollutants with meteorological effects on daily death tolls, there have been few researches considering non-linear relationship between air pollutants and daily death toll. In this paper we take into account the non-linear relationships between air pollutants and daily death tolls. By separating total data into training data and testing data, we conduct the cross validation. Using generalized additive models and generalized linear models we determine the best fitted models with minimum Akaike Information Criterion. Seasonal factors are also considered. By the sensitivity analysis, we investigate and measure how each air pollutant affects the mortality. In case of all seasons, CO and SO 2 have nonlinear associations with daily death tolls. Our findings show that the PM 10 (RR= for IQR µ g / m increment) doesn t has strong association with death tolls, however, NO 2 (RR= for IQR increment) has a light association with the mortality. The results are discussed. Keywords: Generalized Additive Model; Generalized Linear Model; Cross Validation; Relative Risk; Daily Mortality; Air Pollution; Seasonal Factors 1. I TRODUCTIO Researchers have been interested in the relationships between the air pollutions and the public health for a long time. There have been severe deadly well-known incidents of air pollution resulting in high death tolls in Meuse Valley, Belgium (Dec. 1930), in Yokohama, Japan (1946), in Donora, Pennsylvania, U.S. (Oct. 1948), in Poza Rica, Mexico (Nov. 1950), in London, U.K. (Dec. 1952) and in Los Angeles, California, U.S. (Jul. 1954). After these incidents, many researchers have been interested in air pollution much more than before. 1

2 From OECD report [1] OECD Environmental outlook to 2030, they mentioned that without new policy, the number of premature deaths per million inhabitants caused by ground-level ozone would quadruple worldwide by 2030 compared to current levels in And the number of premature deaths per million inhabitants linked to PM 10 (fine particulates) could double by 2030, increasing to over 3 million premature deaths per year, and with an estimated loss of more than 25 million years of life in So many researchers have investigated the relationship between air pollution and public health and tried to figure out the best methods to analyze air pollutants effects on the daily mortality [2-23]. The generalized additive model has been acknowledged as one of the best fitted models and mostly used in the statistical mortality literature [7, 20, 23-29]. Other methodologies include case-cross over studies [11], a case-control study [30, 31] and Bayesian hierarchical models with Monte Carlo Markov chain [21, 32]. Hierarchical Bayesian distributed lag model was suggested to incorporate prior information about the time course of pollution effects and combine information from researched area such as weather factors [21, 32]. Researchers from many countries, for example, U.S. [14, 16-19, 33] and Korea [2-13] have conducted similar studies to find the association between air pollutants and death tolls in their countries. Especially, in the U.S., researchers initiated National Morbidity, Mortality and Air Pollution Study (NMMAPS) for 108 U.S. cities ( ) to collaborate data and provide easy access to daily mortality, weather and air pollution data [18, 19, 21, 25, 32]. Similarly, many literatures can be found on efforts to find the relationship between the death tolls and each of the five main air pollutants, such as particulate matter, carbon monoxide, nitrogen dioxide, surfur dioxide and ozone. Additionally, there are also studies combining several air pollutants [4, 5, 7, 8, 10-18, 34-36]. And there are investigations on the relationship between the stroke and air pollutants [3, 37-39]. Further, other studies have shown positive relationships between air pollution with or without Asian dust and the death tolls [13]. Asthma is also another interesting topic to be investigated under the air polluted condition [35, 40]. Several data mining methods are applied for censored survival data [41]. Cross-validation is commonly useful mining tool for the analysis [41-43]. 2

3 In this paper, we find the best fitted models to explain the relationship between air pollutants and the death tolls. We ve considered several air pollutants as a whole and seasonality to find the seasonal effects on mortality. Generalized additive model (GAM) is mainly used. After we use generalized additive models and generalized linear models, we compare those two types of models. The associations between the death toll and air pollutants are linear and meteorological variables are usually applied in a nonparametric smoothing function. In other words, meteorological variables have nonlinear relationship with the death toll. However, in GAM, air pollutants linear assumption about the death tolls is questionable and several studies have shown a possibly non-linear association between ozone and death toll [4, 8]. Additionally, other studies have reported a negative relationship between the death toll and ozone when the ozone levels were low [4]. So, we consider every air pollutants including meteorological variables are nonlinear related to the death toll. In the GAM, explanatory variables can be explained not by linear terms but by smoothing functions whereas many researchers have thought that the air pollutants have linear associations with a daily death toll. This is because it is easy to measure how each air pollutant affects mortality by using of relative risk. Based on the method of cross validation, we are able to observe the nonlinear association with mortality and determine the affects of each air pollutant on the mortality. For the cross-validation method, we separate the entire data (Jun ~ Dec. 2003) into training data (Jun ~ Dec. 2002) and testing data (Jan. ~ Dec. 2003). Based on the training data, we search for the best fitted models and based on those models we then use to measure the effects on the daily death toll. Using smooth functions, we develop models which have non-linear variables. Afterwards, stepwise function enables us to determine the best fitted model. Consequently, we consider four different models as follows: 1) Air pollutants are assumed to have linear association with the mortality and meteorological variables are assumed to have non-linear association by using a smoothing function (Generalized Additive model 1; GAM1); 2) Each variable has a non-linear relationship with the death toll by using a smoothing function (Generalized Additive model 2; GAM2); 3) Each variable has a linear relationship with the death toll including interaction terms (Generalized Linear Model 1; GLM1), and 4) Each variable has a linear 3

