--- category: literaturenote citekey: wongwouldrelaxingspeedlimits2005 title: Would relaxing speed limits aggravate safety? authors: "Wong, S.C.; Sze, N.N.; Lo, Hong K.; Hung, W.T.; Loo, Becky P.Y." year: 2005 date: 2005-00-00 2005 doi: 10.1016/j.aap.2004.09.008 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2004.09.008" zotero_key: XGAPNGQE zotero_storage: DIEA2AEU collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Wong, S.C." status: converted --- ![](_page_0_Picture_0.jpeg) Accident Analysis and Prevention 37 (2005) 377–388 ![](_page_0_Picture_2.jpeg) # Would relaxing speed limits aggravate safety? A case study of Hong Kong S.C. Wonga,∗, N.N. Szea, Hong K. Lob, W.T. Hungc, Becky P.Y. Lood a *Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China* b *Department of Civil Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, P.R. China* c *Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, P.R. China* d *Department of Geography, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China* Received 30 June 2004; received in revised form 8 September 2004; accepted 9 September 2004 #### **Abstract** This paper studies the effect of the changed speed limits on accident counts for major roadways in the urban environment of Hong Kong. In 1999–2002, the speed limits of a number of sections of roadway were reviewed and increased. Nineteen of them were major roadways. Their speed limits were raised by 10–20 km/h from 50 to 70 km/h. Before and after studies were carried out to investigate the changes in accident counts with respect to the set of carefully chosen comparison groups. Qualification tests for these comparison groups were conducted to confirm their suitability for the studies. In the majority of the treatment sites, the accident counts were worse after the increase in speed limits, both for the category of fatal, serious and slight (FSS) accidents, and for the category of fatal and serious (FS) accidents. Overall, the relaxation of the speed limit from 50 to 70 km/h increased the FSS accident counts by 15% and the FS accident counts by 1%. The relaxation of the speed limit from 70 to 80 km/h increased the FSS accident counts by 18% and the FS accident counts by 36%. © 2004 Elsevier Ltd. All rights reserved. *Keywords:* Road safety; Speed limit; Accident counts; Before and after study; Treatment group; Comparison group #### **1. Introduction** No one would dispute that excessive speed is an important factor in road accidents, both in terms of their number and severity. Defining precisely what "excessive speed" means, however, is not as easy as it seems. It is recognized that speed limits play an important role. In fact, the relationship between speed limits and speed has been well studied ([Wilmot and](#page-11-0) [Khanal, 1999; McCarthy, 2001\).](#page-11-0) In general, lowering (raising) the speed limit decreases (increases) the average speed, but the change in the speed limit does not incur the same change in average speed. Generally, the latter is only one half to one-quarter of the former. However, it is contended that accidents are not only associated with absolute speed, but also, and perhaps more importantly, with speed disper- *E-mail address:* hhecwsc@hkucc.hku.hk (S.C. Wong). sion [\(West and Dunn, 1971; Lave, 1985\). T](#page-11-0)he impact of speed limits on speed dispersion, unfortunately, does not seem to have a definitive trend. For example, in Arizona, after a rise in the speed limit on the rural interstates from 55 to 65 mph, an increase in speed dispersion was observed ([Upchurch and](#page-11-0) [Rahman, 1989\),](#page-11-0) but the average speed and speed variance were negatively correlated when the nationwide data on all highways in the United States was examined ([TRB, 1984\).](#page-11-0) Other studies have shown that the speed variance remains unchanged despite an increase in average speed. As far as traffic accidents are concerned, a great number of studies have pointed to the increase in fatalities on these high-speed freeways when speed limits were relaxed [\(Garber](#page-11-0) [and Graham, 1990; Baum et al., 1991; Godwin, 1992; Chang](#page-11-0) [et al., 1993; Rock, 1995; Farmer et al., 1999; Ossiander and](#page-11-0) [Cummings, 2002; Vernon et al., 2004](#page-11-0)). However, the relationship between speed limits, speed, speed dispersion, and traffic accidents is understandably complex. A host of issues enter into consideration. One important issue is driver ∗ Corresponding author. Tel.: +86 852 2859 2668; fax: +86 852 2559 5337. Table 1 Some examples of the effect of speed limit changes | Speed limit changes | Effect | |---------------------------------|------------------------------------------------------------------------------------------------------------------| | Motorways: from 110 to 100 km/h | Accident count fell 18% in the short term and 14% in the long term | | Motorways: from 120 to 100 km/h | The number of casualties fell 4% and the severity of accidents fell 11.5% | | Motorways: from 120 to 100 km/h | Accidents involving casualties fell 10% on motorways and 11% on main roads | | | Outside built-up areas: from 90 to 80 km/h
