Pedestrian–vehicle crashes and analytical techniques for stratified contingency tables

Accident Analysis and Prevention 34 (2002) 205– 214 www.elsevier.com/locate/aap

Pedestrian –vehicle crashes and analytical techniques for stratified contingency tables Ali S. Al-Ghamdi College of Engineering, King Saud Uni6ersity, P.O. Box 800, Riyadh 11421, Saudi Arabia Received 18 September 2000; received in revised form 28 December 2000; accepted 3 January 2001

Abstract In 1999 there were 450 fatalities due to road crashes in Riyadh, the capital of Saudi Arabia, of which 130 were pedestrians. Hence, every forth person killed on the roads is a pedestrian. The aim of this study is to investigate pedestrian– vehicle crashes in this fast-growing city with two objectives in mind: to analyze pedestrian collisions with regard to their causes, characteristics, location of injury on the victim’s body, and most common patterns and to determine the potential for use of the odds ratio technique in the analysis of stratified contingency tables. Data from 638 pedestrian– vehicle crashes reported by police, during the period 1997–1999, were used. A systematic sampling technique was followed in which every third record was used. The analysis showed that the pedestrian fatality rate per 105 population is 2.8. The rates were relatively high within the childhood (1 –9 years) and young adult (10–19 years) groups, and the old-age groups (60– \ 80 years), which indicate that young as well as the elderly people in this city are more likely to be involved in fatal accidents of this type than are those in other age groups. The analysis revealed that 77.1% of pedestrians were probably struck while crossing a roadway either not in a crosswalk or where no crosswalk existed. In addition, the distribution of injuries on the victims’ bodies was determined from hospital records. More than one-third of the fatal injuries were located on the head and chest. An attempt was made to conduct an association analysis between crash severity (i.e. injury or fatal) and some of the study variables using chi-square and odds ratio techniques. The categorical nature of the data helped in using these analytical techniques. © 2002 Elsevier Science Ltd. All rights reserved. Keywords: Pedestrians; Fatality rate; Crash severity; Injuries; Behavior; Stratified tables

1. Introduction Motor vehicle crashes result in approximately 6000 pedestrian injuries and 1000 pedestrian deaths in the Kingdom of Saudi Arabia each year (Official Statistics, 1999). More than one-fourth of the severe crashes in this developing country are pedestrian related. During 1999, there were 450 fatalities due to road crashes in Riyadh, the capital of Saudi Arabia; of these, pedestrians accounted for 130 (29%). Hence, every fourth person killed on the roads is a pedestrian. In this city Koushki (1988) studied walking characteristics and found that the average walking distance was about 859 m, which when compared with corresponding distances in other Asian cities was fairly low (Tanaboriboon and Jing, 1999). In fact, since the oil boom in the early E-mail address: [email protected] (A.S. Al-Ghamdi).

1970s, the motorization rate in Saudi Arabia has increased dramatically (about 50-fold). The typical mode of travel in this country is the private car (MOC, 1997). However, the problem of pedestrian crashes is still increasing (Official Statistics, 1999). Pedestrian –vehicle collisions are a serious concern because of the severe nature of injuries to those who are struck by vehicles. Past research has established that pedestrians suffer very serious injuries compared with vehicle occupants. The traditional view of pedestrian traffic safety tends to place the burden of responsibility on the behavior of pedestrians and emphasizes education as the means to prevent accidents (Harruff, 1998). This view has been investigated by data from developed countries showing that educational efforts are less effective than efforts aimed at modifying the physical and social environment of the transportation system (Roberts and Coggan, 1994). In order to help prevent pedestrian accidents, it is necessary to answer questions

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about the circumstances of pedestrian accidents and the characteristics of the persons involved (Fontaine and Gourlet, 1997). This study attempts to determine the extent of pedestrian responsibility in crashes between motor vehicles and pedestrians in Riyadh. The objectives therefore are twofold: to analyze pedestrian collisions with regard to their causes, characteristics, location of injury on the victim’s body, and most common patterns and to determine the potential for the use of the odds ratio technique in the analysis of stratified contingency table. It should be said that the a certain setup for some of the study variables during the data-collection stage were prepared to be consistent with the analytical needs of stratified contingency tables, in particular, the nature of the data was categorical.

crashes were examined. A brief summary of the investigative crash records was made, and a database was constructed containing the circumstances of the crash in which the pedestrian was involved. It appeared during this stage that not all necessary data could be found in crash records. The problem with crash data in terms of completeness, clarity, and accessibility is still a major issue in this country, as previous researchers have indicated (Al-Amr et al., 1998; Al-Ghamdi, 1998). Data collection and record keeping are not computerized but are still done manually. Therefore, the study data, which had been entered manually, were obtained from archived files in the Riyadh Traffic Police Department. A systematic sampling technique was followed in which every third record was used.