4 relationship with the death toll and they follow Poisson distribution (Generalized Linear Model 2; GLM2). Our goal is to compare these models and obtain the best fitted model by using minimum AIC (Akaike Information Criteria). Based on the selected best fitted models, we investigate on how air pollutants affect the public health in Seoul, Korea considering seasonal effects based on mortality data obtained from June 1999 to December While we find the four best fitted models in each category group, additional three criteria such as residual value, predictive frequency and predictive ratio risk are used to generalize the best fitted model. As mentioned above, previous studies assumed that there was a linear relationship between air pollutants and mortality based on the relative risk. In this paper, we use the cross validation as well as the relative risk. For seasonal analysis, definition of each season varies by researchers. Kim et al. [8] assumed that March, April and May were defined as Spring, June, July and August as Summer, September, October and November as Fall, and December, January and February as Winter. They studied the meteorological data from Korea. Peng et al. [19] assumed that Winter, Spring, Summer and Fall are defined as the beginning of on December 21 st, March 21 st, June 21 st and September 21 st, respectively for U.S. data. In this paper, we use the seasonal period as defined by Kim et al. [8]. The outline of the paper is as follows. Section 2 focuses on data description and explains statistical methods and methodologies. Section 3 presents the results of those methodologies. Several models are given in Section 3 to illustrate how the fitted models reflect the seasonal data and finally, concluding remarks and discussion are presented in Section DATA A D METHODS In this paper, we examine five air pollutants (i.e., PM 10, CO, NO 2, SO 2, and O 3 ) and three meteorological variables such as temperature, relative humidity and air pressure and in addition to three other factors (week day, seasonal factor and long term time trend) which 4

5 may affect the number of daily death tolls in Seoul, Republic of Korea, based on the data period from June 1999 to December Data Description and Analysis In this subsection, we describe the basic information about the explanatory variables and response variable (death toll). The numbers of daily death tolls in Seoul, Korea were provided by the Korean National Statistics Offices. We excluded the deaths due to accidents or violence from the total death tolls. The Korean Ministry of the Environment supplied data on ozone, carbon monoxide, particulate matter less than or equal to 10µ m in aerodynamic diameter, sulfur dioxide and nitrogen dioxide. Data on 24-h mean temperatures, relative humidity and sea-level air pressures were obtained from a centrally located weather station in Seoul. Meteorological variables are temperature ( C ), relative humidity (%) and air pressure (hpa). As mentioned above, air pollutants are PM 10, CO, NO 2, SO 2 and O 3, and 5 air pollutants and 3 meteorological variables are obtained by daily mean values. Three additional factors are an indicator function of weekday, seasonal factor and long term time trend. The population size of Seoul is about 10 million. The population in Seoul, Korea slightly decreased from 10,321,449 in 1999 to 10,276,968 in In Table 1, descriptive statistics of the explanatory variables and the death toll are presented in case of all seasons and four seasons. We describe the seasonal data such as spring, summer, fall and winter for the seasonal analysis. From June 1999 to December 2003, the daily average number of death toll is 242, minimum value is 177 and maximum value is 348. It isn t difficult to find out that the death toll in the winter is larger than the death toll in summer. There is a seasonal variation that death tolls increase in winter and decrease in summer because of the weather difference. Several studies [9, 38] have shown that temperature is severe relationships with the death toll. Some basic statistical seasonal information results are shown in Table 1. Table 1 Descriptive statistics: all seasons, spring, summer, fall and winter All Variable Min. 25% Median Mean 75% Max. SD IQR* 5

6 Season Death PM CO NO SO O Tem Hum Pre Variable Min. 25% Median Mean 75% Max. SD IQR* Death PM CO Spring NO SO O Tem Hum Pre Variable Min. 25% Median Mean 75% Max. SD IQR* Death PM CO Summer NO SO O Tem Hum Pre Variable Min. 25% Median Mean 75% Max. SD IQR* Death PM CO Fall NO SO O Tem Hum Pre Winter Variable Min. 25% Median Mean 75% Max. SD IQR* 6

7 Death PM CO NO SO O Tem Hum Pre (*) Inter-quartile range We use Pearson correlations coefficients to measure the relationship between each variable. By the Pearson correlation coefficients, given in Table 2, ozone (-0.225), temperature (-0.365) and humidity (-0.147) have negative relationships with the death tolls. On the contrary, air pollutants, PM 10 (0.129), CO (0.281), NO 2 (0.268) and SO 2 (0.263) have positive associations with the death tolls. CO (0.281) is mostly related to the mortality. Note that CO, NO 2 and SO 2 have severe relationships with each other. Their Pearson correlations coefficients are much larger than 50%. Ozone (0.521) is the only variable which has a positive relationship with temperature. Also, ozone (-0.449) is the only variable which has a negative relationship with air pressure. So we figure out ozone is easily affected by meteorological variables. Table 2 Air pollution and Death toll s Pearson Correlations. PM 10 CO NO 2 SO 2 O 3 Tem Hum Pre Death PM CO NO SO O Tem Hum Pre Death 1 Statistical Methods 7

