BMJ Open. Application of Autoregressive Integrated Moving Average Model for Predicting Injury Mortality in Xiamen, China

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1 Application of Autoregressive Integrated Moving Average Model for Predicting Injury Mortality in Xiamen, China Journal: BMJ Open Manuscript ID: bmjopen--00 Article Type: Research Date Submitted by the Author: -Apr- Complete List of Authors: Lin, Yilan Chen, Min Chen, Guowei Wu, Xiaoqing Lin, Tianquan <b>primary Subject Heading</b>: Epidemiology Secondary Subject Heading: Research methods, Public health Keywords: EPIDEMIOLOGY, PUBLIC HEALTH, STATISTICS & RESEARCH METHODS -

2 Page of BMJ Open 0 Application of Autoregressive Integrated Moving Average Model for Predicting Injury Mortality in Xiamen, China Yilan Lin, Min Chen, Guowei Chen, Xiaoqing Wu, Tianquan Lin Department of Chronic and Non-communicable Diseases Control and Prevention, Xiamen Center for Disease Control and Prevention, Xiamen, China Department of pharmacy, Xiamen Municipal Maternal and Child Health Hospital, Xiamen, China. Correspondence to Tianquan Lin, No.0, Zhenhai Road, Siming District, Xiamen, Fujian Province, China. lintianquan0@.com. Phone: ---; Keywords: injury; prediction; times series; epidemiology Word count:. -

3 Page of 0 ABSTRACT Objective Injury is currently an increasing public health problem in China. Reducing the loss due to injuries has become a main priority of public health policies. Early warning of injury mortality based on surveillance information is essential for reducing or controlling the disease burden of injuries. we conducted this study to predict the mortality of injuries in Xiamen using the autoregressive integrated moving average (ARIMA) model. Method The monthly mortality data on injuries in Xiamen (Jan st, 0 to Dec, ) were used to fit the ARIMA model with the conditional least squares method. Three methods were adopted in the process of evaluating the constructed models, including the Schwarz's Bayesian Criterion, Akaike Information Criterion, and the mean absolute percentage error (MAPE) between observed and fitted values. Results A total of injury-related deaths in Xiamen were identified during the study period, of which the average annual mortality rate was. per 00,000 persons. Three models, ARIMA(0,,), ARIMA(,,0), and ARIMA(,,()), passed the parameter and residual tests. We chose ARIMA(0,,) as the optimum model, of which the MAPE value (.%) was similar to that of other models but with the fewest parameters. According to the model, there would be persons dying of injuries each month in Xiamen in. Conclusions The ARIMA(0,,) model could be applied to predicting the mortality of injuries in Xiamen. -

4 Page of BMJ Open 0 Strengths and limitations of this study Few studies have been used ARIMA model to forecast the future injury mortality. Our modeling approach shows that the ARIMA(0,,) model could reflect the trend of injury mortality in Xiamen and forecast the future mortality reliably for a short time period. Some reported data from the Death Surveillance System were collected retrospectively from the bereaved who did not know all of the illnesses of the dead. The possible biases in disease reporting might affect the precision of our model. The model did not consider the possible impact factors related to the injury mortality, such as behavioral factors and weather changes. INTRODUCTION Injuries that affect all ages of the population have become a serious worldwide public health threat. Deaths caused by injuries have a serious impact on communities and families. According to the latest report from the World Health Organization (WHO), approximately. million people died of injuries in, an incidence of per one million persons. With its rapid economic growth, China has undergone many substantial changes in modes of lifestyles and transports, all of which cause many unexpected issues. Injury, the leading cause of death in the Chinese population from ages to, is now an additional public health problem in China. According to the China Ministry of Health, the annual incidence of injuries for all ages was between.% and.%: injury-related deaths accounted for nearly 0% of all -

5 Page of 0 deaths during 0-0. Therefore, reducing the loss due to injuries has become a priority for public health policies. Early warning of injury mortality based on surveillance information is essential for reducing or controlling the disease burden of injuries. To reduce the loss due to injuries, statistical methods such as time series should be used to describe possible patterns of sequences with the ultimate aim of predicting future events. The autoregressive integrated moving average (ARIMA) model, one of the most classic methods of time series analysis, was first proposed by Box-Jenkins in. It is represented as a moving average (MA) model with an auto regression (AR) model to fit the temporal dependence structure of a time series using the shift and lag of historical information. In epidemiology, this model has been widely used to predict the incidence of infectious diseases such as Dengue Fever in Singapore, avian influenza HN in Egypt, hepatitis E in China. These predictions are useful for public health or clinical services departments to control the prevalence of disease. However, to the best of our knowledge, this model has not been used to predict the mortality of injuries in China. Predicting the number of mortalities due to injuries for the imminent month will generate useful information for designing strategies of public health services. The objective of this study was to describe the temporal trends of the injury mortality in Xiamen and to forecast the injury mortality in the upcoming month using ARIMA models. MATERIALS AND METHODS -

