Julius Nyerere OdhiamboSC384-3290/2013

Supervisors: Dr. Anthony Kibira Wanjoya, PhDDr. Anthony Gichuhi Waititu, PhD

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology

MODELING ROAD TRAFFIC ACCIDENT INJURIES IN NAIROBI COUNTY:

MODEL COMPARISON APPROACH

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• Introduction• Background and Motivation• Statement of the problem• Justification • Objectives• Methodology• Empirical Results• Concluding remarks• References

Presentation Overview

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Key terms

• Road Traffic Accident (RTA)- Is a stochastic event that results from a collision between vehicles; vehicles and pedestrians; between vehicles and animals; or between vehicles and fixed obstacles.

• Road Traffic Injuries (RTI)- Is the number of people injured in a RTA

• Road User- Pedestrians and vehicles users which include all occupants (i.e. driver or rider and passengers).

• Fatality- Death resulting from a road traffic accident.• Risk factor- Is a factor that increases the incidence of a road traffic

accident (e.g. speeding, drunk-driving)

Background and Motivation

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Road Traffic Accidents

• RTAs causes approximately 13 million deaths and 20-50 million sustain injuries worldwide.

• Globally it is ninth among the major cause of mortality and disability. Without action, it has been forecasted to rise to third position by the year 2020 by causing 1.9 million deaths.

• They cause considerable economic and social loss to victims.• Unlike HIV, TB, Ebola and malaria, where there are dozens of

researches, less attention has been given to RTAs injuries.

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Review of Previous Research• Abdelwahab et al (1997) modelled accident data from Central

Florida. The performance of an artificial neural network trained by Levenberg-Marquardt algorithm and Fuzzy ARTMAP were compared. Results suggested that artificial neural network (ANN) model performed better than Fuzzy ARTMAP

• Bedard (2002) applied a multivariate logistic regression so as to determine the independent contribution of crash, driver and vehicle characteristics to driver’s fatality risk. Increasing seatbelt use, reaching speed, and reducing the number and severity of driver-side impacts was found to be preventing fatalities.

• Kim et al (1995) developed a log-linear model to clarify the role of driver characteristics and behaviors in the causal sequence leading to severe RTAs.

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• Evanco (1999) conducted a multivariate population-based statistical analysis to determine the relationship between fatalities and accident notification times. Evanco’s analysis demonstrated that accident notification time was an important determinant of the number of fatalities for accidents on rural roadways.

• Abbassi (2005) studied road accidents in Kuwait using an Autoregressive Integrated Moving Averages (Box Jenkins) model and compared it with the Artificial Neutral Networks (ANN) Analysis to predict fatalities of the Road Traffic Accidents in Kuwait. He found that ANN was better in case of long term series without seasonal fluctuations of accidents or autocorrelation components.

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• RTIs is a neglected cause of death and disability and currently a serious public health concern to middle and low income countries, where 90% of traffic accidents occur despite them having only 48% of the world’s vehicle population.

• In Africa, deaths due to RTA are highest among the most active population aged 15-29 years and they constitute 25% of all injury-related deaths.

• RTAs cost Kenya between 1% - 3% of its gross national product. i.e. medical expenses, insurance, material costs. Interestingly the annual losses in developing countries occasioned by RTAs exceed the total annual development aid and loans received by these countries. (World Bank, 2010).

Statement of the problem

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• Kenya has one of the highest road fatality rates in relation to

vehicle ownership in the world, with an average of 7 deaths from 35 crashes occurring daily, which is 30-40 times greater than in highly motorized countries.

• The study will fit a model for better prediction of monthly RTIs occurrences in Nairobi County. This will be aid policy makers, medical practitioners, traffic police and the general public to combat the neglected cause of death and disability.

Justification

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Objectives

General Objective• To model road traffic accident injuries in Nairobi County

using artificial-neural network and negative-binomial regression model.

Specific objectives

• To model road traffic injuries in Nairobi County by negative-binomial regression.

• To model road traffic injuries in Nairobi county by artificial neural network.

• To comparatively analyze the performance of the artificial neural network and negative-binomial regression models.

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• Monthly accident data between January 2002 and December 2014 obtained from the Nairobi Traffic Police Department was used in the study.

• The network inputs were driver, pedal-cyclists, pedestrians, passengers, animals, obstruction, vehicle-defects, road-defects and weather. The output was the number of injuries.

• The data was divided into 90% training set and 10% testing set. The training set was used to optimize the weights and the bias of the network, while the testing set was used to determine the generalization ability of the network.

• The sigmoid activation function [0,1], was used as the transfer function for the hidden and output layer.

• Backward propagation algorithm was used to train our feed-forward multi-layer perceptron network.

Methodology

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• To measure the performance of the artificial neural network and the negative binomial model, the following performance measures were used.

• Mean Squared Error(MSE)

……………………… …………………………………(1)

• Root Mean Squared Error(RMSE)

…………………………….……………………………………..(2)

• The coefficient of determination, and the non-parametric to be utilized only by the ANN. ………………….…………………………………..……..(3)

…………………………………………………..(4)

Where:

- predicted value

– actual value

– average of the actual values

Performance Measures

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Normality Test: Accident data significantly deviated from a normal distribution.

Kolmogorov-Smirnov test

• Study data is normally distributed against Study data is not normally distributed.

Results

D-value 0.6994

P-value <0.001

• The normality of the accident data was also determined graphically as indicated, and the study observed that data points strayed from the line in a non-linear fashion

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Autocorrelation Test: Durbin-Watson test: With 95% certainty there, was no significant evidence of autocorrelation.