8 We obtain the fitted GAM considering not only statistically but also environmentally in order to determine the affect between meteorological variables and air pollutants and the daily death tolls. GAM extends GLM by replacing linear explanatory variables of the form i i ( ) β with f ( ) a i i a i, where i β is i th air pollutant s coefficient, ai is i th air pollutant and f is nonparametric functions. There are two ways to estimate nonparametric functions such as smoothing splines or LOESS smoothers. Using smoothing splines, we study two different GLMs and two different GAMs considering five air pollutants and three weather factors. Additionally, we consider seasonality, long term trends and an indicator function of a week day. A generalized model is formulated as follows: Daily mortality ~ Five air pollutants+ three weather factors + seasonality+ long term trends+ week day In GAM1, smoothing functions are used for meteorological factors. Its formula is defined as follows: 5 8 ( ) = β 0 + βi i + j( j) + ( j k) + ( 6 7 8) log E Death a S m S m, m S m, m, m i= 1 j= 6 j k ( ) + seasonality+ long term trends+ I week day ai are air pollutants, i= 1, 2, L, 5. m j and (1) (2) mk are meteorological variables, j, k = 6, 7,8. The cubic spline smoothing function is used for a covariate. I(week day) is an indicator variable of week days. Air pollutants commonly assume to have a linear relationship with the death toll. As for the meteorological variables, smoothing functions are used to explain the association between the meteorological variables and the death toll. It is easy to obtain relative risks for air pollutants. In this paper, we consider that all variables including air pollutants can have smoothing function. Therefore, we finally propose the following model: where 5 8 ( ) = β 0 + i( i) + j( j) + ( j k) + ( 6 7 8) log E Death S a S m S m, m S m, m, m i= 1 j= 6 j k ( ) + seasonality+ long term trends+ I week day ai are air pollutants, i= 1, 2, L, 5. m j and mk (3) are meteorological variables, j, k = 6, 7,8. The cubic spline smoothing function are used for a covariate. In GAM2 8

9 model, eq.(3), only the meteorological variables are assumed to have cubic spline terms. Then, using stepwise function methods, we obtain the best fitted model. In GAM1 model each variable has two cases of which if the variable has no impact to the mortality then it could be removed from the model otherwise assume linear relation with expected mortality. However, GAM2 model could be more reasonable because there are three possibilities for each variable. They could be removed from the model or have linear relations with the expected mortality or have non-linear relations with the expected mortality. Nonetheless, if we use the GAM2 model, it is difficult to measure the effect of air pollutants on the daily death toll based on the relative risk. So we have to find out other measurement to use the smoothing function. We use a data mining method such as the cross validation to separate the data into testing data and training data. When we can increase percentages of the air pollutant of testing data based on the training period s models, then we would know the change of the death toll in the testing period. Now, we consider two other generalized linear models for comparison with GAMs. The first one is GLM with interaction terms which are limited to square terms is given by ( ) E Death = β + β a + β m + β a m + seasonality i i j j ij i j i= 1 j= 6 i, j ( ) + long term trends+ I week day where ai are air pollutants, i = 1, 2, L, 5 and m j are meteorological variables, j = 6, 7,8 The second model is GLM with Poisson distribution. That is given by (4) ( ) log E Death = β + β a + β m + seasonality i i j j i= 1 j= 6 ( ) + long term trends+ I week day where ai is air pollutant, i= 1, 2, L, 5. m jis meteorological variable, j = 6, 7, 8 (5) Using these models, we study the relationships between the death toll and air pollutants. R software is used to analyze their relationships [27, 44, 45]. Also, lag effects are considered in this paper, because the air pollutant can affect death tolls with lag effects. Recently, there are several studies about the lag effects [6, 21, 23, 32, 33, 46, 47]. Denote lag 1 be the just previous day and denote lag 2 be the day before previous day and so on. 9

10 We consider the lag effects by the four previous days, singly (lag 1, lag 2, lag 3, lag 4) and in moving averages. MA1 stands for the mean value of lag 0 and lag 1 and MA2 stands for the means value of lag 0, lag 1 and lag 2 and so on. We investigate each case by using the AIC to find the best fitted models for each of the five pollutants that yield strong air pollution and the daily death tolls. We review models with one air pollutant using different lag effects and select one with a minimum AIC value. According to that result, for all seasons, moving average of lags 0 and 1 (MA 01) is useful for PM 10, lag 1 for CO, moving average of lags 0, 1, 2, 3 and 4 (MA 01234) for NO 2, lag1 for SO 2, lag 4 for O 3. For spring, MA is useful for PM 10, moving average of lags 0, 1, 2 and 3 (MA 0123) for CO, lag 3 for NO 2, lag 3 for SO 2, MA for O 3. For summer, lag 1 is useful for PM 10, lag 3 for CO, MA for NO 2, lag 4 for SO 2, lag 1 for O 3. For fall, MA 01 is useful for PM 10, MA 0123 for CO, lag 4 for NO 2, MA 012 for SO 2, MA 012 for O 3. For winter, MA is useful for PM 10, CO and SO 2, lag 3 for NO 2 and O RESULTS Degrees of freedom were chosen to minimize AIC. For four model groups, the best four models with the lowest AIC values were chosen for each season to analyze the relationships between air pollutants and daily death tolls. Model Selection In GAM, an air pollutant could be removed, be associated linearly or be associated nonlinearly with death tolls using stepwise method. We select the best fitted models using stepwise function based on two GAMs and two GLMs. GAM2 s minimum AIC value is We observe that GAM2 s minimum AIC is lower than any other models minimum AICs. It means that in terms of AIC, GAM2 is the best model amongst four models category groups. The best fitted model using GAM2 is given by Death ~ s(co) + NO 2 + s(so 2 ) + O 3 + Pressure + Temperature + s(date) + IWeek + s(temperature, Humanity) + s(temperature, Pressure) + s(humanity, Pressure) 10