6 Page of BMJ Open 0 Materials Xiamen is a coastal city located in the southeast of China, and had a population of nearly two million in. It covers six districts, including two rural regions (Xiang an and Tong an districts), two suburbs (Haicang and Jimei districts), and two urban areas(huli and Siming districts). In Xiamen, the Death Surveillance System was established throughout the city except for in the Haicang and Jimei districts in, so the death record was incomplete until 0, when that system covered the entire city and the cause of death was classified according to the International Classification of Disease, Tenth Revision (ICD-0). In this study, demographic data was retrieved from the Xiamen Municipal Public Security Bureau, and monthly injury mortalities in Xiamen were provided by the Xiamen Center for Disease Control and Prevention (CDC). Model fitting The values p, q, and d in the ARIMA (p, d, q) model refer to the numbers of auto-regressive lags, moving-average lags, and differences respectively. The Box-Jenkins methodology was adopted to fit the ARIMA (p, d, q) model. Before constructing the model, we have to identify the stationary of observed data in the series, of which the mean value remains constant. If non-stationary, the data would be transformed into a stationary time series by taking suitable difference. The Ljung-Box test was used to measure the white noise and the residuals in the study. Three steps were performed to determine the degree of ARIMA: model identification, parameter estimation and testing, and application. We have utilized the autocorrelation function (ACF) and partial autocorrelation function (PACF) to identify the orders of the model. -

7 Page of 0 Conditional least squares method was used for parameter estimation. Akaike s information (AIC) criterion and Schwartz s Bayesian (SBC) criterion were used to select an optimal model. In addition, the mean absolute percentage error (MAPE) was calculated to assess forecast accuracy. A lower MAPE value indicates a better fit of the data. n MAPE = n ( x xˆ ) i= t t xˆ t, where n is the number of training data; xˆ t is the actual value; and x t is the predicted value. Among models with similar values of MAPE, the model with the fewest parameters is preferred. Finally, the fitted model was applied to forecasting the injury mortalities in future months. Ethical review The Medical Ethics Committee of Xiamen Center for Disease Control and Prevention found that the utilization of injury mortality from disease surveillance system didn t involve personal private information and the present study was retrospective without any biological experiment related to human or animal bodies. They waived the need for ethical approval for the utilization of the data. Statistical Analysis The rates reported were the mean annual rates. The mean age was calculated with % confidence intervals (CI). The Cochran-Armitage trend test was used to examine the temporal trends in annual injury mortality for different genders. Significance was calculated for P< 0.0. All data analysis was performed using SAS version.. RESULTS Temporal analysis There were injury-related deaths in all in Xiamen from 0 to, including males and females, with the valley in December ( cases) and -

8 Page of BMJ Open 0 the peak in August ( cases). The mean ages were. years (%CI:.-.) for the total deaths in this study,. years (%CI:.-.) for male deaths, and.00 years (% CI:.-.) for female deaths. It was. per 00,000 persons that the average annual injury mortality rate during these years, of which males was. times as many deaths as females. There was a statistically significant declining trend year by year in the total mortality rates of injuries during this period (showed in Figure); the same was found for male and female mortality rates (all P<0.0). The annual mortality rates in total decreased from./00,000 in 0 to.0/00,000 in (a.% decline). On average, mortality rates in total declined by approximately.0% per year. For males, the annual mortality rates decreased from./00,000 in 0 to./00,000 in (a.% decline). For females, the above rates decreased from./00,000 to./00,000 (a.% decline) over the same period. Modeling fitting The result of the above temporal trend test showed that the series of monthly injury mortality in Xiamen from 0 to were a non-stationary sequence. Therefore, we took the first-order differentiation to stabilize the variances. The data after first-order differentiation, which were not white noise (P<0.0), were dispersed horizontally surrounding zero (showed in Figure ), suggesting they were stationary. The ACF and PACF for first-order differentiated data were shown in Figure. The ACF graph cutoff at lag with slow decay in the PACF graph suggested a MA model (q=) (showed in Figure ). Through adjusting the parameters frequently, three models ultimately passed the -

9 Page of 0 parameter tests (all P<0.0) and residual tests (P>0.0 in each lag): ARIMA(0,,) with AIC value 0., and SBC value 0., and MAPE value.%; ARIMA(,,0) with AIC value 0., and SBC value 0.0, and MAPE value.%; and ARIMA(,,()) with AIC value 0., and SBC value 0., and MAPE value.0%. We chose the ARIMA(0,,) model, whose MAPE value was similar to that of the other models but which had the fewest parameters, as the most appropriate model. The ACF graph and PACF graph for residuals of the ARIMA(0,,) model confirmed that the data were fully modeled and that the model was suitable for prediction (showed in Figure ). The % CI of the predicted values contained most of the actual observed data. The predictions for monthly mortality due to injuries in the upcoming twelve months in in Xiamen are all approximately persons (showed in Figure ). DISCUSSION The ARIMA (p, d, q) model is one of the most classic methods of time series analysis, which has wider applicability and greater ability of prediction than non-temporal techniques. Predictions of the injury mortality would generate useful information for designing strategies of public health services. At present, the ARIMA model has been applied successfully in describing the temporal trend and predicting the incidence of various infectious diseases such as hand-foot-mouth disease, 0 malaria, and tuberculosis. However, few have been used to forecast the future injury mortality. In our study, we tried to predict the injury mortalities in China using the ARIMA model and we ultimately obtained an ARIMA(0,,) model that closely -