Main roads: from 100 to 80 km/h
Main roads: from 100 to 80 km/h | compliance to the speed limit, which is related to their perception of the "reasonableness" of the speed limit vis-a-vis ` the design speed of the road facility (that is based on engineering and sight-distance considerations). An "unreasonably" low speed limit may increase the speed differentials between law-abiding drivers and drivers who believe that exceeding the speed limit does not constitute an increased accident and injury risk to themselves and others. Therefore, the notion that lowering the speed limit automatically leads to a lower accident rate is somewhat questionable. However, lowering the speed limit from 50 to 30 km/h in urban and residential areas in many Scandinavian countries did reduce the number of road fatalities, as well as serious and slight injuries. The types of road facilities, their geometric designs, and the extent of traffic interactions, among other factors, also enter into the relationship between speed limit, speed, and accident rate. An important illustrative example is that local streets and roads have the highest fatality rates even though they have the lowest speed limits ([USDOT, 1995\),](#page-11-0) because the volume of vulnerable road users, such as pedestrian and cyclist, is higher. In contrast, the road fatality rates on the interstate highways are much lower despite their higher speed limits. Nevertheless, because of the greater speed outside the built-up area, the accident severity index (e.g., killed/100 person injury accidents) is considerably higher than that inside the built-up area. Indeed, many studies have been conducted on the effect of speed limits on accident counts and accident rates for highways with high design speeds of around 100 km/h. Some of the results, as excerpted from [ECMT](#page-11-0) [\(1996\),](#page-11-0) are shown in Table 1. As for roadways in built-up areas, according to the [ECMT](#page-11-0) [\(1996\)](#page-11-0) report, European countries such as Belgium, France, Hungary, and Spain lowered their speed limits from 60 to 50 km/h in the 1990s. The end result was reductions in the number of accidents and fatalities, such as 5 and 10% reductions, respectively, for Switzerland, especially on major roads with low to medium traffic densities. Nevertheless, the report also stated that "the speed limit should be consistent with the traffic conditions and that a higher but more appropriate speed does not systematically have an adverse impact on road safety". One example was that in 1960 an increase of the speed limit in Greater London to 40 mph did not increase the number of accidents. In fact, the number of accidents fell in Kent [\(ECMT, 1996\).](#page-11-0) Although the effects of speed limits on traffic accident for high-speed roads are quite well established, their effects on highways in urban environments are less conclusive. Hong Kong offers the rare opportunity to revisit the effect of speed limits on accident counts for major roadways in an urban environment. During 1999–2002, in response to the public suggestions including professional drivers and various groups in the trade, together with her own initiatives, the Transport Department raised the speed limits on a number of roadway sections in Hong Kong. Nineteen were major roadways, the speed limits of which were raised by 10–20 km/h from 50 to 70 km/h. The rest were highways with higher speed limits that are not of concern in this study, or with incomplete information for analysis. Based on the accident counts in the "before" and "after" periods, we determine whether the increases in the speed limits had any effect on accident counts. We take great care in establishing the comparison group for this before and after study, as detailed in Section 2. For each treatment site, we estimate the accident count that would have occurred had the treatment (in this case, relaxing the speed limit) not been applied, and compare this with the observed accident count after the treatment was applied. #### **2. Accident data for the analysis** The 19 treatment sites, which form the context of this study, are major urban roadway sections with original speed limits of 50–70 km/h. These road sections are given in[Table 2,](#page-2-0) and their locations are shown in [Fig. 1. T](#page-3-0)he analysis is based on the annual accident statistics of the Transport Department and the Hong Kong Police Force from 1991 to 2003. The data contain the details of each traffic accident, including severity, speed limit, time of accident, number of vehicles involved, weather, road surface, and number of lanes. The question is whether relaxing the speed limits results in more or less accidents of different severity levels. From the accident record, the accident counts of different severity levels for each of the treatment sites before and after the change in speed limit are known. One should not, however, directly compare these before and after accident counts, because other factors may have occurred between the before and after periods that have safety implications. An example is that the accident counts might