3. Variables studied 2. Data collection To achieve the study objectives, 638 pedestrian– vehicle crashes in Riyadh (over the period 1997– 1999) were analyzed. Using data collected from traffic police and hospital records, some of the characteristics of these

The counts in number of victims (in each crash one victim (i.e. injury or fatality) is involved), and proportion of occurrence of the study variables related to pedestrians involved in pedestrian–vehicle crashes are summarized in Table 1, and those for the drivers in-

Table 1 Pedestrian data and 95% confidence intervals Variable

Frequency

Proportion of sample (%)

95% CI

Age 0–15 16–30 31–50 50+ Unknown

272 104 160 92 10

42.63 16.30 25.08 14.42 1.57

(0.38–0.47) (0.14–0.19) (0.22–0.29) (0.12–0.17) (0.01–0.03)

Sex Male Female

517 121

80.88 18.97

(0.78–0.84) (0.16–0.22)

Education Literate Illiterate Unknown

269 201 168

42.17 31.50 26.33

(0.39–0.46) 0.28–0.35) (0.23–0.30)

Nationality Saudi Non-Saudi Unknown

295 338 5

46.24 52.98 0.78

(0.42–0.50) (0.49–0.57) (0.003–0.019)

Social status Married Single Unknown

204 330 104

32.0 51.72 16.30

(0.28–0.36) (0.48–0.56) (0.14–0.19)

Cause Play on roads Not paying attention Crossing not at crosswalk The above two causes Pedestrian not at fault Other

36 55 225 209 98 15

5.64 8.62 35.27 32.76 15.36 2.35

(0.04–0.08) (0.07–0.11) (0.32–0.39) (0.29–0.37) (0.13–0.18) (0.01–0.04)

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207

Table 2 Driver data and 95% confidence intervals Variable

Frequency

Proportion of sample (%)

Age B18 18–20 21–30 31–40 41–50 50+ Unknown

49 94 250 151 47 31 16

7.58 14.73 39.18 23.67 7.37 4.86 2.51

(0.06–0.10) (0.12–0.18) (0.35–0.43) (0.20–0.27) (0.05–0.10) (0.03–0.07) (0.01–0.04)

Education Literate Illiterate Unknown

564 38 36

88.40 5.96 5.64

(0.86–0.91) (0.04–0.08) (0.04–0.08)

Nationality Saudi Non-Saudi Unknown

441 187 10

69.12 29.31 1.57

(0.65–0.73) (0.26–0.33) (0.01–0.03)

Social status Married Single Unknown

315 281 42

49.37 44.05 6.58

(0.45–0.53) (0.41–0.48) (0.048–0.09)

Cause Speeding Not paying attention Speeding and not paying attention Other

137 166 257 78

21.47 26.02 40.28 12.23

(0.18–0.25) (0.23–0.30) (0.37–0.44) (0.09–0.15)

volved are shown in Table 2. For those variables shown in both tables, the frequencies were sufficiently large to perform confidence-interval analyses assuming a normal distribution. It should be emphasized that the primary purpose of these initial tables was to provide an overall view of the data and to suggest variable levels or factors for further analysis.

3.1. Age, sex, and nationality The age of pedestrian victims ranges from about 2 to 67 years, with an average of 28.02 years (S.D.= 11.1). From Table 1, it can be seen that the largest proportion of victims was aged 15 years and under (42.63%). The fatality data among those victims (75 deaths out of 272 victims) also revealed that that the fatality rate (fatalities per victim) is highest for this group (27.57%), indicating that there is a need for close attention to the analysis for this age group. Fig. 1 shows the distribution of age-specific fatality rates based on the population of Riyadh (National Census, 1998). The overall fatality rate per 105 population is 2.8. The rates were lowest in the age range 20 –29 years; compared with this group, the childhood (1– 9 years) and young adult (10– 19 years) groups had slightly higher rates and the old-age groups (60– \ 80 years) had the highest rates (Fig. 1).