11 Figure 1 presents its plots. They describe CO, SO 2 and date which have nonlinear relationship with the daily mortality. We consider meteorological variables as cubic spline smoothing terms. So there are s(tem., Hum.), s(tem., Pre.) and s(hum., Pre.) terms. Degrees of freedom were chosen from 0, 2, 4, 6, 8, 10, 20 and 30 by using of stepwise function to minimize AIC values. We consider only integer degrees of freedom in GAM for simplicity. For all seasons, degrees of freedom for temperature and date are each 10 in the GAM1. The degrees of freedom for CO, SO 2 and date are, respectively, 4, 6 and 30 in GAM2. s(co,4) s(so2,6) s(date,30) CO SO Date Figure 1 Smoothing function of air pollutants, temperature, date and 95% Confidence interval including cubic terms about daily death toll in Korea Similarly to all seasons, we can obtain the best fitted models for each of four seasons that shown in Table 3. In Table 3, we remove the detail procedures and show the selected best models and their minimum AIC values. Based on the AIC values, the fall season has the lowest AIC value and summer has the highest AIC values. In spring and fall, the GAM2s do not include air pollutants which need smoothing function after we check from using 11

12 stepwise function. So GAM1 and GAM2 are the same in both the seasons, spring and fall. For every seasons and all seasons, GAM2 s AICs are at least less than or equal to the other models AICs. Table 3 Model Selection : All seasons and four seasons Type The Chosen Models with the lowest AIC AIC GAM1 PM 10 + CO + NO 2 + O 3 + s(tem) + s(date) +IWeek +Sea+s(Tem,Hum)+s(Tem,Pre)+s(Tem,Hum,Pre) + Pre All GAM2 s(co) + NO 2 + s(so 2 ) + O 3 + Tem + s(date) + IWeek+s(Tem,Hum) +s(tem,pre) +s(hum,pre) + Pre Season GLM1 PM 10 + CO + NO 2 + SO 2 + O 3 + Tem + Hum + Pre + Tem:Hum + CO:Pre + PM 10 :CO + SO 2 : O 3 + PM 10 :Pre GLM2 PM 10 + CO + NO 2 + O 3 + Tem + Pre GAM1 CO+s(Hum)+s(Date)+Seas+s(Tem,Hum)+s(Tem,Pre) + Pre GAM2 CO+s(Hum)+s(Date)+Seas+s(Tem,Hum)+s(Tem,Pre) + Pre Spring GLM1 NO 2 + O 3 + Tem + Hum + Tem:Hum + NO 2 : O GLM2 NO 2 + O 3 + Hum GAM1 NO 2 + SO 2 + O 3 + s(tem) + s(date) + IWeek + s(tem, Pre) + s(hum, Pre) + Pre GAM2 s(pm 10 ) + s(co) + s(no 2 ) + SO 2 + s(o 3 ) + s(tem) + s(date) + IWeek +s(tem,hum)+s(tem,pre) + Pre Summer GLM1 PM 10+CO+ NO 2 + SO 2 + O 3 +Tem+Hum+Pre+ PM 10 :Tem+ O 3 :Tem+ SO 2 :Tem+CO: NO 2 + NO 2 : SO 2 + SO 2 : Hum+ O 3 :Pre GLM2 NO 2 + O 3 + Tem + Pre GAM1 SO 2 + s(date) + IWeek + Seas +s(tem,pre)+s(hum,pre) +s(tem,hum,pre) + Pre Fall GAM2 SO 2 + s(date) + IWeek + Seas +s(tem,pre)+s(hum,pre) +s(tem,hum,pre) + Pre GLM1 PM 10 + CO + NO 2 + O 3 + Tem + Pre + O 3 :Pre + PM 10 : NO 2 + PM 10 : O 3 + PM 10 :CO + CO: NO GLM2 PM 10 + Tem GAM1 PM 10 + CO + NO 2 + Tem + s(date) + IWeek + Seas + Pre GAM2 s(pm 10 ) + CO + NO 2 + s(date) + IWeek + Seas + Pre Winter GLM1 CO + NO 2 + SO 2 + O 3 + Hum + Pre + SO 2 : O 3 + CO:Pre + SO 2 :Pre + O 3 :Pre + CO: NO GLM2 PM 10 + CO + NO 2 + O 3 + Tem + Hum We found out the best fitted models for all seasons, spring, summer, fall and winter, using four different kinds of models as in Table 3. Then by using those best fitted models, we try to measure the degree of effect of an explanatory variable has over a response variable, the daily death toll. In Table 4, we summarize the level of each air pollutant affects the daily death toll in Seoul, Korea. If an air pollutant is not included as a type of smoothing function, we can express the measurement by using relative risks. This is a commonly used method to express how each pollutant affects the daily death tolls. However, if an air pollutant is included as a type of smoothing function, then we have to consider other method, because it is difficult to obtain the coefficient of each pollutant s relative risk. Therefore, we consider cross validation. The period of training data is from June 1999 to December 2002 and the testing data is from January 2003 and December 12

