A Case of Nairobi County Follow this link for my journal publication http://article.sciencepublishinggroup.com/html/10.11648.j.ajtas.20150403.24.html

1. Julius Nyerere Odhiambo
SC384-3290/2013
Supervisors:
Dr. Anthony Kibira Wanjoya, PhD
Dr. 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
1

2. • Introduction
• Background and Motivation
• Statement of the problem
• Justification
• Objectives
• Methodology
• Empirical Results
• Concluding remarks
• References
Presentation Overview
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3. 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
3

4. 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.
4

5. 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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6. • 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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7. • 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
7

8. • 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
8

9. 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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10. • 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
10

11. • To measure the performance of the artificial neural network and the negative binomial model, the
following performance measures were used.
• Mean Squared Error(MSE)
𝑀𝑆𝐸 =
1
𝑛 𝑖=1
𝑛
𝑦 − 𝑦𝑖
2
……………………… …………………………………(1)
• Root Mean Squared Error(RMSE)
𝑅𝑀𝑆𝐸 = (𝑀𝑆𝐸)
1
2…………………………….……………………………………..(2)
• The coefficient of determination, 𝑅2
and the non-parametric 𝑅2
to be utilized only by the ANN.
𝑅2
= 1 − 𝑖=1
𝑛
𝑦−𝑦 𝑖
2
𝑖=1
𝑛 𝑦 𝑖− 𝑦 𝑛
2………………….…………………………………..……..(3)
𝑅2
= 𝑖=1
𝑛
𝑦 𝑖− 𝑦 𝑛 𝑦− 𝑦 𝑛
2
𝑖=1
𝑛
𝑦𝑖− 𝑦 𝑛
2
𝑖=1
𝑛
𝑦− 𝑦 𝑛
2…………………………………………………..(4)
Where:
𝑦 - predicted value
𝑦𝑖 – actual value
𝑦 𝑛 – average of the actual values
Performance Measures
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12. Normality Test: Accident data significantly deviated from a normal distribution.
Kolmogorov-Smirnov test
• 𝐻 𝑜: Study data is normally distributed against 𝐻𝐴: Study data is not normally
distributed.
Results
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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

13. 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
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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.

14. Over-dispersion test results:
• 𝐻 𝑜: 𝑉𝑎𝑟 𝑌𝑖 = 𝐸 𝑌𝑖 , test for equi-dispersion ( ∝ =0) against 𝐻 𝑜: 𝑉𝑎𝑟 𝑌𝑖 =
𝐸 𝑌𝑖] +∝ 𝑔(𝐸[𝑌𝑖 ).
• The function 𝑔(. ) 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.
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z-value 4.3073
P-value <0.001
∝ 6.3376

15. • 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
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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

16. 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.
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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

17. ANN Architecture
Artificial Neural Network Model
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• 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
𝑥1
𝑥 𝑑−1
𝑥 𝑑
∝0
∝1
∝2
∝
H
2
H

18. Number of hidden nodes (tuning parameter).
Artificial Neural Network Model
18
• The following equation was utilized in
determining the number of hidden nodes
(Yuen and Lam, 2006)
𝑛 =
𝑁 𝐼+𝑁 𝑂
2
+∝
where 𝑛 the number of hidden nodes is,
𝑁𝐼 is the number of input neurons, 𝑁 𝑂 is
the number of output neurons and ∝ was
arbitrarily taken to be 2

19. • 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.
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Data-set Number of samples Mean Squared
Error
Non-parametric 𝑹 𝟐
-
value
Training 144 0.0040 0.8946
Testing 12 0.0000 0.9697

20. • 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
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Model Mean Squared Error RMSE R-squared
Negative Binomial 148.3875 12.1814 0.7148
Artificial Neural
Network
0.0040 0.0632 0.8946

21. 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. 21
0
50
100
150
200
250
300
350
400
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
NUMBEROFINJURIES
MONTH(2014)
Actual Observed ANN Prediction Negative -Binomial Prediction

22. • 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
22

23. References
Abbassi 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): 53-61
Koptis, 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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24. Don’t be a Road Traffic Accident “Statistic”
24
Better a minute late than "dead on time"

25. Julius Nyerere 25
THANK YOU