10 Page of BMJ Open 0 fitted monthly injury mortality in Xiamen. The P value in each lag in the Ljung-Box test for the residuals was greater than 0.0 indicated that the fitted ARIMA(0,,) model had already contained all the trends in the original series. Therefore, we could use this model to forecast the future injury mortality. The moving and autoregression average parameters in our model imply the mortality of injury in a month can be evaluated by the residual occurring one month prior. The use of ARIMA models enables us to create short-term predictions of the injury mortality in China. However, certain point must be taken into account in the course of building the model. First, the predicted outcomes would be affected due to small changes in various parameters. In order to improve the accuracy of prediction, the most recent data model should be added to update the ARIMA model. The ARIMA(0,,) model in our study is able to show the epidemic trend of injury curve and forecast the future mortality relatively accurate. However, the % confidence intervals of the predicted value in our study cannot include all of the actual observed data and enlarge rapidly over time, indicating the fitted model cannot accommodate the extreme values and only suitable for short-term prediction. It requires frequent updating. Second, when the mean of the fitted series is more than zero, the errors between the predicted values and the actual values would be too great to forecast if deleted the constant term without statistical significance. Therefore, the model should include the constant term unless the mean of the fitted data is close to zero. In our model, it was close to zero that the mean of the fitted series, which were after first-order differentiation data from original monthly injury mortality. As a result, the -

11 Page 0 of 0 forecast was not affected after deleting the absolute term which was not statistical significant. Finally, model identification is the hardest step in the course of fitting a model. We usually explore the orders with a step-by-step method from in accordance with the feature of ACF or PACF (cut or decay). It is too hard for non-experts to build the model quickly. The SAS software could supply the values of Bayesian Information criterion (BIC) (namely SBC) where the orders of p and q are both less than or equal to and directly point out the order with the smallest value of BIC. The new learner could attempt to identify the initial order on the basis of the above BIC values from small to large and select the best model according to the AIC value (the smaller, the better) among those pass the parameter and residual tests. In this study, the ARIMA (0,,) model could reflect the trend of injury mortality in Xiamen and forecast the future mortality reliably for a short time period. However, two limitations at least have to be considered when interpreting the outcomes. First, some reported data from the Death Surveillance System were collected retrospectively from the bereaved who did not know all of the illnesses of the dead. The possible biases in disease reporting might affect the precision of our model. In addition, the model did not consider the possible impact factors related to the injury mortality, such as behavioral factors and weather changes (e.g., rainfall, temperature). This may partly explain the MAPE (approximately.%) in this study is larger than the value of.% in Hye-Kyung s research, which applied the ARIMA model to forecasting the number of Human Immunodeficiency Virus Infections in Korea. More research on improving the accuracy of prediction -

12 Page of BMJ Open 0 associating with the injury mortality trend based on Death Surveillance System data should be conducted, and more sophisticated prediction techniques such as multiple or hybrid models should be applied. CONCLUSION The government urgently needs to evaluate the loss caused by injuries with some statistical methods such as time series. Our modeling approach shows that the ARIMA models of time series applied to forecasting injury mortality in Xiamen is feasible. ARIMA models based on historical surveillance data are important tools for monitoring and forecasting injuries. ACKNOWLEDGMENTS We thank Director Long Dai and other colleagues in the Department of Chronic Non-communicable Disease Control and Prevention of the Xiamen Municipal CDC for data collection. Contributors: YL for conceiving and designing the research and writing the paper, TL for statistical analysis: MC and GC for materials and analysis tools, XW for study supervision. All authors were involved in the revision of the manuscript for important intellectual content. Competing interests: None Funding: None Data sharing statement: all data reported in this article are available on request from the corresponding author. REFERENCE -

13 Page of 0 Takala J, Hamalainen P, Saarela KL, et al. Global estimates of the burden of injury and illness at work in. J Occup Environ Hyg ; (): -. World Health Organization. Health statistics and information systems/estimates for 00 /CAUSE-SPECIFIC MORTALITY., Available Accessed September. Zhao J, Tu EJ, McMurray C, Sleigh A. Rising mortality from injury in urban China: demographic burden, underlying causes and policy implications. Bull World Health Organ ; 0(): -. Zhang L, Li Z, Li X, et al. Study on the trend and disease burden of injury deaths in Chinese population, 0-0. PLoS One ; (): e. Xiao Z, Guo M. Time Series Analysis and Application with SAS. WUHAN UNIVERSITY PRESS 0:. Earnest A, Tan SB, Wilder-Smith A, et al. Comparing statistical models to predict dengue fever notifications. Comput Math Methods Med ; : -. Kane MJ, Price N, Scotch M, et al. Comparison of ARIMA and Random Forest time series models for prediction of avian influenza HN outbreaks. BMC Bioinformatics ; :. Ren H, Li J, Yuan ZA, et al. The development of a combined mathematical model to forecast the incidence of hepatitis E in Shanghai, China. BMC Infect Dis ; :. Sato RC. Disease management with ARIMA model in time series. Einstein (Sao -