13 2003. If we change the air pollutant s level in the testing data, we can observe the daily death toll changes using the best fitted models with training data. So there are two types of measurements such as relative risks for non-smoothing function variable and cross validation for smoothing function variables. We use a 95% confidence interval for relative risks. We can obtain the lowest AIC models for each season and if the selected model doesn t have all air pollutants, then we investigate the second lowest AIC model with remaining air pollutants. In case of all seasons, results from the best fitted models controlling for weather conditions (temperature, humidity and air pressure) and seasonal variations show that PM 10 (RR= : 95% CI, ~ for µg / m increment) and NO 2 (RR= : 95% CI, ~ for 100 ppb increment) have a slightly positive and negative relationship with the daily variation of death counts, respectively. Also, they show that O 3 (RR= : 95% CI, ~ for 100 ppb increment) have a slightly negative relationship with the daily variation of death counts. And CO and SO 2 have smoothing function in the fitted model in Table 4. The results from cross validation show in Table 5 that CO has a slightly positive non-linear relationship with the daily variation of death counts. If CO increases by 10 ppb, then death tolls would increase 2.7% roughly. Also, SO 2 has a nonlinear relationship with the daily variation of death counts. If SO 2 increases by 10 ppb, then death tolls decrease by 1.7% roughly. In spring, the first line in Table 4 is the best fitted model and only air pollutant, CO, is included in that model without smoothing function. So we can use relative risk and only PM 10 is included in the second best fitted model without smoothing function and so on. In spring, every air pollutant has non-smoothing function. The results from the best fitted models for spring show that CO (RR = : 95% CI, ~ for 10 ppm increment) and O 3 (RR= : 95% CI, ~ for 10 ppm increment) have a slightly negative relationship with the daily variation of death counts. Also, they show that PM 10 (RR = : 95% CI, ~ for 10 3 µg / m increment), NO 2 (RR= : 95% CI, ~ for 10 ppm increment) and SO 2 (RR= : 13

14 95% CI, ~ for 100 ppm increment) have a slightly positive relationship with the daily variation of death counts. In summer, the best fitted model has every air pollutant so we need only this model to investigate how much they would affect the daily toll. Only SO 2 doesn t need a smoothing function and others need smoothing functions. From the best fitted model, SO 2 (RR = : 95% CI, ~ for 10 ppm increment) has a negative relationship with the daily variation of death counts. The results from the best fitted models for summer show in Table 6 that PM 10 (If PM 10 (10%) increases, then death tolls (0.0002%) increase.), NO 2 (If NO 2 (10%) increases, then death tolls (1.27%) increase.) have some relationships with the daily variation of death counts. In the other hand, the results from the best fitted models for summer show that O 3 (If O 3 (10%) increases, then death tolls (0.0166%) decrease.) have a negative relationship with the daily variation of death counts. Amongst them, NO 2 has relatively severe relationship with the daily variation of death counts in summer. More detail sensitivity analyses for the smoothing functions are in Table 6. In fall, any air pollutant doesn t have a smoothing function, so relative rates are used. From the best fitted model, only CO (RR = : 95% CI, ~ for 100 ppm increment) has a negative relationship with the daily variation of death counts. The results from the best fitted models for fall show that SO 2 (RR = : 95% CI, ~ for 10 ppm increment), NO 2 (RR = : 95% CI, ~ for 10 ppm increment), O 3 (RR = : 95% CI, ~ for 10 ppm increment), and PM 10 (RR = : 95% CI, ~ for 10 3 µg / m increment) have positive relationships with the daily variation of death counts. Amongst them, SO 2 has relatively severe relationship with the daily variation of death counts in fall. In winter, only PM 10 needs a smoothing function and others don t need smoothing functions. From the best fitted model, NO 2 (RR = : 95% CI, ~ for 10 ppm increment) and SO 2 (RR = : 95% CI, ~ for 10 ppm increment) have negative relationships with the daily variation of death counts. O 3 (RR = : 95% CI, ~ for 10 ppm increment) and CO (RR = : 95% 14

