## Materials and Methods
### Phase-I: Application of DEA for Risk Calculation and Ranking  
As there were two major phases of modeling, we had decide on the variables for both phases. The initial target was to evaluate risk with reference to the variables that were basically exposure variables. In the basic DEA model, the definition of the best practice relied on the assumption that inputs had to be minimized, and outputs have to be maximized (such as in the economics field). However, to use DEA for road safety risk evaluation, the target became the output, i.e., the number of traffic crashes, to be as low as possible with respect to the level of exposure to risk. There are two basic concepts in application of DEA, starting from efficiency as in Equation (3), and converting into calculation of risk as shown in Equation (4). \begin{table}
\begin{tabular}{c l l c c c c} \hline \hline
**Stage** & **Variables** & **Description** & **Mean** & **SD** & **Min.** & **Max.** \\ \hline \multirow{4}{*}{1 st Stage} & NoC & No. of Crashes & 9.58 & 13.12 & 1 & 74 \\ \cline{2-6}  & NoAP & No. of Affected Persons (Injured and Killed) & 14.36 & 19.55 & 1 & 105 \\ \cline{2-6}  & V/C & Average Volume to Capacity on each segment & 0.4405 & 0.1807 & 0.08 & 0.6435 \\ \cline{2-6}  & VMT & Total daily Vehicles Miles Travelled on each Segment & 1828 & 1388 & 77 & 5186 \\ \cline{2-6}  & VHT & Total daily Vehicles hours Travelled on each Segment & 1093 & 879 & 38 & 3616 \\ \hline \multirow{4}{*}{2 nd Stage ANN} & Flow & Average annual daily traffic on each segment (vph) & 968.1 & 449.6 & 31.5 & 1483.4 \\ \cline{2-6}  & Speed & Average Travel Speed for each segment (kph) & 110.99 & 8.23 & 96.89 & 120 \\ \cline{2-6}  & Horz\_Curve & 0 = Tangent, 1 = Curve & – & – & 0 & 1 \\ \cline{2-6}  & Vert\_Curve & 1 = Upward, 2 = Downward, 3 = Flat & – & – & 1 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description Statistics of the Variables. Efficiency: The basic concept of DEA-Efficiency calculation is as follows:  
\[Efficiency\ =\ \frac{Weighted\ Sum\ of\ Output}{Weighted\ Sum\ of\ Input}\ =\ \frac{Maximize\ Output}{Minimize\ Input} \tag{3}\]  
Risk: The basic concept of DEA-Risk calculation in connection between Equations (1) and (3):  
\[Risk\ =\ \frac{Weighted\ Sum\ of\ Output}{Weighted\ Sum\ of\ Input}\ =\ \frac{Minimize\ Output}{Maximize\ Input}\ =\ \frac{Road\ Safety\ Outcome}{Exposure} \tag{4}\]  
So the equation to calculate the Risk value through DEA is as follows:  
\[Risk\ =\ \frac{U_{2}(NoC)+U_{1}\ (NoAP)}{V_{1}\ (V/C)+V_{2}\ (VMT)+V_{3}\ (VHT)} \tag{5}\]  
where \(U_{1}\) = weights for 1 st output (\(NoC\)), \(U_{2}\) = weights for 2 nd output (\(NoAP\)); \(V_{1}\) = Weights for 1 st Input (\(V/C\)), \(V_{2}\) = weights for 2 nd Input (\(VMT\)), \(V_{3}\) = weights for 3 rd Input (\(VHT\)). After calculation of Risk value, for ranking purposes, a cross-efficiency approach was one of the best methods to calculate A cross-risk value for ranking purposes. DEA has an attractive feature in that each DMU can have its own input and output weights, which leads to difficulty in making a comparison between DMUs. To compare DMUs, a Cross efficiency matrix (CEM) was developed as a DEA extension tool to assist in identifying the overall best or worst performer among all DMUs and rank them. Its basic idea is to apply DEA in a peer assessment instead of a self-assessment mode. Specifically, the CEM calculates the performance of a DMU with a concept by using not only its own optimal input and output weights, but also those of all other DMUs. Results can then be accumulated in a CEM as shown in Table 2. In the CEM, the element in the _ith_ row and _jth_ column signifies the risk scores of DMU \(j\) using the optimal weights of DMU \(i\). The basic DEA risk is thus positioned in the principal diagonal. The average of each column of the CEM is calculated as a mean cross risk value for each DMU [20].