95% CI

Although women involved in pedestrian crashes accounted for only 18.97% of the sample (vs. 80.88% for men) and their sex is underrepresented in the city (risk index (i.e. the ratio of percent crash involvement in group to percent population in group) of 0.43 vs. 1.5 for men), their fatality rate (deaths per 105 population) is much higher than that for men, 28.93 versus 19.15%. Further analysis based on sex will be given later. It appears from the data in Table 1 that more non-Saudis were involved in pedestrian–vehicle crashes on the basis of the study sample (52.98%). To read the picture more accurately, a risk index based on the

Fig. 1. Distribution of age-specific fatality rates (deaths per 105 population).

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208 Table 3 Location of crashes

crashes in the study sample (35.31%) occurred during weak light conditions.

Roadway

Frequency

Two-way with median 382 Two-way without median 52 One way 7 Service road 9 Residential street 97 Signalized intersection 6 Unsignalized intersection 20 Freeway 52 Other 13

Proportion of sample (%) 59.88 8.15 1.10 1.41 15.20 0.94 3.13 8.15 2.04

Table 4 Age of pedestrians involved in crashes on residential streets Age group

Frequency

Proportion of sample (%)

15 and below 16–30 31–50 51 and above Unknown

54 12 25 3 3

55.67 12.37 25.78 6.18 6.18

proportion of non-Saudis in the population of this city was obtained. Accordingly, the risk index for nonSaudis is 1.6 (vs. 0.68 for Saudis), indicating that the involvement of this group in pedestrian– vehicle crashes is disproportionate to their representation in the population (they are overrepresented). In other words, nonSaudis are at much greater risk than Saudis to be involved in such crashes. It should be noted that this result is considered general because of the lack of data on unit exposure (e.g. walking distance traveled). Other characteristics are listed in Table 1.

3.2. Time of crashes For day of crash, it appears from the study data that Saturday (the first day of the week in Saudi Arabia) has the highest proportion of pedestrian– vehicle crashes (16.93%) and Friday has the least (12.07%). The weekend days in this country (Thursday and Friday) reported the lowest proportion of crashes among all days. This result is consistent with the general trend in traffic accidents for the country. Official statistics show that Saturday has the highest number of crashes (Official Statistics, 1999). From the study data, it is clear that pedestrian-related crashes were more likely during the night (52.82%). Although 56% of all traffic crashes occurred in this city during the day (Official Statistics, 1999), pedestrian crashes occurred more during the night, which can be attributed to visibility problems, particularly when it is known that more than one-third of such

3.3. Dri6er characteristics Looking at the data for drivers in Table 2, it may be noted that illegal-age drivers (under 18 years) were responsible for about 8% (significant at the 5% level) of pedestrian-related crashes. Under-age driving is a serious problem in this developing country (Official Statistics, 1999). The group with the greatest involvement in these crashes is aged 21–30 (39.18%). It is clear that the three youngest groups (30 years and under) account for more than half of the driving population (61.49%). By nationality, although non-Saudis form about one-third of the population in Riyadh, their involvement proportion as shown in Table 2 (29.31%) is less, indicating that this involvement is disproportionate to their representation in the population (the risk index is less than 1, i.e. 0.94).

3.4. Location of crashes Most pedestrian–vehicle crashes (59.88%) in this sample occurred on divided roadways where posted speed limits were fairly high (from 70 to 120 km/h), as shown in Table 3. It should be noted that divided roads in Riyadh are typically busy with business activities (i.e. very congested). This result (i.e. median roadways have higher crashes) does not seem consistent with US or European Studies. However, the study data show that more than two thirds (68.6%) of the women involved in pedestrian crashes (based on the study sample) were struck on median roadways and we know that women wear black clothing (cultural cloth), which might lead to visibility problems and hence higher crashes on this type of roadway. In short, one can say that women with their cultural clothing may over-represent the problem of such crashes on median roadways in Riyadh. Unlike results from international research, fewer crashes (less than 5%) occurred at intersections, which may be partly because pedestrians like to cross anywhere, even where no crossing is marked, and partly because of the absence of crosswalks at locations where they should be available (Al-Faraj, 1998). Residential streets account for 15.2% of victims (97 victims), the second-highest proportion. In Riyadh, no school bus system is available for public schools. Each neighborhood has at least one public school. Breaking down the 97 victims by age as shown in Table 4, it is apparent that more than half (55.67%) of the victims were 15 years old or younger, indicating the great risk for children of this age to be involved in a crash on this type of road. Another study showed that a typical mode for a school trip in residential neighborhoods is