15 All Season Spring Summer Fall Winter CI, ~ for 10 ppm increment) have positive relationships with the daily variation of death counts. Amongst them, CO has relatively severe relationship with the daily variation of death counts in winter. From Table 4, spring and fall s seasonal effects make their association linear. In spring and fall, each air pollutants don t need the smoothing function in selected best fitted models. Seasonal factors would be considered to investigate the associations between air pollutants and mortality. In summer, we observe that CO, O 3, NO 2 and PM 10 would need smoothing functions and SO 2 doesn t need smoothing functions. Table 4 How each air pollutant affects the number of death toll in Seoul, Korea The Chosen Models Pollutants Type* 95% CI ** s(co)+ O 2 +s(so 2 )+ O 3 +s(tem)+s(date)+pre+iweek +s(tem,hum)+s(tem,pre)+s(tem,hum,pre) s(co) CV Table 5 NO 2 RR (0.8817, ) s(so 2 ) CV Table 5 O 3 RR (0.9399, ) PM 10 + s(co) + NO 2 + s(so 2 ) + O 3 + Pre + s(tem) + s(date) + IWeek + s(seas) PM 10 RR (0.9988, ) CO+s(Hum)+s(Date)+Seas+Pre+s(Tem,Hum)+s(Tem,Pre) CO RR (0.9678, ) PM 10 + CO + s(hum) + s(date) + Seas + Pre + s(tem, Hum) + s(tem, Pre) PM 10 RR (1.0003, ) PM 10 + CO + O 2 + Tem + s(hum)+ Date + Seas + s(tem, Hum) + s(tem, Pre) NO 2 RR (1.0014, ) PM 10 + CO + NO 2 + O 3 + Pre + Tem + Hum+Date+IWeek+Seas+s(Tem,Hum)+s(Tem,Pre) O 3 RR (0.9977, ) PM 10 + CO + NO 2 + SO 2 + O 3 + Date+IWeek+Seas+Tem+Hum+Pre+s(Tem,Hum)+s(Tem,Pre) SO 2 RR (1.0091, ) s(pm 10 ) s(pm 10 ) + s(co) + s( O 2 ) + SO 2 + s(o 3 )+ Pre + s(tem) + s(date) + IWeek +s(tem,hum)+s(tem,pre) s(co) s(no 2 ) CV Table 6 SO 2 RR (0.8957, ) s(o 3 ) CV Table 6 SO 2 +s(date)+iweek+seas+pre+s(tem,pre)+s(hum,pre)+s(tem,hum,pre) SO 2 RR (1.1581, ) O 2 +SO 2 +Pre+s(Date) + IWeek + Seas +s(tem,pre)+s(hum,pre)+s(tem,hum,pre) NO 2 RR (1.0050, ) NO 2 + SO 2 + O 3 + Pre+ Tem+Hum+s(Date) + IWeek+Seas+s(Tem,Pre)+s(Hum,Pre) O 3 RR (1.0020, ) PM 10 + CO + NO 2 + SO 2 + s(o 3 ) + Pre + Tem + Hum + Date + IWeek +Seas+s(Tem,Pre)+s(Hum,Pre)+s(Tem,Hum,Pre) s(pm 10 ) + CO + O 2 + Pre + s(date) + IWeek + Seas PM 10 RR (1.0010, ) CO RR (0.9772, ) s(pm 10 ) CV 1% % CO RR (1.0482, ) NO 2 RR (0.9832, ) s(pm 10 ) + CO + NO 2 + SO 2 + O 3 + Pre + Tem + Hum + s(date) + IWeek + Seas SO 2 RR (0.9330, ) s(pm 10 ) + CO + NO 2 + O 3 + Pre + Tem + Hum + s(date) + IWeek + Seas O 3 RR (1.0035, ) (*) RR=relative rate, CV=cross validation (**) 95% CI= 95% Confidence Interval 15

16 Statistical results In Table 5, we conduct sensitivity analyses when air pollutants are in the smoothing functions. In all seasons, only two air pollutants, CO and SO 2, have smoothing functions. It means CO and SO 2 have nonlinear relationships with death tolls. So, we change the air pollutant in testing data and we investigated the change of sum of death toll in testing period, Furthermore, we use several criteria such as mean squared errors, predictive frequency and predictive ratio risk. Using these four criteria, we conduct sensitivity analysis. Their formulas are as follows; ( ) AIC= 2log likelihood function at its maximum value + 2m MSE : Mean squared errors= i= 1 ( y yˆ ) 2 n y ˆ i y i PF : Predictive Frequency= i= 1 yi n y ˆ i y i PR : Predictive Ratio Risk = i= 1 yˆ i n i n m m is unknown parameters in the chosen model. yi is the true value and yˆi is the predicted value. In Table 5 and Table 6, the level of CO is 8.09 ppb averagely in And, % means the change of daily death toll. For example, if we increase CO by 1%, then the daily death toll is increased by %. Similarly, if we increase CO by 5 ppb, then the mortality is increased by %. And RV stands for residual value which is same as mean squared errors. PF stands for predictive frequency. PR stands for predictive ratio risk. i 2 2 (6) Table 5 How each air pollutant with smoothing function affects the number of death toll in case of all seasons by air pollutants change (%) s(co) 8.09 ppb 1% 5% 10% 20% 30% + 5 ppb + 10 ppb + 15 ppb + 20 ppb + 25 ppb + 30 ppb RV* PF** PR*** Sum % ++ N/A % % % % % % % % % % % 16