14 Page of BMJ Open 0 Paulo) ; (): -. 0 Tan T, Chen L, Liu F. Model of multiple seasonal autoregressive integrated moving average model and its application in prediction of the hand-foot-mouth disease incidence in Changsha. Zhong Nan Da Xue Xue Bao Yi Xue Ban ; (): 0-. Ramirez AP, Buitrago JI, Gonzalez JP, et al. Frequency and tendency of malaria in Colombia, 0 to : a descriptive study. Malar J ; :. Zhang G, Huang S, Duan Q, et al. Application of a hybrid model for predicting the incidence of tuberculosis in Hubei, China. PLoS One ; (): e0. Lankarani KB, Heydari ST, Aghabeigi MR, et al. The impact of environmental factors on traffic accidents in Iran. J Inj Violence Res ; (): -. Yu HK, Kim NY, Kim SS, et al. Forecasting the number of human immunodeficiency virus infections in the korean population using the autoregressive integrated moving average model. Osong Public Health Res Perspect ; ():

15 Page of 0 Figure legends Figure. The annual mortality rate of injuries in Xiamen, China, from 0 to. Figure. Series of monthly mortality after first differentiation. The data after first order differentiation are dispersed horizontally surrounding zero, suggesting they are stationary. Figure. The autocorrelation and partial autocorrelation (ACF and PACF) graphs after first differentiation. The shadowed portion is the % confidence intervals (%CI) range. The ACF cuts off at lag with slow decay in the PACF suggested a MA model (q=) Figure. The autocorrelation and partial autocorrelation (ACF and PACF) graphs of the residuals for ARIMA(0,,) model. The shadowed portion is the % confidence intervals (%CI) range. As their correlation values are not outside the %CI limits, the residuals error is considered to be white noise, indicating that this model is appropriate for prediction. Figure. Actual and predicted mortalities and % confidence intervals (%CI) of predicted mortalities. Most actual observed data are contained within the % CI of the predicted value, revealing that the prediction for the monthly injury mortality in Xiamen using the ARIMA(0,,) model is acceptable. -

16 Page of BMJ Open 0 The annual mortality rate of injuries in Xiamen, China, from 0 to. xmm (0 x 0 DPI) -

17 Page of 0 Series of monthly mortality after first differentiation. The data after first order differentiation are dispersed horizontally surrounding zero, suggesting they are stationary. xmm (0 x 0 DPI) -

18 Page of BMJ Open 0 The autocorrelation and partial autocorrelation (ACF and PACF) graphs after first differentiation. The shadowed portion is the % confidence intervals (%CI) range. The ACF cuts off at lag with slow decay in the PACF suggested a MA model (q=). xmm (0 x 0 DPI) -

19 Page of 0 The autocorrelation and partial autocorrelation (ACF and PACF) graphs of the residuals for ARIMA(0,,) model. The shadowed portion is the % confidence intervals (%CI) range. As their correlation values are not outside the %CI limits, the residuals error is considered to be white noise, indicating that this model is appropriate for prediction. xmm (0 x 0 DPI) -

20 Page of BMJ Open 0 Actual and predicted mortalities and % confidence intervals (%CI) of predicted mortalities. Most actual observed data are contained within the % CI of the predicted value, revealing that the prediction for the monthly injury mortality in Xiamen using the ARIMA(0,,) model is acceptable. xmm (0 x 0 DPI) -

21 Page of 0 Title Keywords Word count Abstract Strengths and limitations of this study Ethical approval Main text Reporting Checklist Application of Autoregressive Integrated Moving Average Model for Predicting Injury Mortality in Xiamen, China injury; prediction; times series; epidemiology words; including objective, method, results, and conclusions Few studies have been used ARIMA model to forecast the future injury mortality. Our modeling approach shows that the ARIMA(0,,) model could reflect the trend of injury mortality in Xiamen and forecast the future mortality reliably for a short time period. Some reported data from the Death Surveillance System were collected retrospectively from the bereaved who did not know all of the illnesses of the dead. The possible biases in disease reporting might affect the precision of our model. The model did not consider the possible impact factors related to the injury mortality, such as behavioral factors and weather changes. The Medical Ethics Committee of Xiamen Center for Disease Control and Prevention found that the utilization of injury mortality from disease surveillance system didn t involve personal private information and the present study was retrospective without any biological experiment related to human or animal bodies. They waived the need for ethical approval for the utilization of the data. Including introduction, materials and methods, results, discussion, conclusions, acknowledge, contributors, competing interests, Funding, data sharing statement, references, and figure legends. Competing interests None Funding None Data sharing statement all data reported in this article are available on request from the corresponding author References Tables 0 Figures -

