A study on injury severity is helpful for identifying risk factors of increasing the death rate of vehicle-pedestrian accidents. Eluru et al. (2008) and Ma et al. (2017) have comprehensively concluded that many researchers have tried to analyze the injury severity through statistical models, like multinomial logit, ordered probit and so forth [29] [36]. Binary logistic regression has also been used to establish models of fatality risk in studies [5] [32]. The Beijing accident dataset classifies the injury severity into fatal, severe and light. However, it should be mentioned that the criterion of injury severity among different countries is not identical. For that reason, it is decided to use binary classification (fatal and not fatal) to compare and analyze the result. Logistic regression is useful when you are predicting a binary outcome from a set of continuous and/or categorical predictor variables. Consequently, the binary logit model is supposed to be the most appropriate method to examine each variable in this study.

According to the outcome for each accident, fatality risk is defined: fatal or not fatal (injury). A binary logistic regression model can be used to express the pedestrian’s death probability. A fatal accident outcome is represented by the value of 1, and other consequences are represented by 0. Considering the outcome is dichotomous, the probability ( P n ) of death for pedestrian n can be determined by:

P n = e f ( X n ) 1 + e f ( X n ) = 1 1 + e − f ( X n ) , (1)

where P n is the probability of being killed for pedestrian n; f ( X n ) is a linear function of the explanatory variables.

In the logistic regression model, this linear function is related to the expected value of the response, which is composed by K independent variables and coefficients:

f ( X n ) = β 0 + β 1 X 1 n + β 2 X 2 n + ⋯ + β j X j n + ⋯ + β K X K n , (2)

where X_in is the j^th vector of independent variables for pedestrian n, with β as the corresponding coefficient.

When there are two or more independent variables in the experimental study, the effect of one of the independent variables is inconsistent at each level of the other independent variable. This phenomenon is called interaction effects. In this study, we mainly focused on the first-degree interaction effects, which are only between two explanatory variables. Therefore, function f ( X n ) can be formulated by the following expression:

f ( X n ) = β 0 + β 1 X 1 n + β 2 X 2 n + ⋯ + β K X K n + β K + 1 X 1 n X 2 n + ⋯ + β M X K n X ( K − 1 ) n , (3)

where K is the number of independent variables; M is the number of variables and interaction effects, M = K ( K + 1 ) / 2 .

Goodness-of-fit tests are calculated in order to decide whether the logistic regression model is correctly specified. If the p-value is above 0.05, then the model passes the test. In consideration of our model containing both categorical and continuous variables, Hosmer-Lemeshow test can be used to examine whether the model is consistent with data. The formula of Hosmer-Lemeshow test can be expressed as:

H L = ∑ i = 1 G ( ( O i − E i ) 2 N i θ i ( 1 − θ i ) ) , (4)

where HL is the Hosmer-Lemeshow statistic; O_i is the observed accidents of a fatal outcome; E_i is the expected accidents of a fatal outcome; N_i is the number of observations; θ_i is the predicted risk for the i^th risk decile group, and G is the number of groups. The test statistic asymptotically follows a χ² distribution (G − 2) degrees of freedom. To help avoid singular decile groups, the number of risk groups may be fine-tuned depending on how many fitted risks are identified by the model.

In the logistic regression model, coefficients of categorical variables at statistically significant levels can be used to calculate the odds ratio (OR) of fatality under some situations. OR is given by the formula:

O R ( X i ) = exp ( β i ) , (5)

Odds ratio can represent the relative death risk of pedestrians in an accident when some condition occurs comparing with when it does not occur. In the study, we compare different accident conditions with the control level.