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209

Crossing activity

Frequency

Proportion of sample (%)

within 100 m, indicating either that pedestrians are not aware enough of the danger of crossing at an unmarked place or that the crosswalk is not conveniently placed. Table 5 also reveals that discipline in crossing roads is not generally observed in Riyadh. This result is consistent with a field survey conducted by AlFaraj (1998), who studied the attitudes of pedestrians in Riyadh toward crossing facilities. He found that pedestrians were not enthusiastic about using crossing facilities (either at signalized intersections or at underpass or overpass facilities). Similar attitudes have been observed in other developing countries (Tanaboriboon and Jing, 1999). Compared with those crossing the roadway, pedestrians less commonly (less than 2%) were struck as they were walking along or just standing in the roadway or on its shoulder. This finding might be due to the typical curb design in this city, which is higher from the pavement by at least 20 cm and thus may make it less likely for a vehicle to run onto the shoulder. Of all the cases studied, 13 pedestrians (2.04% of the sample) were struck as they were working on or otherwise attending to their own stalled vehicles or providing assistance to another motorist.

Crossing roadway at crosswalk Crossing roadway not at crosswalka Crossing roadway where no crosswalk existsb No crosswalk defined

36 185

5.64 29

3.5. Vehicles in6ol6ed

307

48.12

110

17.24

walking and that children use residential roads as play areas (Al-Faraj, 1998). In Riyadh the definition of a crosswalk does not depend upon markings on the pavement, and from the data it was sometimes difficult to determine whether the pedestrian was in a marked crosswalk or not in any defined crosswalk at the time of the crash. Unfortunately, even medical examiner reports did not always make a distinction between pedestrians struck within marked crosswalks and those struck in unmarked areas. Table 5 shows that most pedestrians (77.12%) were probably struck while crossing a roadway either not in a crosswalk or where no crosswalk existed. Of those, 48.12% were crossing the roadway where no crosswalk existed within 500 m, indicating that there is an availability problem (i.e. a crosswalk is not available where it might be used). On the other hand, 29% were crossing where a crosswalk was available Table 5 Location of crossing activity

a b

Table 6 shows the types of vehicles involved in the crashes studied. Light vehicles, including passenger cars and light trucks, were responsible for 66.9 and 22.1% of the cases, respectively. Heavy vehicles (trucks and buses) and vans together accounted for 10.4% of all cases.

When marked crosswalk is available within 100 m. When no marked crosswalk is available within 300 m.

Table 6 Distribution of type of vehicle involved in crashes Vehicle type

Frequency

Proportion of sample (%)

Passenger car Light truck Van Heavy truck Bus Other/unspecified/unidentified

427 141 36 11 20 3

66.9 22.1 5.6 1.7 3.1 0.6

3.6. Causes and error distribution

Table 7 Distribution of error Error (%)

0% (not at fault) 550% \50%

Drivers

Pedestrians

Frequency

%

Frequency

%

15 319 304

2.35 50 47.65

98 251 289

15.36 39.80 45.61

More than half of pedestrian crashes (76.65%) were caused by not paying attention and by crossing the roadway without being in a crosswalk, as listed in Table 1. Overall, the proportion of crashes in which drivers were at fault accounted for more than half (47.65%) of all crashes, as listed in Table 7. This result may indicate that drivers do not yield the rightof-way properly to pedestrians, who share this rightof-way with drivers. From the pedestrians’ point of view, 45.61% were reported to be at fault (Table 7), indicating that many pedestrians do not pay attention and cross the roadway improperly, as shown from the large proportion mentioned earlier (57.68%). It seems from the two proportions (47.65 and 45.61%, of which the difference is insignificant, P-value=0.40) that drivers and pedestrians share the burden of responsibility. Although there is a problem with availability and accessibility of marked crosswalks, as discussed earlier.

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210

injury cases form a little more than one-fourth (27.65%) of all fatal cases (Fig. 3). The proportion of head injuries in fatalities (16.67%) is almost four times that in all cases (4.7%), indicating that these injuries are the most severe in pedestrian–vehicle crashes.

4. Association analysis

Fig. 2. Injury locations for severely injured victims.