22 Application of Autoregressive Integrated Moving Average Model for Predicting Injury Mortality in Xiamen, China Journal: BMJ Open Manuscript ID bmjopen--00.r Article Type: Research Date Submitted by the Author: -Aug- Complete List of Authors: Lin, Yilan; Xiamen Center for Disease Control and Prevention, Department of Chronic and Non-communicable Diseases Control and Prevention Chen, Min; Xiamen Center for Disease Control and Prevention, Department of Chronic and Non-communicable Diseases Control and Prevention Chen, Guowei; Xiamen Center for Disease Control and Prevention, Department of Chronic and Non-communicable Diseases Control and Prevention Wu, Xiaoqing; Xiamen Center for Disease Control and Prevention, Department of Chronic and Non-communicable Diseases Control and Prevention Lin, Tianquan; Xiamen Municipal Maternal and Child Health Hospital, Department of Pharmacy <b>primary Subject Heading</b>: Epidemiology Secondary Subject Heading: Research methods, Public health Keywords: EPIDEMIOLOGY, PUBLIC HEALTH, PREVENTIVE MEDICINE, STATISTICS & RESEARCH METHODS -

23 Page of BMJ Open 0 Application of Autoregressive Integrated Moving Average Model for Predicting Injury Mortality in Xiamen, China Yilan Lin, Min Chen, Guowei Chen, Xiaoqing Wu, Tianquan Lin Department of Chronic and Non-communicable Diseases Control and Prevention, Xiamen Center for Disease Control and Prevention, Xiamen, China Department of pharmacy, Xiamen Municipal Maternal and Child Health Hospital, Xiamen, China. Correspondence to Tianquan Lin, No.0, Zhenhai Road, Siming District, Xiamen, Fujian Province, China. lintianquan0@.com. Phone: ---; Keywords: injury; prediction; times series; epidemiology Word count:

24 Page of 0 ABSTRACT Objective Injury is currently an increasing public health problem in China. Reducing the loss due to injuries has become a main priority of public health policies. Early warning of injury mortality based on surveillance information is essential for reducing or controlling the disease burden of injuries. We conducted this study to find the possibility of applying the autoregressive integrated moving average (ARIMA) models to predict the mortality of injuries in Xiamen. Method The monthly mortality data on injuries in Xiamen (Jan st, 0 to Dec, ) were used to fit the ARIMA model with the conditional least squares method. The Ljung-Box test was used to measure the white noise and the residuals. The mean absolute percentage error (MAPE) between observed and fitted values was adopted to evaluate the predicted accuracy of the constructed models. Results A total of injury-related deaths in Xiamen were identified during the study period, of which the average annual mortality rate was. per 00,000 persons. Three models, ARIMA(0,,), ARIMA(,,0), and ARIMA(,,()), passed the parameter (P<0.0) and residual tests (P>0.0) with the MAPE.%,.% and.0%, respectively. We chose ARIMA(0,,) as the optimum model, of which the MAPE value was similar to that of other models but with the fewest parameters. According to the model, there would be persons dying of injuries each month in Xiamen in. Conclusions The ARIMA(0,,) model could be applied to predicting the mortality of injuries in Xiamen. -

25 Page of BMJ Open 0 Strengths and limitations of o this study Few studies have been used ARIMA model to forecast the future injury mortality. Our modeling approach shows that the ARIMA(0,,) model could reflect the trend of injury mortality in Xiamen and forecast the future mortality reliably for a short time period. Some reported data from the Death Surveillance System were collected retrospectively from the bereaved who did not know all of the illnesses of the dead. The possible biases in disease reporting might affect the precision of our model. The model did not consider the possible impact factors related to the injury mortality, such as behavioral factors and weather changes. INTRODUCTION Injuries that affect all ages of the population have become a serious worldwide public health threat. Deaths caused by injuries have a serious impact on communities and families. According to the latest report from the World Health Organization (WHO), approximately. million people died of injuries in, an incidence of per one million persons. With its rapid economic growth, China has undergone many substantial changes in modes of lifestyles and transports, all of which cause many unexpected issues. Injury, the leading cause of death in the Chinese population from ages to, is now an additional public health problem in China. According to the China Ministry of Health, the annual incidence of injuries for all ages was -