have been already following some sort of trend before the change in speed limit, possibly due to changes in traffic flow, vehicle performance, etc. [\(Wong et](#page-11-0) [al., 2004\).](#page-11-0) Hence, the direct before and after accident counts Table 2 The 19 road sections with speed limit changes in this study | No. | Road sections | Speed limit change (km/h) | Implement date | |-----|-------------------------------------------|---------------------------|----------------| | 1 | Castle Peak Road (KWC) – North Bound | 50→70 | December, 2000 | | 2 | Castle Peak Road (KWC) – South Bound | 50→70 | December, 2000 | | 3 | Kwun Tong Road – West Bound | 50→70 | April, 2001 | | 4 | Lung Cheung Road – East Bound | 50→70 | May, 1999 | | 5 | New Clear Water Bay Road – Kowloon Bound | 50→70 | May, 1999 | | 6 | New Clear Water Bay Road – Sai Kung Bound | 50→70 | May, 1999 | | 7 | Princess Margaret Road – North Bound | 50→70 | April, 1999 | | 8 | Princess Margaret Road – South Bound | 50→70 | April, 1999 | | 9 | Tai Chung Kiu Road – East Bound | 50→70 | January, 2001 | | 10 | Tai Chung Kiu Road – West Bound | 50→70 | January, 2001 | | 11 | Ting Kok Road – Tai Mei Tuk Bound | 50→70 | January, 2001 | | 12 | Ting Kok Road – Tai Po Bound | 50→70 | January, 2001 | | 13 | West Kowloon Corridor – South Bound | 50→70 | March, 1999 | | 14 | Lion Rock Tunnel Road – East Bound | 70→80 | October, 1999 | | 15 | Lion Rock Tunnel Road – West Bound | 70→80 | October, 1999 | | 16 | Tuen Mun Road – Kowloon Bound | 70→80 | May, 1999 | | 17 | Tuen Mun Road – NT Bound | 70→80 | May, 1999 | | 18 | Yuen Long Highway – San Tin Bound | 70→80 | May, 1999 | | 19 | Yuen Long Highway – Tuen Mun Bound | 70→80 | May, 1999 | could be attributable to the a priori trend and not necessarily due to the speed limit change [\(Hauer, 1997\).](#page-11-0) To estimate the difference in the effect on safety between the before and after periods, it is essential to predict what the accident counts of the sites would have been had the treatment (or the speed limit change in this case) not been applied. To do so, for each treatment group, one needs to select a comparison group that did not receive the treatment but its historical accident record has been similar to the treatment group. In establishing the base for estimating the difference in accident counts between the before and after periods, we exercise great care in selecting the comparison group. In this study, as each speed limit relaxation was only implemented over a section of the road, the comparison group was selected by choosing the remaining part on the corresponding road that did not receive the speed limit relaxation. In this way, the traffic volume and pattern between the treatment site and the comparison group would be similar, hence neutralizing the possible effect of other factors that might have affected accident counts. Nevertheless, for each treatment group we conduct thorough statistical tests to ensure that the treatment site and its corresponding comparison group are indeed similar in terms of accident counts, as discussed below. ### **3. Qualification tests for the comparison group** The validity of a comparison group to the corresponding treatment group is assessed through an odds ratio test. Consider the following notation: | | Treatment group | Comparison group | |--------|-----------------|------------------| | Before | K, k, κ | M, m, µ | | After | L, l, λ | N, n, ν | where*K*, *L*, *M*, and*N*are the corresponding observed accident counts, *k*, *l*, *m*, and *n* are the corresponding random variables, and κ, λ, µ, and ν are the corresponding expected values. We further assume that the accident counts follow a Poisson distribution. Hence, we have *E*(*k*) = Var(*k*) = κ, *E*(*l*) = Var(*l*) = λ, *E*(*m*) = Var(*m*) =µ, and *E*(*n*) = Var(*n*) = ν. Moreover, *K* is an estimator for *E*(*k*) and Var(*k*), *L* is an estimator for *E*(*l*) and Var(*l*), etc. Let π be the expected accident counts on the treatment group that would have been occurred had the treatment not been applied, and *i* be the corresponding random variable. Let *r*c = ν/µ be the ratio of the expected accident counts for the comparison group; *r*t = π/κ be the ratio for the corresponding treatment site; ω = *r*c/*r*t = νκ/πµ be the odds ratio. For the comparison group to be a good candidate for this comparison group (CG) method, we require that the odds ratio is equal to 1. Note that the random variable π is not directly observable, referring as it does to the accident counts for the treatment group had the treatment not been applied. Before estimating the accident changing factor for the treatment group in the after period, we perform qualification tests on the odds ratios for the 19 road sections. Both the [Hauer \(1997\)](#page-11-0) and [Allsop \(1995\)](#page-11-0) approaches are used to analyze the historical data (8 years before the treatment date) to ascertain whether the odds ratio is equal to 1. Only those highway sections that pass both hypothesis tests are selected and considered for further analysis. #### *3.1. The Hauer approach* For the comparison group to be considered as