• Asymptotically under the null hypothesis of no autocorrelation, the test statistic ‘D-value’ had a chi-square distribution with 1 degree of freedom

D-value 1.7687

P-value 0.1169

• The distinct feature of input variables of neural networks is that the input variables should not be much correlated, since the correlated input variables may worsen the prediction performance by interacting with each other and generating a biased effect.

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Over-dispersion test results: • , test for equi-dispersion (=0) against .

• The function was a linear monotonic function, and the test statistic was a t-statistic, asymptotically normal under the null

• Thus the study concluded that there was significant evidence of over-dispersion.

z-value 4.3073

P-value <0.001 ∝ 6.3376

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• The study at 95% confidence interval concluded that drivers, pedal-cyclists, pedestrians and passengers significantly determined the monthly number of RTIs in Nairobi County.

Negative-Binomial Regression Model

Estimate Std. Error Z-value P-value

Drivers 0.0047 0.0005 9.1470 <0.0010

Pedestrians 0.0026 0.0004 5.3960 <0.0010

Pedal-Cyclist 0.0048 0.0019 2.5690 0.0102

Passengers 0.0042 0.0021 2.0060 0.0449

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Likelihood Ratio Test Statistic

• For an adequate model, the asymptotic distribution of the deviance statistic is a chi-square distribution with n-k-1 degrees of freedom.

• The study assessed the fitness of the model by dividing the residual deviance by the degree of freedom and the value found was 1.1008, approximately equal to 1.

• The p-value of the LR-Statistic was calculated from a chi-square distribution with one degree of freedom. Under the null hypothesis that the model had only an intercept term, the study had a strong evidence of including the explanatory variables.

Assessment of Model Fit

Deviance Value Degree of Freedom

Null 408.57 143

Residual 147.51 134

LR-Statistic P(>|Chi|)

148.193 0.0000

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ANN Architecture

Artificial Neural Network Model

• The sum of squared errors (SSE) was used to train our multilayered neural network.

F

Input Layer

Output Layer

Number of injuries

Hidden Layer

Bias

��

1

�� 𝑑−1

�� 𝑑

∝ 0 ∝1

∝ 2

∝H

2

H

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Number of hidden nodes (tuning parameter).

Artificial Neural Network Model

• The following equation was utilized in determining the number of hidden nodes (Yuen and Lam, 2006)

where the number of hidden nodes is, is the number of input neurons, is the number of output neurons and was arbitrarily taken to be 2

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• The ANN training set was used to optimize the weights and the network bias of the network, while the testing set was used to determine the generalizability of the network.

• For the training data set, 89.46% of the of the monthly number of RTAs injuries was explained by the network input variables. For the testing data set, 99.97% of RTAs injuries for the year 2014.

Data-set Number of samples Mean Squared Error

Non-parametric -value

Training 144 0.0040 0.8946

Testing 12 0.0000 0.9697

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• The objective of any modelling technique is to fit an accurate model that is to be used to predict future trends.

• The artificial neural network model predicted data with 89.46 % coefficient of determination as compared to 71.48 % coefficient of determination.

• The ANN outperformed the negative-binomial model in all performance metrics.

Performance Measures

Model Mean Squared Error RMSE R-squaredNegative Binomial 148.3875 12.1814 0.7148

Artificial Neural Network

0.0040 0.0632 0.8946

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Model Generalizability

• The objective of any modelling technique is to identify the best fitting and the most parsimonious model that describes the relationship between an outcome variable and a set of independent variables.

• The ANN prediction for the monthly number of RTIs, yielded optimal values when compared to the negative binomial prediction.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

50

100

150

200

250

300

350

400

Actual Observed ANN Prediction Negative -Binomial Prediction

Month(2014)

Num

ber o

f Inj

urie

s

• Results indicated that ANN outperformed the negative-binomial regression model in all factors. ANN offers a robust non-parametric model to policy makers for the prediction of monthly RTIs, and can be used as a decision support tool.

• ANN successfully provided a more valid and better prediction model which accounted for the majority of the variability (89.46%) and provided lesser MSE.

• Future research should focus on the spatial modeling of RTAs to include locational information

Concluding Remarks

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ReferencesAbbassi AH 2005. Statistical methods for predicting fatalities of Road Traffic Accidents in Kuwait. Egyptian Population and Family Planning Re-view, June, 2005: 2-19.Odero W, Khayesi M, Heda PM 2003. Road traffic injuries in Kenya:Magnitude, causes and status of intervention. Inj Con trol Saf Promo t,10 (1-2): 53-61Koptis, E. and Cropper, M. (2003). Traffic fatalities and economic growth. Policy Research Working Paper No. 3035, World Bank, Washington, DC.Bayata HF, Hinislioğlu S (2009). Modeling of monthly accident numbers in Turkey by Box-Jenkins method, 10.Econometric and Statistics Symposium, Erzurum, Turkey.Ogendi J., Odero W, Mitullah W., and Khayesi M. (2013) Pattern of Pedestrian Injuries in the City of Nairobi: Implications for Urban Safety Planning. Journal of Urban Health: Bulletin of the New York Academy of Medicine, (90), 5.World Health Organization (2013). Global Status Report on Road Safety 2013: Supporting a decade of action. World Health Organization, 2013. Luxenburg.Abdelwahab, H. T. & Abdel-Aty, M. A. Development of Artificial Neural Network Models to Predict Driver Injury Severity in Traffic Accidents at Signalized Intersections. Transportation Research Record 1746, Paper No. 01-2234.

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Don’t be a Road Traffic Accident “Statistic”

Better a minute late than "dead on time"

Julius Nyerere 25

THANK YOU