17 s(so 2) NO 2 O 3 PM 10 (*) Residual Value 5.31 ppb 1% 5% 10% 20% 30% + 5 ppb + 10 ppb + 15 ppb + 20 ppb + 25 ppb + 30 ppb RV PF PR Sum % N/A % % % % % % % % % % % 35.71ppb 1% 5% 10% 20% 30% + 5 ppb + 10 ppb + 15 ppb + 20 ppb + 25 ppb + 30 ppb RV PF PR Sum % N/A % % % % % % % % % % % 21.09ppb 1% 5% 10% 20% 30% + 5 ppb + 10 ppb + 15 ppb + 20 ppb + 25 ppb + 30 ppb RV PF PR Sum % N/A % % % % % % % % % % % µ g / m 1% 5% 10% 20% 30% + 5 ppb + 10 ppb + 15 ppb + 20 ppb + 25 ppb + 30 ppb RV PF PR Sum % N/A % % % % % % % % % % % (**) Predictive Frequency (***) Predictive Ratio Risk ( + ) Sum of Death toll (++) Change(%) of Death toll We conduct sensitivity analyses by changing of the air pollutants percentage. In Table 5, we conduct sensitivity analysis by adding 1% ~ 30% and 5ppb ~ 30ppb for each air pollutants. And we find out how these changes affect daily death tolls. Amongst four seasons, AIC values in summer are relatively high compared to those in other seasons, thus its air pollutants need smoothing functions. Similarly to all seasons, we obtain Table 6 by changing pollutants percentage for summer. If we change the percentage of air pollutants during summer, we obtain the change of death tolls. For example, the first air pollutant is PM 10. It needs smoothing function. It means that PM 10 has nonlinear 3 relationship with daily death tolls. In Table 6, the first cell number 56.82µ g / m is averagely PM 10 level in the air during summer from 1999 to

18 s(pm 10) s(co) s(no 2) s(o 3) SO 2 (*) Residual Value Table 6 How each air pollutant with smoothing function affects the number of death toll in case of summer by air pollutants change (%) ppb 1% 5% 10% 20% 30% + 5 ppb + 10 ppb + 15 ppb + 20 ppb + 25 ppb RV* PF** PR*** Sum (**) Predictive Frequency % ++ N/A % % % % % % % % % % 6.01 ppb 1% 5% 10% 20% 30% + 3 ppb + 5 ppb + 7 ppb + 9 ppb + 11 ppb RV PF PR Sum % N/A % % % % % % % % % % ppb 1% 5% 10% 20% 30% + 5 ppb + 10 ppb + 15 ppb + 20 ppb + 25 ppb RV PF PR Sum % N/A % % % % % % % % % % ppb 1% 5% 10% 20% 30% + 5 ppb + 10 ppb + 15 ppb + 20 ppb + 25 ppb RV PF PR Sum % N/A % % % % % % % % % 4.07 ppb 1% 5% 10% 20% 30% + 5 ppb + 10 ppb + 15 ppb + 20 ppb + 25 ppb RV PF PR Sum (***) Predictive Ratio Risk ( + ) Sum of Death toll % N/A % % % % % % % % % (++) Change(%) of Death toll In Table 7, we compare the results with other studies. Although there are several similar studies on this interesting subject, we only select those similar studies using the same or similar data, in this case would be in Seoul, Korea, duration about the same period ( ) and same kinds of air pollutants for model comparisons. According to several existing studies, researchers often covered several trials to find out how each air pollutants can affect the daily death tolls. For each comparison, we selected inter-quartile range (IQR). As we can see from Table 7, we obtained similar results with other two 18

19 existing studies by Lee [13] and Cho [2]. In Lee et al. [13], they considered Asian dust in their studies. And In Cho et al. [2], they considered seven major cities including Seoul. Table 7 The paper s results as compared with other studies results Paper Air pollutant Pollution change Death change Notes This paper Seoul, Korea Y.S.Cho et al. (2006) Six Cities & Seoul, Korea [2] J.T.Lee et al. (2007) Seoul, Korea [13] * 1 ppm = 1000 ppb PM 10 3 IQR(41.54µ g / m ) 0.27% CO IQR(4.1, 100 ppb) 1.89% NO 2 IQR(17.29 ppb) 1.08% SO 2 IQR(3.02 ppb) 0.46% O 3 IQR(17.56 ppb) -0.43% 3 PM 10 IQR (41.17µ g / m ) 1.10% CO IQR (N/A) 1.30% NO 2 IQR (N/A) 2.10% SO 2 IQR (N/A) 1.90% O 3 IQR (N/A) 0.60% 3 PM 10 IQR (41.49µ g / m ) 0.70% CO IQR (0.54 ppm) 3.30% NO 2 IQR (17.93 ppb) 2.40% SO 2 IQR (3.06 ppb) 2.50% O 3 IQR (21.03 ppb) 0.40% Asian Dust are considered Table 8 shows the air pollutant, ozone s estimated effects and its level from several previous studies. In Kim et al. [8], they summarized when ozone level is less than 25 ppb, ozone has a negative relationship with daily death tolls. However, when ozone level is larger than 25 ppb, ozone has a positive relationship with the daily death toll. So it has J shape line with the mortality and the threshold point is 25 ppb. In the paper, the ozone level is ppb which is less than the threshold point level 25 ppb in case of all seasons, and the RR and CI are (0.9399, ). This is similar to other papers results consistently as we check in Table 8. But they are not exactly same. That is because their research periods are not same and because there are a difference to pick up the representatives of data. For example, some researchers pick up the air pollutants maximum value and other pick up their mean value. Table 8 Comparisons with other studies results specialized in Ozone 19

