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International Journal of Injury Control and Safety Promotion Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/nics20
Estimating national road crash fatalities using aggregate data a
a
a
a
Anwaar Ahmed , Beenish Akbar Khan , Muhammad Bilal Khurshid , Muhammad Babar Khan & Abdul Waheed
a
a
National Institute of Transportation, School of Civil & Environmental Engineering, National University of Sciences and Technology, Islamabad, Pakistan Published online: 09 Jan 2015.
Click for updates To cite this article: Anwaar Ahmed, Beenish Akbar Khan, Muhammad Bilal Khurshid, Muhammad Babar Khan & Abdul Waheed (2015): Estimating national road crash fatalities using aggregate data, International Journal of Injury Control and Safety Promotion, DOI: 10.1080/17457300.2014.992352 To link to this article: http://dx.doi.org/10.1080/17457300.2014.992352
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
International Journal of Injury Control and Safety Promotion, 2015 http://dx.doi.org/10.1080/17457300.2014.992352
Estimating national road crash fatalities using aggregate data Anwaar Ahmed*, Beenish Akbar Khan, Muhammad Bilal Khurshid, Muhammad Babar Khan and Abdul Waheed National Institute of Transportation, School of Civil & Environmental Engineering, National University of Sciences and Technology, Islamabad, Pakistan
Downloaded by [University of Nebraska, Lincoln] at 19:50 02 April 2015
(Received 25 May 2014; accepted 21 October 2014) Injuries and fatalities from road traffic crashes have emerged a major public health challenge in Pakistan. Reliable estimates of road crash fatalities (RCF) of a country, is a vital element needed for identification and control of key risk factors, road-safety improvement efforts and prioritizing national health. Reliability of current annual RCF estimates for Pakistan becomes highly questionable due to serious underreporting. This study aimed to predict annual RCF for Pakistan using data from World Health Organization and International Road Federation sources. An ordinary least square (OLS) regression model that relates fatality rate with different explanatory variables was developed. RCF were predicted for Pakistan for year 2012 and 2013, and results were compared with national police reported estimates. Study results indicated that there is serious underreporting of RCF in Pakistan and immediate measures are needed to improve the existing road crash recording and reporting system at the national and subnational levels. Keywords: road/national highway accidents; Pakistan; prediction, aggregate data, underreporting
Introduction According to the World Health Organization (WHO) “Global Status Report on Road Safety 2013”, nearly 1.24 million people die each year on world’s roads and approximately 2050 million sustain non-fatal injuries due to road traffic crashes (RTC) (WHO, 2013). The issue is of more serious nature in low- and middle-income countries, where rapid motorization has taken place in recent past without adequate road-safety strategies. Approximately, 90% of the world’s road crash fatalities (RCF) occur in low- and middle-income countries even though they account for only 48% of the world’s registered vehicles (WHO, 2009). RCF and road traffic injuries (RTI) are expected to increase by 65% in next 20 years unless there are renewed efforts to improve the current state of road safety around the globe (Peden et al., 2004). In recent past, an overall downward trend in RCF has been observed in high-income countries, while RCF continue to increase in low- and middle-income countries (Koptis & Cropper, 2005). If current trends continue continue and efforts are not undertaken to improve the road safety situation, especially in low- and middle-income countries, RTI will become overall the fifth leading cause of death by year 2030, which is already the leading cause of death for young people aged 1524 years (Mathers, Fat, & Boerma, 2008; Patton et al., 2009). RTC are human tragedy, as these incur huge socio-economic cost in terms of injuries and *Corresponding author. Email: [email protected] Ó 2015 Taylor & Francis
untimely death. RTC not only cause economic loss by pushing many families more deeply into poverty by the loss of working member, but also are huge burden on health care services (Peden et al., 2004). Pakistan is a developing country of South Asian region having the sixth largest population in the entire world (180.71 million as of 2012) (Government of Pakistan, 2012). Pakistan has experienced a slow economic growth in recent past and also road infrastructure has improved at a moderate pace. However, in Pakistan, vehicle population has grown at much faster pace as compared to economy and road infrastructure. Motorized vehicle population has increased from about 5.3 million in year 2002 to 11 million vehicles of all type in year 2012 (Government of Pakistan, 2012; National Transport Research Centre, 2011). In the last decade, there has been approximately 110%, 150%, 45% and 30% increase in motorcycles, passenger cars, trucks and buses, respectively (National Transport Research Centre, 2011). The rapid motorization and increase in proportion of vulnerable road users have brought with them higher number of RTC. Pakistan is facing a serious issue of RCF and RTI that cost Pakistan’s economy approximately Rs 100 billion per annum (Ahmed, 2007). A study based on national health survey revealed that RTI result into more handicaps than any other injury category in Pakistan and have emerged as a national challenge that needs immediate attention of policy makers (Fatmi et al., 2007).