a good candidate for the CG method, we require that the odds ratio $$\omega = \frac{r_{\rm c}}{r_{\rm t}} = \frac{\nu \kappa}{\pi \mu} \tag{1}$$ ![](_page_3_Figure_2.jpeg) Fig. 1. The locations of the road sections on which the speed limits were relaxed. to be equal to 1. To ascertain whether this hypothesis holds true between the treatment group and the corresponding comparison group, we use the historical time series data before the treatment as a basis for the significance test. As the expression for the odds ratio is not linear, an unbiased estimator for the mean can be determined by ([Hauer, 1997\),](#page-11-0) $$\hat{\omega} = \frac{NK}{IM} \left( 1 + \frac{1}{I} + \frac{1}{M} \right)^{-1} \tag{2}$$ and the unbiased estimator for the variance is $$\hat{s}_{\omega}^{2} = \left(\frac{NK}{IM}\right)^{2} \left(\frac{1}{N} + \frac{1}{K} + \frac{1}{I} + \frac{1}{M}\right) \left(1 + \frac{1}{I} + \frac{1}{M}\right)^{-2} \tag{3}$$ Suppose that the following data were obtained in the past *P* periods (in this study, we use 2 years for each period). | Period | Treatment group | Comparison group | |--------|-----------------|------------------| | 1 | K1 | M1 | | 2 | K2 | M2 | | | | | | p | Kp | Mp | | p + 1 | Kp
+ 1 | Mp
+ 1 | | | | | | P | KP | MP | We consider period *p* as the "before" period and *p* + 1 as the "after" period, by which we compute the estimator of the average odds ratio (assuming Poisson distribution) for each period as $$\hat{W}_p = \frac{M_{p+1}K_p}{K_{p+1}M_p} \left( 1 + \frac{1}{K_{p+1}} + \frac{1}{M_p} \right)^{-1}$$ (4) Because there are a total of *P* − 1 sample points, the expected value and variance of the sample mean of the odds ratio (including the temporal effect over the periods and the randomness of accident counts in accordance with the Poisson distribution) can be determined by $$\bar{W} = \frac{1}{P-1} \sum_{p=1}^{P-1} \hat{W}_p \tag{5}$$ and $$s_{\bar{W}}^2 = \frac{1}{(P-1)} \left\{ \frac{1}{(P-2)} \left( \sum_{p=1}^{P-1} \hat{W}_p^2 - (P-1)\bar{W}^2 \right) \right\}$$ (6) Therefore, the comparison group is not considered to be a good candidate if W <¯ 1 − 1.96sW¯ or W >¯ 1 + 1.96sW¯ at the significance level of 5%. If that happens, then another comparison group, if any, should be used. In this study, we deselect the treatment site from further analysis. #### *3.2. The modified Allsop approach* In the Hauer approach we can encounter the problem that the lower limit of the critical value becomes negative if the variance of the odds ratio is large. This outcome is not possible in reality. To overcome this problem, we adopt the Allsop approach with a logarithm transformation ([Allsop, 1995\).](#page-11-0) By defining the auxiliary variable *y* = ln ω, we have $$y = \ln \omega = \ln \nu + \ln \kappa - \ln \pi - \ln \mu \tag{7}$$ Using the random variable *n* as an example, we take Taylor's series expansion of ln *n* around the expected value ν and neglect higher order terms, $$\ln n = \ln v + \frac{1}{v}(n-v) - \frac{1}{2v^2}(n-v)^2$$ (8) Taking expectation on both sides, $$E(\ln n) = \ln \nu + \frac{1}{\nu} E(n - \nu) - \frac{1}{2\nu^2} E(n - \nu)^2$$ $$= \ln \nu - \frac{\text{Var}(n)}{2\nu^2} = \ln \nu - \frac{\nu}{2\nu^2}$$ $$= \ln \nu - \frac{1}{2\nu} = \ln \nu \left(1 - \frac{1}{2\nu \ln \nu}\right)$$ (9) The expectation is applied to represent the repeated applications of such an estimation procedure in all future studies. Even if all of the conditions remain the same, it is clear that this estimation procedure (i.e., using ln *n* to estimate ln ν)*systematically underestimates* the target value, ln ν, which we want to estimate, because (1 − 1/(2ν ln ν)) < 1 for ν > 1. To correct for this factor, an unbiased estimator for ln ν should read estimator (ln $$\nu$$ ) = (ln $N$ ) $\left(1 - \frac{1}{2N \ln N}\right)^{-1}$ (10) The main difference with the work that was reported by [Allsop \(1995\)](#page-11-0) is that a correction term (1 − 1/(2N ln N))−1 is applied to the logarithm estimate to adjust for the systematic bias in the long run. It follows that the unbiased estimator for the auxiliary variable *y* can be determined by $$\hat{y} = (\ln N) \left( 1 - \frac{1}{2N \ln N} \right)^{-1} + (\ln K) \left( 1 - \frac{1}{2K \ln K} \right)^{-1} - (\ln I) \left( 1 - \frac{1}{2I \ln I} \right)^{-1} - (\ln M) \left( 1 - \frac{1}{2M \ln M} \right)^{-1}$$ (11) Following the same logic as in the Hauer approach, by considering period *p* as the "before" period and *p* + 1 as the "after" period we can compute the estimator of the transformed | Tab
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39 | 1.1
61 | Pas
sed | – | 0.0
17 | 0.1
66 | 0.0
91 | −0
.14
7 | 0.1
47 | Pas
sed | Pas
sed | Odds ratio cannot be determined because the observed number of accident counts in one of the denominators of the equation is zero. Yuen Long Highway was opened in 1993, and no accident records were available before their openings. Table 4Results of the odds ratio tests for FS accidents | | ch
Ha
uer
app
roa | | | | | | | | difi
ed
All
ch
Mo
sop
app