26 Page of 0 between.% and.%; injury-related deaths accounted for nearly 0% of all deaths during 0-0. Therefore, reducing the loss due to injuries has become a priority for public health policies. Early warning of injury mortality based on surveillance information is essential for reducing or controlling the disease burden of injuries. To reduce the loss due to injuries, statistical methods such as time series should be used to describe possible patterns of sequences with the ultimate aim of predicting future events. The autoregressive integrated moving average (ARIMA) model, one of the most classic methods of time series analysis, was first proposed by Box-Jenkins in. It is represented as a moving average (MA) model with an auto regression (AR) model to fit the temporal dependence structure of a time series using the shift and lag of historical information. In epidemiology, this model has been widely used to predict the incidence of infectious diseases such as Dengue Fever in Singapore, avian influenza HN in Egypt, hepatitis E in China. These predictions are useful for public health or clinical services departments to control the prevalence of disease. However, to the best of our knowledge, this model has not been used to predict the mortality of injuries in China. Predicting the number of deaths due to injuries for the future months will generate useful information for designing strategies of public health services. The objective of this study was to describe the temporal trends of the injury mortality in Xiamen and to find the possibility of applying the ARIMA models to forecast the injury mortality in the upcoming month. -

27 Page of BMJ Open 0 MATERIALS AND METHODS Materials Xiamen is a coastal city located in the southeast of China, and had a population of nearly two million in. It covers six districts, including two rural regions (Xiang an and Tong an districts), two suburbs (Haicang and Jimei districts), and two urban areas(huli and Siming districts). In Xiamen, the Death Surveillance System was established throughout the city except for in the Haicang and Jimei districts in, so the death record was incomplete until 0, when that system covered the entire city and the cause of death was classified according to the International Classification of Disease, Tenth Revision (ICD-0). In this study, demographic data was retrieved from the Xiamen Municipal Public Security Bureau, and monthly injury mortalities in Xiamen were provided by the Xiamen Center for Disease Control and Prevention (CDC) which is responsible for managing the Death Surveillance System. The ICD-0 codes of injury included all X and Y codes. Model fitting The values p, q, and d in the ARIMA (p, d, q) model refer to the numbers of auto-regressive lags, moving-average lags, and differences respectively. The Box-Jenkins methodology was adopted to fit the ARIMA (p, d, q) model. Before constructing the model, we have to identify the stationary of observed data in the series, of which the mean value remains constant. If non-stationary, the data would be transformed into a stationary time series by taking suitable difference. The Ljung-Box test was used to measure the white noise and the residuals in the study. Three steps -

28 Page of 0 were performed to determine the degree of ARIMA: model identification, parameter estimation and testing, and application. We have utilized the autocorrelation function (ACF) and partial autocorrelation function (PACF) to identify the orders of the model. Conditional least squares method was used for parameter estimation, and t test was used for parameter testing. The mean absolute percentage error (MAPE) was calculated to assess forecast accuracy and to select an optimal model. A lower MAPE value indicates a better fit of the data. n MAPE = ( xt xˆ t ) n i= number of training data; xˆ t is the actual value; and t xˆ t, where n is the x is the predicted value. Among models with similar values of MAPE, the model with the fewest parameters is preferred. Finally, the fitted model was applied to forecasting the injury mortalities in future months. Statistical Analysis The rates reported were the mean annual rates. The mean age was calculated with % confidence intervals (CI). The Cochran-Armitage trend test was used to examine the temporal trends in annual injury mortality for different genders. Significance was calculated for P< 0.0. All data analysis was performed using SAS version.. RESULTS Temporal analysis There were injury-related deaths in all in Xiamen from 0 to, including males and females, with the trough in December ( cases) and the peak in August ( cases). The mean ages were. years (%CI:.-.) for the total deaths in this study,. years (%CI:.-.) for male deaths, -

29 Page of BMJ Open 0 and.00 years (% CI:.-.) for female deaths. The average annual injury mortality rate during these years was. per 00,000 persons,nearly. times as many males as females. There was a statistically significant declining trend year by year in the total mortality rates of injuries during this period (showed in Figure); the same was found for male and female mortality rates (all P<0.0). The annual mortality rates in total decreased from./00,000 in 0 to.0/00,000 in (a.% decline). On average, mortality rates in total declined by approximately.0% per year. For males, the annual mortality rates decreased from./00,000 in 0 to./00,000 in (a.% decline). For females, the above rates decreased from./00,000 to./00,000 (a.% decline) over the same period. Modeling fitting The result of the above temporal trend test showed that the series of monthly injury mortality in Xiamen from 0 to were a non-stationary sequence. Therefore, we took the first-order differentiation to stabilize the variances. The data after first-order differentiation (d=), which were not white noise (P<0.0), were dispersed horizontally surrounding zero (showed in Figure ), suggesting they were stationary. The ACF and PACF for first-order differentiated data were shown in Figure. The autocorrelations of the series after first-order differentiation is within % confidence intervals except the first lag. The ACF graph cutoff at lag with slow decay in the PACF graph suggested a MA model (q=) (showed in Figure ). Through adjusting the parameters frequently according to the values of Bayesian -