Downloaded by [University of Nebraska, Lincoln] at 19:50 02 April 2015
2
A. Ahmed et al.
Past studies provide different estimates of RCF and RTI for Pakistan with wide variations. According to NTRC, in the year 1999, approximately, 1.4 million RTC occurred in Pakistan that resulted in 7000 fatalities (National Transport Research Centre, 2003). Ghaffar, Hyder, and Masud (2004) found that approximately 1500 individuals per 100,000 populations sustain injuries due to RTC in Pakistan annually. Ahmed (2007) estimated that approximately 2 million RTC occurred in the Pakistan in year 2006 and 0.418 million were of serious nature. As per the police reported data, there were total of 8988 RTC that resulted into 4719 fatalities in the year 2012 (Government of Pakistan, 2014). Recent data suggested that the total number of injuries and fatalities could be much higher than those reported officially (WHO, 2009). WHO, “Global Status Report on Road Safety” 2009 estimated that there were approximately 41,494 annual RCF in Pakistan in 2007 (WHO, 2009). A recent WHO study estimated 30,131 RCF for Pakistan for year 2010 (WHO, 2013). This dichotomy between reported and estimated number of fatalities is an indication of the extent of underreporting of fatal crashes in Pakistan, and highlights the need for renewed efforts using improved methods to get reliable estimates of RCF. Past research has revealed that police-reporting-based crash data collection system of Pakistan has serious shortcoming as police’s main focus of crash data collection is to meet legal requirements (Hyder, Ghaffar, & Masood, 2000). One possible option to get reliable estimate of annual number of RCF is to develop a statistical model that relates the crash fatality rate with socio-economic factors, like gross national income (GNI) per capita, size of road network, motorization level, road-safety legislation and enforcement level of road-safety laws and policies (Anwaar et al., 2012; Kumara & Chin, 2004). Present research effort investigated such relationship using data from Asia.
Methods Data set For developing statistical relationship between RCF rate and socio-economic factors, data were obtained from WHO and International Road Federation (IRF) data sources for 40 Asian countries. Data from Asian countries
only were considered as it is believed that driving and socio-economic conditions in these countries are more closely related. Out of the total of 40 countries considered for model estimation, five are low-income countries (GNI less than or equal to 1005 US dollars), 25 are middleincome countries (GNI between 1,006 12,276 US dollars) and 10 are high-income countries (GNI greater than 12,276 US dollars) based on World Bank definition (WHO, 2013). Data on total number of annual fatalities, population, GNI per capita and registered vehicles for year 2010 were retrieved from WHO’s Global Status on Road Safety 2013. Data on enforcement level, policies and road-safety legislation for year 2011 were also extracted from WHO report that included: (1) effectiveness of overall enforcement level of speed limits, drinkdriving law, motorbike helmet law, seatbelt law and vehicle child restraint law on a scale of 010 (minimum to maximum effectiveness); (2) information on vital registration system; (3) national policy for promoting walking and cycling; (4) public access to pre-hospital care system; (5) maximum speed on rural/urban roads; (6) legislation on cell phone use while driving; (7) audits of existing/new roads; (8) national drink-driving, vehicle child restraint, seatbelt and helmet standards laws and (9) funding of lead road-safety agency. Data on road density for year 2010 defined as the kilometre (km) of road network per square kilometre were retrieved from IRF’s database (IRF, 2010). Summary statistics of significant variables is presented in Table 1. Model estimation Exposure-based response variables such as number of fatalities per hundred thousand vehicle kilometres travelled are more appropriate to use in statistical models that use data from different countries having different motorization level. Since it is difficult to collect reliable data on vehicle kilometres travelled particularly in low- and middle-income countries, other response variables that can act as suitable surrogates for exposure to potential road crash situation are the number of fatalities per hundred thousand population (FPHTP), the number of fatalities per hundred thousand registered vehicles and number of fatalities per hundred thousand kilometre of road network (Bester, 2001; Roess et al., 2004).