In this paper, traffic accident data in the whole year of 2015 from Beijing Traffic Management Bureau are used for modeling. The number of accidents of vehicle hitting pedestrian in Beijing was 23,378. These accidents occurred mostly at three places: mid-blocks, intersections and roundabouts, and their proportions are presented in Figure 1(a). Among all vehicle-pedestrian accidents, those occurred at mid-blocks account for 48%, which was equivalent to percentage of accidents occurred at intersections, with only 4% of accidents occurred at roundabouts. However, Figure 1(b) shows that fatal accidents occurred at mid-blocks were more than half (56%), and the percentage of fatal accidents occurred at intersections decreased to 41%, with the portion of roundabout accidents changing slightly. It can be concluded that vehicle-pedestrian accidents that occur at mid-blocks are more likely to have a fatal outcome. In later sections, this issue will be thoroughly analyzed, and several underlying causes will be excavated.

The intention of this study is to identify risk factors leading to a higher death rate of pedestrians. After preliminary analysis, potential explanatory variables selected from the dataset are listed as follows:

・ weather (normal, adverse)

・ area type (urban, rural)

・ road type (one-way, two-way undivided, divided)

・ road speed limit (continuous: km/h)

・ pedestrian location (roadside, pedestrian crossing, crossing elsewhere)

・ lighting condition (daylight, dark no lighting, dark street lights, dusk or dawn)

・ vehicle type (motorcycle, car, light vehicle, heavy vehicle)

・ pedestrian gender (male, female)

・ pedestrian age (continuous: years)

Levels of each variable are given in parenthesis and the reference level is underlined. Road speed limit and pedestrian age are two continuous variables, and several dummy variables are also defined for categorical variables. In each case, the number of dummy variables should be one less than the number of levels (subtracting reference level).

After data manipulation, 10,948 reported vehicle-pedestrian accidents occurred at mid-blocks. The distributions of these accidents as well as pedestrians killed and injured are shown in Table 1, according to several characteristics including weather, area type, road type, lighting conditions, vehicle type, and pedestrian location. By calculating the number of fatalities per 100 accidents, we can define the accident severity in the last column of Table 1. It can be found that the importance of these factors seems different from two perspectives: frequency and severity. For example, a large number of accidents (80.8%) occurred at urban areas while fatalities only comprising 45.2%. The accident severity of the urban area is only 3.1, about one-fifth of the rural area. Mid-blocks on divided two-way roads also seem to be a concern: 10.5% of accidents occurred there sharing 41.7% of fatalities, with accident severity being equal to 21.7.

As for the vehicle type, almost 81.0% of accidents and 65.8% of fatalities occurred between cars and pedestrians. Accidents severity is 8.9 killed per 100 hundred for light vehicles, and 14.8 for heavy vehicles. Table 1 also shows that 64.9% of accidents were located at carriageways resulting in 80.2% of killed victims (accident severity is 6.8). It should be noted that pedestrians at mid-blocks have larger possibility getting injured or killed when they are crossing elsewhere in carriageways. In fact, the number of pedestrian crossing facilities in Beijing cannot keep the pace of road extensions in newly built-up areas, and additionally traffic schemes changed a lot.

Pedestrians are prominently at risk of fatality during poor light periods. On the one hand, they are less visible during nighttime. On the other hand, vehicles speed faster as a result of relatively lower traffic volumes at the same time. Accidents under normal weather account for 88.6% having 90.3% of fatalities, and its accident severity is even higher comparing with adverse weather. This phenomenon is a little unexpectable and will be discussed later.

During the year of 2015, there were 600 pedestrians killed at mid-blocks, with 10,694 injured. Men comprised 71.7% of fatalities and 57% of injuries. Shown in Table 2, victims of these crashes are distributed by several age groups. With regard to numbers, juveniles under 15 have the largest percentage of both total

victims and the injured, while their percentage killed (1.1%) is the lowest. It is obvious that older age groups consist of higher proportion of fatalities. Pedestrians between 36 and 45 share 17.8% of fatalities, which is the highest among all age groups. The percentage killed of seniors between 66 and 75 is the greatest, reaching 13.6%. Practically 33.4% of killed pedestrians were over 55 years. It can be concluded that old age groups should be targeted especially in road safety campaigns.