30 Page of 0 Information criterion (BIC) showed directly by SAS software from low to high, three models ultimately passed the parameter tests (P<0.0) and residual tests (P>0.0): ARIMA(0,,) with AIC value 0., and SBC value 0., and MAPE value.%; ARIMA(,,0) with AIC value 0., and SBC value 0.0, and MAPE value.%; and ARIMA(,,()) with AIC value 0., and SBC value 0., and MAPE value.0%. We chose the ARIMA(0,,) model, whose MAPE value was similar to that of the other models but which had the fewest parameters, as the most appropriate model. The ACF graph and PACF graph for residuals of the ARIMA(0,,) model confirmed that the data were fully modeled and that the model was suitable for prediction (showed in Figure ). The MA() parameter was equal to 0.00 (t=., P<0.0). The % CI of the predicted values contained most of the actual observed data. The predictions for monthly mortality due to injuries in the upcoming twelve months in in Xiamen are all approximately persons (showed in Figure ). DISCUSSION Predictions of the injury mortality would generate useful information for designing strategies of public health services. However, the causes of injury are complex, including personal factors, family factors, and social factors. 0 traditional regression analysis methods are difficult to predict its trend of occurrence and death. The time series analysis methods use time (t) to take the place of these influencing factors, so it may be a useful tool for predicting the death trend of injury without these related factors. The ARIMA (p, d, q) model is one of the most classic - The

31 Page of BMJ Open 0 methods of time series analysis, which is established on the basis of past values of the series and the previous error terms for forecasting, using the traditional mathematical theory, such as calculus and mathematical statistics. It is a linear conventional model for nonstationary time series, which is transformed to stationary by differentiation; it has wider applicability and greater ability of prediction than non-temporal techniques. The essential modeling data is easily available from the annual or monthly report or even from the literature. At present, the ARIMA model has been applied successfully to describe the temporal trend and to predict the incidence of various infectious diseases such as hand-foot-mouth disease, malaria, and tuberculosis. However, few have been used to forecast the future injury mortality. Therefore, we tried to apply the ARIMA model to predict the mortality trend of injury in Xiamen, China. Before constructing the model, we have to test white noise, a time sequence consists of uncorrelated random variables and could not be used to build a model. The series after first-order differentiation were not white noise (P<0.0 in the Ljung-Box test) in our study, indicating that series was worthy of analyzing and could be used to build the model. In the model identification stage, the autocorrelation function (ACF) is a standard tool used to identify cycles, seasonality, and other patterns in a series. The autocorrelation is considered to be equal to zero if it is within % confidence intervals. All the autocorrelations of the series after first-order differentiation in our study were within % CI ranges except in the first lag, indicating that the series cut off at lag with slow decay without cycles, seasonality, -

32 Page 0 of 0 and other patterns. After identifying the model, conditional least squares method and t test were used to calculate and test the parameters of model. Some parameters may present no statistically significant values (P 0.0); in such cases, these parameters could be taken away from the study in order to improve the arrangement of data. Then, Ljung-Box test was performed again to insure the residuals after parameter estimation and test consist of uncorrelated random variables. If the residuals of the series are white noises, it indicates that the building model fits the data adequately and appropriately, and could be applied in prediction. If not so, the process of identification must be performed again to assess other patterns that fit the data. In our study, three models ultimately passed the parameter tests (all P<0.0) and residual tests (all P>0.0): ARIMA(0,,), ARIMA(,,0), ARIMA(,,()). Finally, the mean absolute percentage error (MAPE) was calculated to assess accuracy of forecast and to select the optimal model. A lower MAPE value indicates a better fit of the data. The model with fewest parameters is preferred among those with similar values of MAPE due to the difficulty of ARIMA model in explaining the parameters. In this study, the MAPE of ARIMA(0,,) model (.%) was less than that of ARIMA(,,0) model (.%), but close to that of ARIMA(,,()) model (.0%). Therefore, We chose the ARIMA(0,,) model, which had the fewer parameters than ARIMA(,,()) model, as the most appropriate model. The P value in the Ljung-Box test for the residuals was greater than 0.0 indicated that the fitted ARIMA(0,,) model had already contained all the trends in the original series. Therefore, we could use this model to forecast the future injury mortality. However, -

33 Page of BMJ Open 0 the % CI of the predicted value in our study cannot include all of the actual observed data and enlarge rapidly over time, indicating the fitted model cannot accommodate the extreme values and only suitable for short-term prediction. It requires updating the newest data frequently. The predictions showed that the value of monthly mortality due to injuries was still high about persons in each month in in Xiamen. So we still have to pay more attention on preventing and controlling of injury. The use of ARIMA models enables us to create short-term predictions of the injury mortality in China. However, certain point must be taken into account in the course of building the model. First, the predicted outcomes would be affected due to small changes in various parameters. In order to improve the accuracy of prediction, the most recent data model should be added to update the ARIMA model. The ARIMA(0,,) model in our study is able to show the epidemic trend of injury curve and forecast the future mortality relatively accurate. But it is only suitable for short-term prediction. We have to update data frequently to predict further future monthly death due to injury. Second, when the mean of the fitted series is more than zero, the errors between the predicted values and the actual values would be too great to forecast if deleted the constant term without statistical significance. Therefore, the model should include the constant term unless the mean of the fitted data is close to zero. The mean of the fitted series after first-order differentiation was close to zero in our model. As a result, the forecast was not affected after deleting the absolute term which was not statistical significant. Finally, model identification is the hardest step in -