Table 1. Summary statistics of significant variables. Variable
Mean
SD
Minimum
Maximum
Fatalities per hundred thousand population Road density (km per square km) Max speed on urban roads (km/hour) Max speed on rural roads (km/hour) Effectiveness of vehicle child restraint law on a scale of 010 Indicator variable for lead agency (1 if lead agency is funded, 0 otherwise)
17.83 0.62 61.82 63.83 0.60 0.69
8.09 1.13 18.21 17.53 1.75 0.46
1.9 0.01 30 40 0 0
38.1 4.93 100 100 7 1
Downloaded by [University of Nebraska, Lincoln] at 19:50 02 April 2015
International Journal of Injury Control and Safety Promotion Instead of traditional count data models (Poisson or negative binomial regression), an alternative methodology [ordinary least square (OLS) regression] was used to model traffic fatalities. In this study, FPHTP was used as response variable for the models estimation as it provides a normalized measure of relative road-safety situation of different countries. The natural logarithm transformation of the response variable was used to ensure that the model outputs are positive. Numbers of explanatory variables as discussed in data part of this paper were tried for model estimation. The significant explanatory variables that are included in the final model are road density (km/km2), maximum speed on urban roads (km/hr), maximum speed on rural roads (km/hr), effectiveness of vehicle child restraint law on a scale of 010 and existence of funded road-safety agency. The model was estimated using LIMDEP (statistical software package) (Greene, 2007). A number of functional forms were investigated and the best estimated model is presented and discussed in the ensuing paragraphs. The general functional form of the OLS model is as follows: j X yðiÞ ¼ bo þ ðbi xi Þ þ ei ;
(1)
i¼1
where, y(i) D fatality rate; b’s are model coefficients; xi is the set of independent variables representing factors affecting RCF and e’s are the error terms. The fatality rate is a non-negative continuous variable, therefore, OLS regression analysis was selected for the development of traffic fatalities models in this study. Results The detailed results of OLS model developed in this study are shown in Table 2. Developed model has a reasonable fit (R2 value of 0.62) for a highly varied data that was collected for 40 countries. The estimated model allows the estimation of country level RCF and identification of
3
main factors affecting fatality rate. Model results revealed that the road density, maximum allowable speed on urban and rural roads, effectiveness of overall enforcement level of vehicle child restraint law and presence of funded lead agency in a country significantly influence the RCF rate of a country. The results shown in Table 2 revealed that road density (defined as the kilometres of roadway per square kilometre) is significantly negatively associated with RCF rate (correlation coefficient (r) D ¡0.490). Also, effectiveness of overall enforcement level of vehicle child restraint law and presence of funded lead agency for road safety are significantly negatively associated with RCF rate (r values of ¡0.493 and ¡0.238, respectively). Two variables (1) maximum allowable speed on urban and (2) maximum allowable speed on rural roads were found to significantly positively associated with RCF rate (r values of C0.194 and C0.344, respectively). The mean absolute percent error (MAPE) value for the estimated model (Equation (1)) is 0.09.
Discussion Number of fatalities/traffic accidents are non-negative integer values that have been traditionally modelled using either Poisson or negative binomial regression techniques (Washington, Karlaftis, & Mannering, 2010). In this study, data from 40 Asian countries were used to model traffic fatalities. These countries had marked variation in annual number of RCF and population. For example, in 2013, China had 275,983 RCF while Laos and TimorLeste had 1266 and 219 RCF, respectively. However, these countries had similar number of FPHTPs: 20.5, 20.4 and 19.5 for China, Laos and Timor-Leste, respectively. Thus, exposure-based differences among individual countries were normalized to avoid scale bias. Since fatality rate (FPHTP) is a continuous variable, thus statistically it is appropriate to use OLS regression techniques to model RCF, instead of count data models (Poisson or negative binomial regression).
Table 2. Model estimation results. Variable Constant Indicator variable for lead agency (1 if lead agency is funded, 0 otherwise) Square root of road density Effectiveness of vehicle child restraint law (scale of 010) Maximum speed on rural roads Maximum speed on urban roads R2 Adjusted R2 Number of observations MAPE
Coefficient
t-statistics
p-values
1.703 ¡0.387 ¡0.374 ¡0.139 0.013 0.012
4.988 ¡2.662 ¡2.203 ¡2.717 3.487 3.076 0.62 0.57 40 0.09
International Journal of Injury Control and Safety Promotion Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/nics20
Estimating national road crash fatalities using aggregate data a
a
a
a
Anwaar Ahmed , Beenish Akbar Khan , Muhammad Bilal Khurshid , Muhammad Babar Khan & Abdul Waheed
a
a
National Institute of Transportation, School of Civil & Environmental Engineering, National University of Sciences and Technology, Islamabad, Pakistan Published online: 09 Jan 2015.