roa | | | | | | | |----------------------------------------------------------------------------|-------------------------------|-------------------|-------------------|------------------------------------------------------|------------------------------------|--------------------------------|--------------------------------|-------------------|----------------------------------------------------|----------------|----------------|----------------|-----------|------------------------|------------------------| | | Od
ds r
atio
, W | | | Co
nfid
lim
it
Od
ds r
atio
ent | | Od
ds r
atio
(
log | Co
nfid
lim
it
ent | | Od
ds r
atio | | | | | | | | | iod
Per
1–2 | iod
Per
2–3 | iod
Per
3–4 | Me
an | test
Lo
Up
we
r
per | iod
Per
1–2 | iod
Per
2–3 | iod
Per
3–4 | Me
an | Lo
we
r | Up
per | test | | | | | 50
70
km
/h
→ | | | | | | | | | | | | | | | | | tle
k R
oad
Cas
Pea
(KW
C)
– N
/B | 0.5
88 | 0.4
71 | 0.8
33 | 0.6
31 | 0.7
91 | 1.2
09 | d
No
t pa
sse | 0.0
00 | −0
.19
2 | 0.1
92 | 0.0
00 | −0
.21
8 | 0.2
18 | sed
Pas | d
No
t pa
sse | | Cas
tle
Pea
k R
oad
(KW
C)
– S
/Ba | 1.6
00 | – | 0.0
00 | – | – | – | Un
defi
ned | – | – | – | – | – | – | Un
defi
ned | Un
defi
ned | | Kw
Ton
Ro
ad
– W
/B
un
g | 1.7
46 | 0.7
50 | 0.1
71 | 0.8
89 | 0.0
99 | 1.9
01 | Pas
sed | 0.7
61 | 0.0
01 | −1
.06
0 | −0
.09
9 | −1
.03
5 | 1.0
35 | Pas
sed | Pas
sed | | Ch
ad
Lun
Ro
– E
/B
g
eun
g | 0.9
21 | 0.8
50 | 6.0
00 | 2.5
90 | −2
.34
0 | 4.3
42 | sed
Pas | 0.0
10 | −0
.01
1 | 1.9
03 | 0.6
34 | −1
.24
4 | 1.2
44 | sed
Pas | sed
Pas | | Ne
w C
lea
r W
Ba
Ro
ad
– K
ln/B
a
ater
y | 0.0
00 | – | 0.6
00 | – | – | – | Un
defi
ned | – | – | – | – | – | – | Un
defi
ned | Un
defi
ned | | Ne
w C
lea
r W
Ba
Ro
ad
– S
K/B
a
ater
y | 0.0
00 | – | – | – | – | – | Un
defi
ned | – | – | – | – | – | – | Un
defi
ned | Un
defi
ned | | Pri
ss M
t R
oad
– N
/B
nce
arg
are | 0.6
59 | 0.4
03 | 1.0
08 | 0.6
90 | 0.6
56 | 1.3
44 | Pas
sed | −0
.25
0 | −0
.72
2 | 0.1
90 | −0
.26
1 | −0
.51
6 | 0.5
16 | Pas
sed | Pas
sed | | Pri
ss M
t R
oad
– S
/B
nce
arg
are | 0.0
90 | 2.2
00 | 0.2
63 | 0.8
51 | −0
.32
6 | 2.3
26 | Pas
sed | −2
.03
0 | 1.0
32 | −1
.03
2 | −0
.67
7 | −1
.76
7 | 1.7
67 | Pas
sed | Pas
sed | | Tai
Ch
Kiu
Ro
ad
– E
/B
ung | 2.5
00 | 1.7
37 | 0.3
39 | 1.5
25 | −0
.24
0 | 2.2
40 | Pas
sed | 1.1
23 | 0.7
12 | −0
.53
0 | 0.4
35 | −0
.97
4 | 0.9
74 | Pas
sed | Pas
sed | | /Ba
Tai
Ch
Kiu
Ro
ad
– W
ung | 0.7
41 | 0.7
62 | 0.1
47 | 0.5
50 | 0.6
05 | 1.3
95 | No
d
t pa
sse | 0.0
00 | – | – | – | – | – | Un
defi
ned | Un
defi
ned | | Tin
Ko
k R
oad
– T
MT
/Ba
g | 0.8
00 | 0.2
35 | 2.4
00 | 1.1
45 | −0
.27
1 | 2.2
71 | Pas
sed | 0.1
05 | – | – | – | – | – | Un
defi
ned | Un
defi
ned | | Tin
Ko
k R
oad
– T
P/B
g | 1.3
04 | 0.2
13 | 0.8
54 | 0.7
90 | 0.3
79 | 1.6
21 | Pas
sed | 0.4
91 | −0
.93
6 | 0.1
41 | −0
.10
1 | −0
.84
1 | 0.8
41 | Pas
sed | Pas
sed | | We
st K
loo
n C
ido
S/B
ow
orr
r – | 0.2
41 | 0.3
38 | 1.5
61 | 0.7
13 | 0.1
68 | 1.8
32 | Pas
sed | – | −0
.76
1 | 0.6
93 | – | – | – | Un
defi
ned | Un
defi
ned | | 70
80 k
m/h
→ | | | | | | | | | | | | | | | | | Lio
ock
nel
ad
/B
n R
Tun
Ro
– E | 0.3
48 | 0.8
24 | 0.7
50 | 0.6
40 | 0.7
10 | 1.2
90 | d
No
t pa
sse | −0
.49
6 | 0.3
04 | 0.0
48 | −0
.04
8 | −0
.46
3 | 0.4
63 | sed
Pas | d
No
t pa
sse | | Lio
n R
ock
Tun
nel
Ro
ad
– W
/Ba | – | – | 0.0
00 | – | – | – | Un
defi
ned | – | – | – | – | – | – | Un
defi
ned | Un
defi
ned | | Tue
n M
Ro
ad
– K
ln/B
un | 0.8
16 | 1.6
01 | 0.6
86 | 1.0
34 | 0.4
39 | 1.5
61 | Pas
sed | −0
.26
7 | 0.3
12 | 0.1
90 | 0.0
78 | −0
.34
6 | 0.3
46 | Pas
sed | Pas
sed | | ad
T/B
Tue
n M
Ro
– N
un | 0.7
16 | 1.2
85 | 1.1
44 | 1.0
48 | 0.6
65 | 1.3
35 | sed
Pas | −0
.13
9 | 0.5
24 | −0
.32
4 | 0.0
20 | −0
.50
5 | 0.5
05 | sed
Pas | sed
Pas | | b
Yue
n L
Hig
hw
– S
T/B
ong
ay | – | 0.8
38 | 0.6
54 | 0.7
46 | 0.8
19 | 1.1
81 | No
d
t pa
sse | – | −0
.01
9 | −0
.26
1 | −0
.14
0 | −0
.23
7 | 0.2
37 | Pas
sed | No
d
t pa
sse | | Bb
Yue
n L
Hig
hw
– T
M/
ong
ay | – | 1.3
55 | 1.3
75 | 1.3
65 | 0.9
80 | 1.0
20 | No
d
t pa
sse | – | 0.5
24 | 0.5
37 | 0.5
31 | −0
.01
3 | 0.0
13 | No
d
t pa
sse | No
d
t pa
sse | Odds ratio cannot be determined because the observed number of accident counts in one of the denominators of the equation is zero. Yuen Long Highway was opened in 1993, and no accident records were available before their openings. variable *y* for a sample point (period) as $$\hat{Y}_{p} = (\ln M_{p+1}) \left( 1 - \frac{1}{2M_{p+1} \ln M_{p+1}} \right)^{-1}$$ $$+ (\ln K_{p}) \left( 1 - \frac{1}{2K_{p} \ln K_{p}} \right)^{-1}$$ $$- (\ln K_{p+1}) \left( 1 - \frac{1}{2K_{p+1} \ln K_{p+1}} \right)^{-1}$$ $$- (\ln M_{p}) \left( 1 - \frac{1}{2M_{p} \ln M_{p}} \right)^{-1}$$ $$(12)$$ As there are a total of *P* − 1 sample points, the expected value and variance of the sample mean of the transformed variable *y* can be determined by $$\bar{Y} = \frac{1}{P-1} \sum_{p=1}^{P-1} \hat{Y}_p \tag{13}$$ and $$s_{\bar{Y}}^2 = \frac{1}{P-1} \left\{ \frac{1}{P-2} \left( \sum_{p=1}^{P-1} \hat{Y}_p^2 - (P-1)\bar{Y}^2 \right) \right\}$$ (14) Assuming that the sample mean is normally distributed around ln (1) = 0, the limits for the significance level of 5% are ±1.96sY¯ . Therefore, the comparison group is not considered to be a good candidate if Y <¯ −1.96sY¯ or Y >¯ 1.96sY¯ . If that