From real traffic accident records, we found that the frequency of accidents varies a lot over time in one day. Figure 2 shows the distributions of vehicle-pedestrian accidents by time of day. Normally, accidents have larger odds of occurrence from 7:00 to 19:00, with two peaks (morning peak and evening peak). Since a great number of people travel during daytime, pedestrians have higher chances of being exposed to vehicles, and the frequency of vehicle-pedestrian accidents rises correspondingly. However, the distribution of fatal ones seems much different. Comparing with daytime, pedestrians have larger odds of being killed in accidents at nighttime. Especially from evening to midnight, the frequency of fatal vehicle-pedestrian accidents is relatively high. This difference may be related to many situations, such as worse visibility, alcohol influences, tiredness after a full-day work, etc. According to above analysis on the temporal distribution, we can conclude that the fatality risk of pedestrians in accidents is higher during dark periods.

To estimate the death probability for pedestrians being hit by a vehicle at mid-blocks, a binary logit model was established. Table 3 shows the calibration results suggesting that the statistical fit (P = 0.0025) of the basic model is fairly good, with χ² statistic = 1468.61 with 15 degrees of freedom. The Hosmer-Lemeshow statistic is 0.27 (>0.05), meaning the model seems to fit well. Except for car and pedestrian crossing, most originally selected variables are significant at 5% level (Pr(>|z|) < 0.05). During model calibrating, variables with confidence level being greater than or equal to 95% were included in the specification.

As shown in Figure 3, odds ratios were calculated for significant variables. For instance, odds ratio of fatality is 4.19 times higher when pedestrians are moving at mid-blocks on a two-way divided road rather than a one-way road. The greater chances of death on divided roads probably are related to the road width. As divided roads usually have more than two lanes, pedestrians have to spend more time on crossing. Besides, intensive traffic flow also increases the risk of pedestrians getting involved in conflicts with vehicles. Some studies argued that speed is also a potential factor considering the road type, which will be examined separately in this study. In fact, a large number of multi-lane roads in Beijing are divided [37]. Unluckily, due to the detailed information about road lanes is not provided in the data, we use “divided” and “undivided” variables here to stand for multi-lane roads. Based on the analysis above, it is not surprising to find that walking across elsewhere in carriageway is riskier by 3.28 times than walking

along the roadside; however, the variable of crossing roads using crosswalks is not significant. When pedestrians are going across the carriageway, they have a higher propensity to be at fault [38]. Possibly due to the improper designing, many pedestrians were not enthusiastic about using crossing facilities [39]. Further, many pedestrians risk jaywalking somewhere at the mid-blocks for convenience as the absence of traffic safety awareness.

As expected, the risk of death is 2.95 times higher in rural areas when compared with urban areas. In general, factors affecting accident severity inside and outside urban areas are different [40] , e.g. relatively high speed of traffic flow and lacking emergency care at suburban areas. Comparing with motorcycles, the odds of pedestrians being killed are 3.02 times higher when they are hit by a light vehicle, and 5.15 times higher by a heavy vehicle. The weight of vehicles places a major role in how much damage it causes to pedestrians in collisions.

As the model revealed, lighting conditions have the largest influence on the death probability of pedestrians. The odds ratios of fatality are higher by 8.77 times in darkness without street lights, taking daylight condition as the control level. The corresponding odds ratios are 2.57 during dark hours with street lighting, and 4.61 during dusk or dawn conditions. Since speed selection behavior of drivers in reduced visibility changes with their varying driving ability, the vehicle’s speed is not always within a safe range, which contributes to the increment in the fatality risk [41].

An interesting finding is that odds of being killed are 1.52 times higher for male victims. This can be presumed that men are taking more dangerous decisions when they are moving at mid-blocks, such as entering the road without proper lookout, running across and so on. Therefore, drivers oftentimes do not have enough time to react, and male pedestrians are more likely hit by a faster vehicle. In addition, alcohol also gives some effect on this issue [42]. However, some existing studies found that female pedestrians have a higher death risk and attributed it mostly to the greater vulnerability of females than males [35] [43]. A somewhat surprising result is that normal weather is 1.98 times more risky than adverse weather. Because of the restricted visibility or even slippery roads, not only drivers drive more carefully, but also pedestrian activities are lower under adverse weather conditions [28] [44]. However, there are also some studies indicating that clear weather reduces the probability of fatal injury [26] [36].