Click for updates To cite this article: Anwaar Ahmed, Beenish Akbar Khan, Muhammad Bilal Khurshid, Muhammad Babar Khan & Abdul Waheed (2015): Estimating national road crash fatalities using aggregate data, International Journal of Injury Control and Safety Promotion, DOI: 10.1080/17457300.2014.992352 To link to this article: http://dx.doi.org/10.1080/17457300.2014.992352
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
International Journal of Injury Control and Safety Promotion, 2015 http://dx.doi.org/10.1080/17457300.2014.992352
Estimating national road crash fatalities using aggregate data Anwaar Ahmed*, Beenish Akbar Khan, Muhammad Bilal Khurshid, Muhammad Babar Khan and Abdul Waheed National Institute of Transportation, School of Civil & Environmental Engineering, National University of Sciences and Technology, Islamabad, Pakistan
Downloaded by [University of Nebraska, Lincoln] at 19:50 02 April 2015
(Received 25 May 2014; accepted 21 October 2014) Injuries and fatalities from road traffic crashes have emerged a major public health challenge in Pakistan. Reliable estimates of road crash fatalities (RCF) of a country, is a vital element needed for identification and control of key risk factors, road-safety improvement efforts and prioritizing national health. Reliability of current annual RCF estimates for Pakistan becomes highly questionable due to serious underreporting. This study aimed to predict annual RCF for Pakistan using data from World Health Organization and International Road Federation sources. An ordinary least square (OLS) regression model that relates fatality rate with different explanatory variables was developed. RCF were predicted for Pakistan for year 2012 and 2013, and results were compared with national police reported estimates. Study results indicated that there is serious underreporting of RCF in Pakistan and immediate measures are needed to improve the existing road crash recording and reporting system at the national and subnational levels. Keywords: road/national highway accidents; Pakistan; prediction, aggregate data, underreporting
Introduction According to the World Health Organization (WHO) “Global Status Report on Road Safety 2013”, nearly 1.24 million people die each year on world’s roads and approximately 2050 million sustain non-fatal injuries due to road traffic crashes (RTC) (WHO, 2013). The issue is of more serious nature in low- and middle-income countries, where rapid motorization has taken place in recent past without adequate road-safety strategies. Approximately, 90% of the world’s road crash fatalities (RCF) occur in low- and middle-income countries even though they account for only 48% of the world’s registered vehicles (WHO, 2009). RCF and road traffic injuries (RTI) are expected to increase by 65% in next 20 years unless there are renewed efforts to improve the current state of road safety around the globe (Peden et al., 2004). In recent past, an overall downward trend in RCF has been observed in high-income countries, while RCF continue to increase in low- and middle-income countries (Koptis & Cropper, 2005). If current trends continue continue and efforts are not undertaken to improve the road safety situation, especially in low- and middle-income countries, RTI will become overall the fifth leading cause of death by year 2030, which is already the leading cause of death for young people aged 1524 years (Mathers, Fat, & Boerma, 2008; Patton et al., 2009). RTC are human tragedy, as these incur huge socio-economic cost in terms of injuries and *Corresponding author. Email: [email protected] Ó 2015 Taylor & Francis
untimely death. RTC not only cause economic loss by pushing many families more deeply into poverty by the loss of working member, but also are huge burden on health care services (Peden et al., 2004). Pakistan is a developing country of South Asian region having the sixth largest population in the entire world (180.71 million as of 2012) (Government of Pakistan, 2012). Pakistan has experienced a slow economic growth in recent past and also road infrastructure has improved at a moderate pace. However, in Pakistan, vehicle population has grown at much faster pace as compared to economy and road infrastructure. Motorized vehicle population has increased from about 5.3 million in year 2002 to 11 million vehicles of all type in year 2012 (Government of Pakistan, 2012; National Transport Research Centre, 2011). In the last decade, there has been approximately 110%, 150%, 45% and 30% increase in motorcycles, passenger cars, trucks and buses, respectively (National Transport Research Centre, 2011). The rapid motorization and increase in proportion of vulnerable road users have brought with them higher number of RTC. Pakistan is facing a serious issue of RCF and RTI that cost Pakistan’s economy approximately Rs 100 billion per annum (Ahmed, 2007). A study based on national health survey revealed that RTI result into more handicaps than any other injury category in Pakistan and have emerged as a national challenge that needs immediate attention of policy makers (Fatmi et al., 2007).