happens, then another comparison group, if any, should be used. In this study, we deselect the treatment site from further analysis. #### *3.3. Odds ratio test results* In each of the Hauer and modified Allsop approaches, we separate accident counts into two categories: fatal, serious and slight (FSS) accidents, and fatal and serious (FS) accidents. The fatal and serious accidents are combined for the latter category, because the number of fatal accidents on the road sections is very small for the statistical analyses in this study. In Hong Kong, the total number of fatal accidents for the whole city was about 200 each year in the past decade [\(Wong et al., 2002, 2004; Allsop, 2005\). T](#page-11-0)aking advantage of the historical accident records, we calculate the odds ratios for the three transitions, from period 1 to 2, period 2 to 3, and period 3 to 4. Each period has a length of 2 years. For example, if the treatment was applied in 1999, then we consider the transitions from 1991–1992 to 1993–1994, 1993–1994 to 1995–1996, and 1995–1996 to 1997–1998. The mean odds ratio of each road is then compared to the confidence limits for reaching a decision about the hypothesis tests. The null hypothesis that the odds ratio is equal to 1 is rejected if the mean odds ratio falls outside the confidence limits. Accordingly, the comparison group is considered to have failed the odds ratio test. [Tables 3 and 4](#page-5-0) show the qualification test results of the individual sites for FSS and FS accidents, respectively. To ensure the quality of the analysis, in the subsequent analysis of the before and after comparison, we only consider the road sections that pass both tests. For FSS accidents as shown in [Table 3, 1](#page-5-0)5 out of 19 road sections pass the Hauer qualification test, and 15 road sections pass the modified Allsop test. The set of road sections that pass the Hauer test is very similar to that pass the modified Allsop test. Nine road sections on which the speed limits have changed from 50 to 70 km/h pass both tests, and five road sections on which the speed limits have changed from 70 to 80 km/h pass both tests. These cases were used for the before and after comparison. For FS accidents, due to the lower accident counts, a smaller number of road sections pass the qualification tests. From [Table 4, 1](#page-6-0)0 out of 19 road sections pass the Hauer qualification test, and 11 road sections pass the modified Allsop test. Similar to FSS accidents, the set of road sections that pass the Hauer test is more or less the same as that passes the modified Allsop test. Six road sections on which the speed limits have changed from 50 to 70 km/h pass both tests, and two road sections on which the speed limits have changed from 70 to 80 km/h pass both tests. These cases were used for the before and after comparison. #### **4. Accident count estimation** #### *4.1. Accident count without treatment* Ideally, the number of accidents that would have occurred had treatment not been applied can be estimated by $$\pi = r_{\mathsf{t}}\kappa \tag{15}$$ The ratio *r*t is not known. However, as shown in the previous section, the odds ratios of the treatment sites selected are close to 1. Therefore, π can be estimated by $$\pi = \left(\frac{r_{\rm c}}{\omega}\right)\kappa = \left(\frac{\nu}{\omega\mu}\right)\kappa\tag{16}$$ The unbiased estimator for π is $$\hat{\pi} = \frac{NK}{M} \left( 1 + \frac{1}{M} + \text{Var}(\omega) \right)^{-1} \tag{17}$$ and $$\hat{s}_{\pi}^{2} = \left(\frac{NK}{M}\right)^{2} \left(\frac{1}{N} + \frac{1}{K} + \frac{1}{M} + \text{Var}(\omega)\right)$$ $$\times \left(1 + \frac{1}{M} + \text{Var}(\omega)\right)^{-2}$$ $$= \hat{\pi}^{2} \left(\frac{1}{N} + \frac{1}{K} + \frac{1}{M} + \text{Var}(\omega)\right)$$ (18) as *E*(ω) ≈ 1 by the hypothesis test. We note that Var(ω) – the variance of the individual odds ratio – should not be equal to s2 W¯ , which is only the variance of the sample mean of the odds ratio. To filter off the randomness effect of the accident counts on the variance of the odds ratio, we use the following formula ([Hauer, 2004;](#page-11-0) Appendix A), $$s_W^2 = \frac{1}{P-2} \left( \sum_{p=1}^{P-1} \hat{W}_p^2 - (P-1)\bar{W}^2 \right) - \frac{1}{P-1} \sum_{p=1}^{P-1} s_{W_p}^2$$ (19) which represents the variance of the odds ratio, to be estimated from the historical data, excluding the randomness effect of accident counts, and $$s_{W_p}^2 = \left(\frac{M_{p+1}K_p}{K_{p+1}M_p}\right)^2 \left(\frac{1}{K_p} + \frac{1}{K_{p+1}} + \frac{1}{M_p} + \frac{1}{M_{p+1}}\right) \times \left(1 + \frac{1}{K_{p+1}} + \frac{1}{M_p}\right)^{-2}$$ (20) represents the part due to the randomness (Poisson distribution) of accident counts. Substituting Eq. (19) into Eqs. [\(17\)](#page-7-0) and [\(18\)](#page-7-0) (i.e., taking Var(ω) ≈ s2 W ), the estimates of πˆ and sˆ2 π are obtained. These estimates are modified from the formulae that are provided in [Hauer \(1997\),](#page-11-0) in which we remove the bias due to the odds ratio when estimating the value of π in Eq. [\(16\)](#page-7-0) and extend to the case of multiple transitions. #### *4.2. Estimation of the