In this section, an analysis of independence is performed to examine the association among some variables of interest selected on the basis of the preliminary analysis. Contingency tables were developed and the chi-square test was used. When the test showed a significant relationship (at the 5% level), the odds ratio technique was used to interpret the relationship. The odds ratio technique is commonly used in the analysis of categorical data. For illustration, a typical 2×2 table is shown (Table 8). Within Row 1, the odds that the response is in Column 1 instead of Column 2 are defined as follows (Agresti, 1990; Al-Ghamdi, 1996): V1 = Y11/(m.1 − Y11) Within Row 2, the corresponding odds are

Fig. 3. Injury locations for deaths.

V2 = Y12/(m.2 − Y12)

Table 8 2×2 table for typical categorical data Columns Rows

1 2 Totals

Y11 m.1–Y11 m.1

Totals Y12 m.2–Y12 m.2

Y1. m..–Y1. m..

a

(2)

where each number in the 2× 2 table represents a cell frequency at row i and column j and hence the estimate of the odds ratio is simply the ratio of the following two odds: „. =

V1 Y11(m.2 − Y12) = V2 Y12(m.1 − Y11)

(3)

Alternatively,

Table 9 Severity versus time of crasha

Fatality Severe injury Light injury Total

(1)

„. =

Day

Night

Total

48 189 64 301

86 175 76 337

134 364 140 638

Significant at 5% level (P-value=0.006).

3.7. Injuries and fatalities Evaluation of severe injuries in pedestrian– vehicle crashes found multiple injuries to be most common in 79.4% of all severely injured victims; 6.32% had head injuries and 4.4% pelvic fracture. In 50% of the cases, multiple injuries involved the head and neck and the trunk and in 8.24% of the cases leg injuries were involved (Fig. 2). In contrast, the most typical injuries in fatal cases were to the head (16.67%) and chest (16.67); both accounted for about one-third of all fatalities. Multiple-

p11(1−p12) p12(1−p11)

(4)

where pij is the probability of the occurrence in cell ij. The odds ratio (a nonnegative number) is also termed the cross-product ratio and the approximate relative risk (Agresti, 1990). The confidence interval for the odds ratio can be obtained as follows (Santner and Diane, 1989): „. exp[9 zh/2 |ˆ 2ln(€ˆ )]

(5)

where „. =estimate of odds ratio, |ˆ = estimated variance, and zh/2 = normal z-value at corresponding level of significance (h). Such an analysis is presented in the following subsections. 2 ln(„. )

4.1. Se6erity 6ersus time of crash Table 9 indicates the significant association (using Chi-Square testing technique) between time of crash and level of severity (P-value= 0.006). The odds of

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211

being killed in a night crash are 1.81 times those for day crashes. One can conclude from this result that visibility might be a problem in this case. It should be recalled that 35.31% of pedestrian crashes occurred in weak light conditions and more than half occurred during the night (Table 1).

higher speed. The odds of being killed when one is struck by a van are almost the same as those when struck by a passenger car. From these odds it can be said that the chance of being killed is the highest when one is struck by a light truck, followed by a heavy vehicle and then by a van versus a passenger car.

4.2. Se6erity 6ersus 6ehicle type

4.3. Se6erity 6ersus location

From Table 10, the odds of being killed when one is struck by any type of vehicle are almost the same. This result was unexpected since it is logical that heavier vehicles would result in more severe crashes. The relationship between severity and vehicle type seems not statistically significant (P-value = 0.096). Accordingly, the odds ratio analysis is not applicable for the data in Table 10. However, when injury cases (the last two rows in Table 9) are aggregated, as presented in Table 11, the association becomes significant (P-value =0.041): the odds of being killed when one is struck by a heavy vehicle (truck or bus) are almost twice (1.95) those for being struck by a passenger car. In contrast, these odds are much higher when one is struck by a light truck (2.4) versus a passenger car, perhaps because of the

When the victims (fatalities and no fatalities) are distributed by roadway type as in Table 12, several odds ratios can be obtained and interestingly interpreted. The freeway location is the reference group for the odds since it is more likely, because of high speed, that the pedestrian will be severely injured when struck on a freeway. The odds of being killed in a pedestrian– vehicle crash on a freeway are 1.88 those of being killed on a two-way roadway with a median. These odds are 4.98 and 2.3 for a two-way roadway with no median and a residential street, respectively. Hence, considering the freeway as a reference group, it can be concluded from these odds that being struck on a two-way roadway with a median becomes the most likely and dangerous situation (recall that due to visibility problems, more women involved in crashes on this type of road-

Table 10 Distribution of victims by severity and vehicle typea

Fatality Severe injury Light injury Total a

Passenger car

Van

Light truck

Heavy vehicle

Total

94 235 98 427

9 21 9 39

20 94 27 141

11 14 6 31

134 364 140 638

Insignificant at 5% level (P-value= 0.096).