Downloaded by [University of Nebraska, Lincoln] at 19:50 02 April 2015
2
A. Ahmed et al.
Past studies provide different estimates of RCF and RTI for Pakistan with wide variations. According to NTRC, in the year 1999, approximately, 1.4 million RTC occurred in Pakistan that resulted in 7000 fatalities (National Transport Research Centre, 2003). Ghaffar, Hyder, and Masud (2004) found that approximately 1500 individuals per 100,000 populations sustain injuries due to RTC in Pakistan annually. Ahmed (2007) estimated that approximately 2 million RTC occurred in the Pakistan in year 2006 and 0.418 million were of serious nature. As per the police reported data, there were total of 8988 RTC that resulted into 4719 fatalities in the year 2012 (Government of Pakistan, 2014). Recent data suggested that the total number of injuries and fatalities could be much higher than those reported officially (WHO, 2009). WHO, “Global Status Report on Road Safety” 2009 estimated that there were approximately 41,494 annual RCF in Pakistan in 2007 (WHO, 2009). A recent WHO study estimated 30,131 RCF for Pakistan for year 2010 (WHO, 2013). This dichotomy between reported and estimated number of fatalities is an indication of the extent of underreporting of fatal crashes in Pakistan, and highlights the need for renewed efforts using improved methods to get reliable estimates of RCF. Past research has revealed that police-reporting-based crash data collection system of Pakistan has serious shortcoming as police’s main focus of crash data collection is to meet legal requirements (Hyder, Ghaffar, & Masood, 2000). One possible option to get reliable estimate of annual number of RCF is to develop a statistical model that relates the crash fatality rate with socio-economic factors, like gross national income (GNI) per capita, size of road network, motorization level, road-safety legislation and enforcement level of road-safety laws and policies (Anwaar et al., 2012; Kumara & Chin, 2004). Present research effort investigated such relationship using data from Asia.
Methods Data set For developing statistical relationship between RCF rate and socio-economic factors, data were obtained from WHO and International Road Federation (IRF) data sources for 40 Asian countries. Data from Asian countries
only were considered as it is believed that driving and socio-economic conditions in these countries are more closely related. Out of the total of 40 countries considered for model estimation, five are low-income countries (GNI less than or equal to 1005 US dollars), 25 are middleincome countries (GNI between 1,006 12,276 US dollars) and 10 are high-income countries (GNI greater than 12,276 US dollars) based on World Bank definition (WHO, 2013). Data on total number of annual fatalities, population, GNI per capita and registered vehicles for year 2010 were retrieved from WHO’s Global Status on Road Safety 2013. Data on enforcement level, policies and road-safety legislation for year 2011 were also extracted from WHO report that included: (1) effectiveness of overall enforcement level of speed limits, drinkdriving law, motorbike helmet law, seatbelt law and vehicle child restraint law on a scale of 010 (minimum to maximum effectiveness); (2) information on vital registration system; (3) national policy for promoting walking and cycling; (4) public access to pre-hospital care system; (5) maximum speed on rural/urban roads; (6) legislation on cell phone use while driving; (7) audits of existing/new roads; (8) national drink-driving, vehicle child restraint, seatbelt and helmet standards laws and (9) funding of lead road-safety agency. Data on road density for year 2010 defined as the kilometre (km) of road network per square kilometre were retrieved from IRF’s database (IRF, 2010). Summary statistics of significant variables is presented in Table 1. Model estimation Exposure-based response variables such as number of fatalities per hundred thousand vehicle kilometres travelled are more appropriate to use in statistical models that use data from different countries having different motorization level. Since it is difficult to collect reliable data on vehicle kilometres travelled particularly in low- and middle-income countries, other response variables that can act as suitable surrogates for exposure to potential road crash situation are the number of fatalities per hundred thousand population (FPHTP), the number of fatalities per hundred thousand registered vehicles and number of fatalities per hundred thousand kilometre of road network (Bester, 2001; Roess et al., 2004).