accident changing factor* We can now estimate the accident changing factor, which is defined as $$\theta = \frac{\lambda}{\pi} \tag{21}$$ The mean and variance of the accident changing factor can be estimated by $$\hat{\theta} = \frac{L}{\hat{\pi}} \left( 1 + \frac{\hat{s}_{\pi}^2}{\hat{\pi}^2} \right)^{-1} \tag{22}$$ and $$\hat{s}_{\theta}^{2} = \frac{L^{2}}{\hat{\pi}^{2}} \left( \frac{1}{L} + \frac{\hat{s}_{\pi}^{2}}{\hat{\pi}^{2}} \right) \left( 1 + \frac{\hat{s}_{\pi}^{2}}{\hat{\pi}^{2}} \right)^{-2} \tag{23}$$ where πˆ and sˆ2 π are determined by Eqs. [\(17\)](#page-7-0) and [\(18\), r](#page-7-0)espectively. From these results, we can show that the treatment has led to a reduction in accident counts by 100(1 − ˆ θ)%, with a standard derivation of ±100sˆθ%. Moreover, with the assumption of a normal distribution, we can say that the treatment is effective if θ < 1 − 1.645sˆθ at the 5% level of significance. #### *4.3. Estimation of the pooled accident changing factor* [Hauer \(2004\)](#page-11-0) raised some concerns about the null hypothesis significance testing for individual sites, in which it was argued that the interpretations of results might be blurred by the noise associated with the small samples in individual sites. This might lead to misinterpretation of results. To address [Hauer \(2004\)](#page-11-0) concerns, we also conducted the pooled analysis to ascertain our findings. The estimation of pooled accident changing factor follows the work in [Hauer \(1997\).](#page-11-0) The pooled (average) accident changing factor is obtained by $$\hat{\Theta} = \frac{\sum L}{\sum \hat{\pi}} \left( 1 + \frac{\sum \hat{s}_{\pi}^2}{\left(\sum \hat{\pi}\right)^2} \right)^{-1} \tag{24}$$ and the variance of the pooled accident changing factor by $$\hat{s}_{\Theta}^2 = \left(\frac{\sum L}{\sum \hat{\pi}}\right)^2 \left(\frac{1}{\sum L} + \frac{\sum \hat{s}_{\pi}^2}{\left(\sum \hat{\pi}\right)^2}\right) \left(1 + \frac{\sum \hat{s}_{\pi}^2}{\left(\sum \hat{\pi}\right)^2}\right)^{-2}$$ (25) where the quantities that are associated with the individual sites are obtained from Sections [4.1 and 4.2,](#page-7-0) and the summation is applied to the set of treatment sites that are pooled together for the analysis. #### *4.4. Discussions of results* For each selected treatment site, the accident counts that would have occurred had treatment not been applied and the corresponding accident changing factor were determined. Assuming a normal distribution, the hypothesis about the effectiveness of each treatment was set at the 5% level of significance. That is, the treatment (or speed limit relaxation) was effective if it was able to reduce accident counts at the specified confidence level. The results of the individual sites that pass both Hauer and modified Allsop qualification tests are shown in [Table 5. F](#page-9-0)or FSS accidents, after the relaxation of speed limit from 50 to 70 km/h, four out of the nine sites show a reduction in accident count, but only the result of Princess Margaret Road – Southbound is significant at 5% level of significance. For the relaxation of speed limit from 70 to 80 km/h, two out of the five sites show a reduction in accident count, but only the result of Lion Rock Tunnel Road – Westbound is significant at 5% level of significance. Overall, the treatment is not effective in almost all of the sites, i.e. the relaxation of speed limits does not reduce the accident count, except for the two sites that are mentioned above. To the contrary, 8 out of the 14 sites (more than half) show an increase in accident count. For FS accidents, after the relaxation of speed limit from 50 to 70 km/h, four out of the six sites show a reduction in accident count, but only the results of Kwun Tong Road – Westbound and Princess Margaret Road – Northbound are significant at 5% level of significance. For the relaxation of speed limit from 70 to 80 km/h, one out of the two sites show a reduction in accident count, but it is not significant at 5% level of significance. Overall, the treatment is not effective in a great proportion (six out of eight) of the sites. Three sites show an increase in accident count. | ing
ang | | | | | | | | | | | | | |----------------------------------------------------------------------------|------------------------------------------------------|------------------------------------------------------|-----------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------|-----------------------------------------------------------------------|------------------------------------------------------|------------------------------------------------------|-----------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------|-------------------------------|--|--| | | Fat
al +
ser | iou
sli
ht
s +
g | (
FS
S)
ide
nts
acc | | Fa
tal
eri
s (
FS
) a
cci
den
ts
+ s
ou | | | | | | | | | | Ob
ved acc
ser
ide
nt
L
nt,
cou | ted acc
Ex
pec
ide
nt
nt,
cou
π | tim
d a
cci
den
Es
ate
t
ˆθ
cha
ing
fac
tor
ng
, | ria
of
ide
Va
nt
nce
acc
ˆ2θ
cha
ing
fac
tor
ng
, s | Tre
atm
ent | Ob
ved acc
ser
ide
nt
L
nt,
cou | ted acc
Ex
pec
ide
nt
nt,
cou
π | tim
d a
cci
den
Es
ate
t
ˆθ
cha