20 Region Reference Ozone(mean,ppb) RR and CI Inchon,Korea [4] (0.918, 0.995) Korea [10] (0.995, 1.001) Ulsan,Korea [12] (0.978, 1.030) Seoul,Korea [12] (1.001, 1.004) Seoul,Korea [8] (1.0231, ) Seoul,Korea This paper (0.9399, ) 4. CO CLUSIO A D DISCUSSIO Analysis of the relationship between air pollutants and mortality in Seoul, Korea from June 1999 to December 2003 presents the change of death tolls when some air pollutants change. We consider five air pollutants all together including three meteorological variables such as air pressure, relative humidity and temperature and additional three other factors such as long term trend, seasonality and weekday. After we investigate several degrees of freedom and lags effects to minimize AIC values, we find out two GAMs and two GLMs which have minimum AIC values in each model groups. In the first GAM model, we assume that all five air pollutants have linear associations with daily death tolls and three meteorological variables have nonlinear associations with the mortality using smoothing functions. This is a traditional model, because we can measure relationships easily using relative risks. For the second GAM model, we assume that every air pollutant and meteorological variables have nonlinear relationships with the mortality. Using cross validation, we find out each associations with the mortality. To find out seasonal differences, we separate the data by spring, summer, fall and winter. It is reasonable to consider the lag effects because the death tolls for those who were exposed to the low level polluted air, is not caused by the air condition of their death rate but caused by lag distributed day s air condition. We consider 4 previous days to study the relationships. In this paper, we don t need to assume linear relationships between air pollutants and mortality. From many previous studies, linear assumption is used for the relative risk, but linear assumption has been questionable. So using cross validation, we can assume nonlinear associations with mortality. And using stepwise function, we narrow down a bunch of models into a few selected well-fitted models. Based on the previous studies [8], 20

21 Ozone has J type or nonlinear effect on deaths. We found that ozone has negative relationship with the mortality. This is consistent with previous studies. For seasonal analysis, we obtain different results, because testing data is one year, And each seasons of testing data are composed of three months or roughly 90 days. Kim et al. [8] found that ozone has a strong seasonal component, and therefore, it is very difficult to separate the main effect of ozone on mortality from the confounding effect of season and temperature. After repeated seasonal analysis, they found the same pattern: a strong threshold effect in the summer, no association in the winter and the usual linear associations without any threshold effects in the spring and autumn. In summer, O 3 need smoothing function, meaning they have non-linear associations with death toll. And in the spring, fall and winter, O 3 does not require smoothing functions. Considering these results, the risks presented by ozone in summer are expected to be more serious than other seasons. Lee et al. [12] reported that the SO 2 was significantly associated with daily mortality, but total suspended particulate was not. Xu et al. [22] found the SO 2 was significantly associated with increased mortality, but TSP was not significant. Based on our results, we come to the similar conclusion about SO 2. It has severe relationship with the death toll. They assume SO 2 has linear association with death toll but based on our research, SO 2 needs smoothing function, i.e. non-linear association in case of all seasons. The potentials of future research are how we handle lag effects more efficiently and how to deal with collinearity. References [1] OECD, OECD Environmental Outlook to 2030: OECD Publishing, [2] Y. Cho, J. Lee, J. Son, and Y. Kim, "A Meta-Analysis of Air Pollution in Relation to Daily Mortality in Seven Major Cities of Korea, ," Korean Journal of Environmental Health, vol. 32, pp , [3] Y. Hong, J. Lee, H. Kim, and H. Kwon, "Air Pollution A New Risk Factor in Ischemic Stroke Mortality." vol. 33: Am Heart Assoc, 2002, pp

22 [4] Y. Hong, J. Leem, E. Ha, and D. Christiani, "PM10 exposure, gaseous pollutants, and daily mortality in Inchon, South Korea," Environ Health Perspect, vol. 107, pp , [5] H. Kim, "An analysis of air pollution and daily mortality," The Korean Journal of Applied Statistics, vol. 13, pp , [6] H. Kim, Y. Kim, and Y. Hong, "The lag-effect pattern in the relationship of particulate air pollution to daily mortality in Seoul, Korea," International Journal of Biometeorology, vol. 48, pp , [7] J. Kim and H. Yang, "Generalized Additive Model of Air Pollution to Daily Mortality," Key Engineering Materials, vol. 277, pp , [8] S. Kim, J. Lee, Y. Hong, K. Ahn, and H. Kim, "Determining the threshold effect of ozone on daily mortality: an analysis of ozone and mortality in Seoul, Korea, 1995?1999," Environmental Research, vol. 94, pp , [9] Y. Kim and S. Joh, "A vulnerability study of the low-income elderly in the context of high temperature and mortality in Seoul, Korea," Science of the Total Environment, The, vol. 371, pp , [10] J. Lee, H. Kim, Y. Hong, H. Kwon, J. Schwartz, and D. Christiani, "Air Pollution and Daily Mortality in Seven Major Cities of Korea, ," Environmental Research, vol. 84, pp , [11] J. Lee and J. Schwartz, "Reanalysis of the effects of air pollution on daily mortality in Seoul, Korea: A case-crossover design," Environmental Health Perspectives, vol. 107, pp , [12] J. Lee, D. Shin, and Y. Chung, "Air pollution and daily mortality in Seoul and Ulsan, Korea," Environmental Health Perspectives, vol. 107, pp , [13] J. Lee, J. Son, and Y. Cho, "A comparison of mortality related to urban air particles between periods with Asian dust days and without Asian dust days in Seoul, Korea, ," Environmental Research, vol. 105, pp , [14] S. Moolgavkar, "Air Pollution and Daily Mortality in Three US Counties," Environmental Health Perspectives, vol. 108, pp ,