Table 11 Aggregated injury levels versus vehicle typea

Fatality Injury a

Passenger car

Van

Light truck

Heavy vehicle

Total

94 235

9 21

20 94

11 14

134 364

Significant at 5% level (P-value=0.041).

Table 12 Distribution of victims by roadway type Roadway

Two-way with median Two-way without median Residential street Freeway Other

Fatality

No fatality

Frequency

Proportion of sample (%)

Frequency

Proportion of sample (%)

84 5 18 18 9

62.69 3.73 13.43 13.43 6.72

298 47 79 34 46

59.89 9.32 15.68 7.75 9.13

A.S. Al-Ghamdi / Accident Analysis and Pre6ention 34 (2002) 205–214

212 Table 13 Stratified 2×2 Tablea

Columns

Rows

a

1 2 Totals

IIs1

IIs2

Totals

Ys1 ms1–Ys1 ms1

Ys2 ms2–Ys2 ms2

Ys. ms+–Ys. ms+

Note that Ysj is Bin(msj, psj ).

Table 14 Fatalities stratified by age groupa Age (0–5) (6–10) (11–15)

Sex

Day

Night

M F M F M F

4 5 3 10 1 4 27

7 9 12 12 3 5 48

a Based on Woolf’s statistic: = d . f . = 2,h = 5% = 1.09, P-value = 0.42.

Table 15 Young victims stratified by age groupa Age (0–5) (6–10) (11–15)

Sex

Fatality

Injured

M F M F M F

37 15 87 24 35 10 208

14 11 22 15 9 3 74

a Based on Woolf’s statistic: =d . f . = 2, 0.30.

h = 5% = 0.71,

P-value=

way, as discussed previously), followed by residential streets and two-way roadways with no median.

5. Odds ratio analysis for stratified 2× 2 tables In this study, an attempt was made to analyze the data in Tables 13 and 14 using the odds ratio analysis. The setup for the data in each table is not typical for a 2 × 2 contingency table. Instead, each table consists of three 2×2 contingency tables stratified by age (one table for each age group). Some statistical methods are introduced that are useful for analyzing binary response data subject to block (strata) and treatment effects. The illustration considered throughout is that of S 2× 2 tables where the sth table consists of Ys1 successes out of ms1 trials from a binomial population IIs1 with success probability ps1 and Ys2 successes out of ms2

trials from a second binomial population IIs2 with success probability ps2, 15s5 S. (‘Strata’ and ‘block’ mean that the table can be stratified by age, race, or any other categorical variable that has two or more levels, each level of which can form one contingency table.) It is assumed that Ysj are mutually independent. The data for stratum s are presented in generic form in Table 13. In transportation applications, there are often many strata, each with a small or large number of trials. The stochastic models used with this type of data have many nuisance parameters, and special methods are required to analyze them. Two techniques are used in the following sections. The first deals with testing the homogeneity of the odds ratios among the 2×2 tables in the stratified table. Once the odds ratios are found to be homogenous, the second technique is to estimate the common odds ratio for the stratum for interpretation purposes. The two techniques are described first and then they are applied to the study data.

5.1. Homogeneity test of odds ratios The test of interest in this study is to investigate whether the data in stratified 2× 2 tables by age (Tables 14 and 15) are homogenous with respect to the odds ratios. In a statistical representation, the following hypothesis is to be tested: H0: „1 = „2 = · · ·= „s H0: „1 " „2 " · · ·" „s

versus

The likelihood ratio technique (LRT) can be used to develop a test statistic for the foregoing hypothesis (Santner and Diane, 1989). This approach requires the iterative computation of the LRT. Alternatively, a test statistic proposed by Woolf in 1955 (Santner and Diane 1989) and used in this study is described. Let „. s denote the estimated odds ratio in the sth stratum: „. =

Ys1(ms2 − Ys2) Ys2(ms1 − Ys1)

(6)

Many authors modify Eq. (6) by adding 0.5 to each Ysj and msj –Ysj. Under large strata asymptotics the empirical logits ln(„. s ) are approximately distributed as



N ln(„s ), | 2s = +

! "n

1 ms2 − Ys2 + .5

for 15 s5 S.