34 Page of 0 the course of fitting a model. We usually explore the orders with a step-by-step method from in accordance with the feature of ACF or PACF (cut or decay). It is too hard for non-experts to build the model quickly. The SAS software could supply the values of BIC where the orders of p and q are both less than or equal to and directly point out the order with the smallest value of BIC. The new learner could attempt to identify the initial order on the basis of the above BIC values from small to large and select the best model according to the BIC and MAPE values (the smaller, the better) among those pass the parameter and residual tests. There is at least one limitation in this study. The ARIMA (0,,) model could reflect the trend of injury mortality in Xiamen and forecast the future mortality reliably for a short time period. However, the model did not consider the possible impact factors related to the injury mortality, such as behavioral factors and weather changes (e.g., rainfall, temperature). This may partly explain the MAPE (approximately.%) in this study is larger than the value of.% in Hye-Kyung s research, which applied the ARIMA model to forecasting the number of Human Immunodeficiency Virus Infections in Korea. In a further study, we would explore more sophisticated prediction techniques such as hybrid or multiple models related to the above impact factors to make more accurate predictions over the longer term. CONCLUSION The government urgently needs to evaluate the loss caused by injuries with some statistical methods such as time series. Our modeling approach shows that the ARIMA models of time series applied to forecasting injury mortality in Xiamen is feasible. -

35 Page of BMJ Open 0 ARIMA models based on historical surveillance data are important tools for monitoring and forecasting injuries. ACKNOWLEDGMENTS We thank Director Long Dai and other colleagues in the Department of Chronic Non-communicable Disease Control and Prevention of the Xiamen Municipal CDC for data collection. CONTRIBUTIONS YL for conceiving and designing the research and writing the paper, TL for statistical analysis: MC and GC for materials and analysis tools, XW for study supervision. All authors were involved in the revision of the manuscript for important intellectual content. COMPETING INTEREST No, there are no competing interests. ETHICAL REVIEW The Medical Ethics Committee of Xiamen Center for Disease Control and Prevention found that the utilization of injury mortality from disease surveillance system didn t involve personal private information and the present study was retrospective without any biological experiment related to human or animal bodies. They waived the need for ethical approval for the utilization of the data. DATA SHARING STATEMENT -

36 Page of 0 All data reported in this article are available on request from the corresponding author. REFERENCE Takala J, Hamalainen P, Saarela KL, et al. Global estimates of the burden of injury and illness at work in. J Occup Environ Hyg ; (): -. World Health Organization. Health statistics and information systems/estimates for 00 /CAUSE-SPECIFIC MORTALITY., Available Accessed September. Zhao J, Tu EJ, McMurray C, Sleigh A. Rising mortality from injury in urban China: demographic burden, underlying causes and policy implications. Bull World Health Organ ; 0(): -. China Ministry of Health. Injury prevention report in China. st edition, Beijing, People s Medical Publishing House 0:0. Zhang L, Li Z, Li X, et al. Study on the trend and disease burden of injury deaths in Chinese population, 0-0. PLoS One ; (): e. Xiao Z, Guo M. Time Series Analysis and Application with SAS. WUHAN UNIVERSITY PRESS 0: -. Earnest A, Tan SB, Wilder-Smith A, et al. Comparing statistical models to predict dengue fever notifications. Comput Math Methods Med ; : -. Kane MJ, Price N, Scotch M, et al. Comparison of ARIMA and Random Forest time series models for prediction of avian influenza HN outbreaks. BMC Bioinformatics ; :. -

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39 Page of BMJ Open 0 Figure legends Figure. The annual mortality rate of injuries in Xiamen, China, from 0 to. Figure. Series of monthly mortality after first differentiation. The data after first order differentiation are dispersed horizontally surrounding zero, suggesting they are stationary. Figure. The autocorrelation and partial autocorrelation (ACF and PACF) graphs after first differentiation. The shadowed portion is the % confidence intervals (%CI) range. The ACF cuts off at lag with slow decay in the PACF suggested a MA model (q=) Figure. The autocorrelation and partial autocorrelation (ACF and PACF) graphs of the residuals for ARIMA(0,,) model. The shadowed portion is the % confidence intervals (%CI) range. As their correlation values are not outside the %CI limits, the residuals error is considered to be white noise, indicating that this model is appropriate for prediction. Figure. Actual and predicted mortalities and % confidence intervals (%CI) of predicted mortalities. Most actual observed data are contained within the % CI of the predicted value, revealing that the prediction for the monthly injury mortality in Xiamen using the ARIMA(0,,) model is acceptable. -

40 Page of 0 The annual mortality rate of injuries in Xiamen, China, from 0 to. xmm (0 x 0 DPI) -