First-degree interaction terms can be expressed as products of every two variables. As new variables, they were introduced one by one into Equation (2). For those that don’t fall within the confidence interval were excluded in the further consideration. Finally, we found three statistically significant interaction terms. After that, the binary logit model described above was re-built incorporating these interaction terms. Table 4 shows the fitting results of the final model, with three interaction terms including (Area type = rural)*(Road type = two-way divided), (Area type = rural)*(Pedestrian location = crossing elsewhere), and (Speed limit)*(Pedestrian age). The final model passes significance test (P = 0.0308), with χ² statistic = 1494.17 with 20 degrees of freedom. The Hosmer-Lemeshow goodness-of-fit test suggests that the final model also seems to fit well (0.11).

Except for those who have significant interaction terms, odds ratios of main factors in the final model (Table 4) have minor changes by comparing with the basic model. In terms of these cases, we can compare their odds ratios from two ways. For example, Figure 4 shows the interaction between area type and road type, with urban area and one-way road as the reference. Higher risk might seem to be associated with rural area type while it only occurs on one-way roads. Both of two area types are identically dangerous on divided roads, with chances of a fatal outcome being about 6 times higher. It can be concluded that divided roads are less sensitive to area types comparing with one-way roads. In other words, one-way roads on rural areas are more dangerous than those on urban areas.

The interaction between area type and pedestrian location is illustrated in Figure 5, with urban area and roadside as the reference. In general, crossing roads is more hazardous than walking along roads, and rural areas are less safe than urban areas for pedestrian traveling. To be more specific, the probability of death for crossing elsewhere in carriageway is 2.06 times higher than for walking along the roadside at urban areas. This difference is even more pronounced at rural areas. The interaction effect further leads to the odds ratio to be as high as 31.81 for pedestrians not using crosswalks at rural areas. Besides, pedestrians walking on roadsides at rural areas are at higher risk of 6.65 times than at urban areas. This can only be explained by assuming that pedestrians are more likely engaged in risky behaviors at rural areas when they are using roads.

The effect of values of continuous variables on the pedestrian’s death risk can be examined through the model Equation (1). For the age of pedestrians, three different values are defined. The model relationship between probability of death and road speed limit are shown in Figure 6. Probabilities are calculated presuming the mean value of each residual variable in the equation. It is visible that older pedestrians have a higher death probability across all values of speed limit. Under conditions of identical speed limit, the average death risk is almost 7.21 times higher for a 70-year-old pedestrian, comparing with a 20-year-old pedestrian. The corresponding odds are about 2.72 times higher for a 45-year-old pedestrian. It can be attributed to that older pedestrians are less responsive and more vulnerable. This further reflects that senior citizens are not well protected during their traveling. Some existing studies also found that fatality risk rises with pedestrian’s age increasing [44] [45].

However, the actual impact speed of vehicle moving at the accident spot is not available in this dataset. Thus, we can only explain this by supposing that the impact speed may be concerned with the posted road speed limit to some extent. Figure 6 also reveals the relationship: when the speed limit increases by 10 km/h, the fatality risk increases by about 46%. It should be noted that this increasing rate seems relatively small when compared with some existing studies [46] [47]. In this study, the model is actually on the basis of multiplicative effect of different factors. Road speed limit is more likely to be correlated with some other factors, such as area type, road type, etc. Besides, the impact speed, in general, may not be proportional to the posted speed limit. In most cases, drivers slow down when they are approaching the crosswalk and brake hard once the collision is happening soon. As a matter of that, their actual impact speed is below the road’s speed limit. With the increment in the speed limit, this difference may be widened correspondingly.