1 1 1 + + Ys1 + .5 Ys2 + .5 ms1 − Ys1 +.5 (7)

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On the basis of that distribution, Woolf reached the following decision rule (called Woolf’s statistic) to reject H0 if and only if



(ln „. s )2 % |ˆ s s S



!

Á %S à s = 1 ln(„. s )/|ˆ s −à à %Ss = 1(|ˆ s ) − 1 Ä

"

2

 à à ]  2h,S − 1 à Å

(8)

The Mantel– Haenszel (MH) estimator for the odds ratio can be used to estimate a common odds ratio for data in stratified tables and is given by the closed form of the following expression (Santner and Diane, 1989): S

% Ys1(ms2 −Ys2)/ms + (9)

s=1

This odds ratio gives a simple mean for interpreting all the data in the table blocks.

5.3. Application to study data Here, the foregoing Woolf and MH techniques are applied to the data presented in Tables 14 and 15. Since there are only three strata in each table, the following hypothesis is written: H0: „1 =„2 = „3

versus

groups, which is the same result obtained when the MH estimator is used. The MH estimator for the common odds can also be computed from Eq. (9). The common odds are 1.08, which is very close from, indicating that the odds for a child to be killed or injured in a pedestrian crash are almost the same regardless of sex.

6. Conclusions

5.2. Mantel– Haenszel estimator

s=1 „. nh = S % Ys2(ms1 − Ys1)/ms +

213

H0: „1 "„2 "„3

The Woolf statistic for the data in Table 14 gives a chi-square value of 1.09 and hence the corresponding P-value is 0.42. Clearly there is no evidence to suggest that the odds ratios of pedestrians involved in day or night crashes differ among sex and age combinations (the null hypothesis is accepted). The common odds ratio for the data in Table 14 is 0.624 („. mh =0.624), which indicates that the odds that a woman will be killed in a day crash are 1.6 times (1.6=1/0.624) those for a male victim. By changing the set of the table, the common odds ratio of female victim versus male victim being killed in a night crash can be obtained. This odds ratio is 1.9, indicating that the odds for a woman being killed in a night crash are about twice (1.9) those for a man. Note that 1.9 is greater than 1.6 largely because of visibility problems during the night and in particular because of the customary black worn by women (even girls of 15 years or less). Similarly, the odds ratios for the data in Table 15 seem homogenous (P-value = 0.3). That is, the odds of being killed or injured in a pedestrian– vehicle crash are almost alike among the three age groups. For the three age groups, the odds of being killed are higher among men than among women. Accordingly, the chances of being killed for men are almost alike in the three

The study provided insight into pedestrian–vehicle crashes in Riyadh. A total of 638 pedestrian-related crashes were analytically investigated. The study illustrated that young and old age groups are at a higher risk of being involved in pedestrian–vehicle crashes. Divided roadways with fairly high posted speeds and residential streets are the most likely locations for this type of crash. With respect to causes of crashes, pedestrians and drivers bear the responsibility equally for being involved in pedestrian–vehicle crashes. Not paying attention and crossing a roadway either not in a crosswalk or where no crosswalk exists are the most common causes among pedestrians. Many drivers often do not respect the right-of-way of pedestrians. The analysis technique of odds ratios (i.e. Woolf’s and Mantel–Haenszel’s) presented in this paper seems reasonable for interpreting the data in stratified contingency tables. The capabilities of this technique allow the author to describe the homogeneity of data in blocks classified by three factors at a time (e.g. age group, sex, and severity). In addition, such techniques enabled the author to compare the relative risk among the various age groups in a simple and clear manner. This analysis showed that for the young groups (15 years or less) of either sex, the likelihood of being killed is almost the same as that of being injured. The women in these groups are 1.9 times more likely to be killed in such a crash than are men. This relatively high odds ratio is partially due to the customary black clothing that women wear. The study results suggest that women should wear a reflective strip on their clothing so that they can be distinguished by drivers when the light is weak. The author suggests that a future study should be conducted to examine women’s risk in pedestrian crashes and the role of clothing in this risk. The techniques used to analyze the strata of 2×2 tables in this study appear to be useful in providing an informative interpretation of the data in such tables. One can look for different odds ratios depending on the table setup, which is based on variables of interest. The results from this study provide a better understanding of some of the risks and problems related to the age of pedestrians involved in these crashes. This knowledge could help in targeting certain age groups in the population with better designed educational and

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