Table 1. Summary statistics of significant variables. Variable
Mean
SD
Minimum
Maximum
Fatalities per hundred thousand population Road density (km per square km) Max speed on urban roads (km/hour) Max speed on rural roads (km/hour) Effectiveness of vehicle child restraint law on a scale of 010 Indicator variable for lead agency (1 if lead agency is funded, 0 otherwise)
17.83 0.62 61.82 63.83 0.60 0.69
8.09 1.13 18.21 17.53 1.75 0.46
1.9 0.01 30 40 0 0
38.1 4.93 100 100 7 1
Downloaded by [University of Nebraska, Lincoln] at 19:50 02 April 2015
International Journal of Injury Control and Safety Promotion Instead of traditional count data models (Poisson or negative binomial regression), an alternative methodology [ordinary least square (OLS) regression] was used to model traffic fatalities. In this study, FPHTP was used as response variable for the models estimation as it provides a normalized measure of relative road-safety situation of different countries. The natural logarithm transformation of the response variable was used to ensure that the model outputs are positive. Numbers of explanatory variables as discussed in data part of this paper were tried for model estimation. The significant explanatory variables that are included in the final model are road density (km/km2), maximum speed on urban roads (km/hr), maximum speed on rural roads (km/hr), effectiveness of vehicle child restraint law on a scale of 010 and existence of funded road-safety agency. The model was estimated using LIMDEP (statistical software package) (Greene, 2007). A number of functional forms were investigated and the best estimated model is presented and discussed in the ensuing paragraphs. The general functional form of the OLS model is as follows: j X yðiÞ ¼ bo þ ðbi xi Þ þ ei ;
(1)
i¼1
where, y(i) D fatality rate; b’s are model coefficients; xi is the set of independent variables representing factors affecting RCF and e’s are the error terms. The fatality rate is a non-negative continuous variable, therefore, OLS regression analysis was selected for the development of traffic fatalities models in this study. Results The detailed results of OLS model developed in this study are shown in Table 2. Developed model has a reasonable fit (R2 value of 0.62) for a highly varied data that was collected for 40 countries. The estimated model allows the estimation of country level RCF and identification of
3
main factors affecting fatality rate. Model results revealed that the road density, maximum allowable speed on urban and rural roads, effectiveness of overall enforcement level of vehicle child restraint law and presence of funded lead agency in a country significantly influence the RCF rate of a country. The results shown in Table 2 revealed that road density (defined as the kilometres of roadway per square kilometre) is significantly negatively associated with RCF rate (correlation coefficient (r) D ¡0.490). Also, effectiveness of overall enforcement level of vehicle child restraint law and presence of funded lead agency for road safety are significantly negatively associated with RCF rate (r values of ¡0.493 and ¡0.238, respectively). Two variables (1) maximum allowable speed on urban and (2) maximum allowable speed on rural roads were found to significantly positively associated with RCF rate (r values of C0.194 and C0.344, respectively). The mean absolute percent error (MAPE) value for the estimated model (Equation (1)) is 0.09.
Discussion Number of fatalities/traffic accidents are non-negative integer values that have been traditionally modelled using either Poisson or negative binomial regression techniques (Washington, Karlaftis, & Mannering, 2010). In this study, data from 40 Asian countries were used to model traffic fatalities. These countries had marked variation in annual number of RCF and population. For example, in 2013, China had 275,983 RCF while Laos and TimorLeste had 1266 and 219 RCF, respectively. However, these countries had similar number of FPHTPs: 20.5, 20.4 and 19.5 for China, Laos and Timor-Leste, respectively. Thus, exposure-based differences among individual countries were normalized to avoid scale bias. Since fatality rate (FPHTP) is a continuous variable, thus statistically it is appropriate to use OLS regression techniques to model RCF, instead of count data models (Poisson or negative binomial regression).
Table 2. Model estimation results. Variable Constant Indicator variable for lead agency (1 if lead agency is funded, 0 otherwise) Square root of road density Effectiveness of vehicle child restraint law (scale of 010) Maximum speed on rural roads Maximum speed on urban roads R2 Adjusted R2 Number of observations MAPE
Coefficient
t-statistics
p-values
1.703 ¡0.387 ¡0.374 ¡0.139 0.013 0.012
4.988 ¡2.662 ¡2.203 ¡2.717 3.487 3.076 0.62 0.57 40 0.09