ing
fac
tor
ng
, | ria
of
ide
Va
nt
nce
acc
ˆ2θ
cha
ing
fac
tor
ng
, s | Tre
atm
ent | | | | 50
70
km
→ | | | | | | | | | | | | | | /h Ca
stle
Pe
ak
Ro
ad
(
KW
C)
– N
/B | 4 | 3.5 | 0.7
86 | 0.4
35 | No
t ef
fec
tiv
e | | | | | | | | | stle
ak
ad
Ca
Pe
Ro
(
KW
C)
– S
/B | 4 | 1.5 | 1.4
29 | 2.2
79 | t ef
fec
tiv
No
e | | | | | | | | | ad
/B
Kw
To
Ro
– W
un
ng | 22 | 12
.3 | 1.5
78 | 0.4
45 | t ef
fec
tiv
No
e | 4 | 6.8 | 0.3
33 | 0.1
14 | Eff
ive
ect | | | | Ch
ad
/B
Lu
Ro
– E
ng
eun
g | | | | | | 15 | 1.0 | 8.7
22 | 59
.82
8 | t ef
fec
tiv
No
e | | | | w C
lea
ad
ln/
Ne
r W
r B
Ro
– K
B
ate
ay | | | | | | | | | | | | | | Ne
w C
lea
r W
r B
Ro
ad
– S
K/B
ate
ay | | | | | | | | | | | | | | Pri
ss M
t R
oad
– N
/B
nce
arg
are | | | | | | 2 | 9.3 | 0.1
57 | 0.0
21 | Eff
ive
ect | | | | Pri
ss M
t R
oad
– S
/B
nce
arg
are | 14 | 35
.1 | 0.3
64 | 0.0
22 | Eff
ive
ect | 4 | 5.5 | 0.3
96 | 0.1
72 | No
t ef
fec
tiv
e | | | | Tai
Ch
Kiu
Ro
ad
– E
/B
un
g | 24 | 12
.6 | 1.7
33 | 0.4
31 | No
t ef
fec
tiv
e | 6 | 2.5 | 1.5
79 | 1.6
44 | No
t ef
fec
tiv
e | | | | Tai
Ch
Kiu
Ro
ad
– W
/B
un
g | 27 | 16
.3 | 1.4
04 | 0.4
33 | No
t ef
fec
tiv
e | | | | | | | | | Tin
Ko
k R
oad
– T
MT
/B
g | 26 | 15
.9 | 1.1
53 | 0.6
13 | No
t ef
fec
tiv
e | | | | | | | | | Tin
Ko
k R
oad
– T
P/B
g | 14 | 13
.3 | 0.8
55 | 0.2
25 | No
t ef
fec
tiv
e | 4 | 6.0 | 0.4
35 | 0.1
48 | No
t ef
fec
tiv
e | | | | We
st K
loo
n C
ido
S/B
ow
orr
r – | 17 | 17
.9 | 0.7
46 | 0.1
85 | No
t ef
fec
tiv
e | | | | | | | | | 70
80
km
→ | | | | | | | | | | | | | | /h Lio
n R
ock
Tu
el R
oad
– E
/B
nn | | | | | | | | | | | | | | Lio
n R
ock
Tu
el R
oad
– W
/B
nn | 39 | 68
.3 | 0.3
31 | 0.0
82 | Eff
ive
ect | | | | | | | | | Tu
Mu
n R
oad
– K
ln/
B
en | 17
4 | 98
.5 | 1.7
03 | 0.1
25 | No
t ef
fec
tiv
e | 55 | 29
.1 | 1.5
25 | 0.6
02 | No
t ef
fec
tiv
e | | | | oad
Tu
Mu
n R
– N
T/B
en | 12
9 | 12
7.0 | 0.9
06 | 0.1
06 | t ef
fec
tiv
No
e | 30 | 28
.6 | 0.9
58 | 0.1
18 | t ef
fec
tiv
No
e | | | | Hi
hw
Yu
Lo
– S
T/B
en
ng
g
ay | 55 | 22
.1 | 2.3
22 | 0.4
86 | t ef
fec
tiv
No
e | | | | | | | | | Hi
hw
M/
Yu
Lo
– T
B
en
ng
g
ay | 31 | 19
.5 | 1.4
46 | 0.2
71 | t ef
fec
tiv
No
e | | | | | | | | *Note*: The shaded cells are cases that do not pass the qualification tests. Table 6 Results of the pooled accident changing factors | | | Fatal + serious + slight (FSS) accidents | | Fatal + serious (FS) accidents | | | | | | |-------------------------------------------------------|------------|------------------------------------------|---------|--------------------------------|------------|---------|--|--|--| | | 50→70 km/h | 70→80 km/h | Overall | 50→70 km/h | 70→80 km/h | Overall | | | | | Number of treatment sites | 9 | 5 | 14 | 6 | 2 | 8 | | | | | Pooled number of accident counts (observed) | 152 | 415 | 567 | 35 | 85 | 120 | | | | | Pooled number of accident counts (estimated) | 128 | 335 | 463 | 31 | 58 | 89 | | | | | Pooled estimated accident changing factor | 1.154 | 1.177 | 1.189 | 1.005 | 1.359 | 1.287 | | | | | Variance of pooled estimated accident changing factor | 0.045 | 0.074 | 0.043 | 0.149 | 0.178 | 0.097 | | | | | Probability of reduction in accident count (%) | 23.3 | 25.8 | 18.2 | 49.5 | 19.7 | 17.9 | | | | | Probability of increase in accident count (%) | 76.7 | 74.2 | 81.8 | 50.5 | 80.3 | 82.1 | | | | To avoid the possible misinterpretation of results that might be blurred by the noise associated with the small samples in individual sites. We conducted the pooled estimations as mentioned in Section [4.3.](#page-8-0) Table 6 summarizes the results of the pooled analysis: - From 50 to 70 km/h, the estimated accident changing factors are 1.154 for FSS accidents, and 1.005 for FS accidents. - From 70 to 80 km/h, the estimated accident changing factors are 1.177 for FSS accidents, and 1.359 for FS accidents. - Combining the results for all of the selected sites, the estimated accident changing factors are 1.189 for FSS accidents, and 1.287 for FS accidents. This implies that in relaxing the speed limit from 50 to 70 km/h the accident counts went up by 15% with a standard deviation of ±21% for FSS accidents, and 1% with a standard deviation of ±39% for FS accidents. The probability of reduction (increase) in accident count was 23.3% (76.7%) for FSS accidents, and 49.5% (50.5%) for FS accidents. In relaxing the speed limit from 70 to 80 km/h, the accident counts went up by 18% with a standard deviation of ±27% for FSS accidents, and 36% with a standard deviation of ±42% for FS accidents. The probability of reduction (increase) in accident count was 25.8% (74.2%) for FSS accidents, and 19.7% (80.3%) for FS accidents. The adverse impact on road safety for the relaxation of speed limit from 70 to 80 km/h was greater than that from 50 to 70 km/h. In addition, the variance of the accident changing factor for the FS accidents was greater than that for the FSS accidents. Overall, the accident counts increased by 19% with a standard deviation of ±21% for FSS accidents, and 29% with a standard deviation of ±31% for FS accidents. The probability of reduction (increase) in accident count was 18.2% (81.8%) for FSS accidents, and 17.9% (82.1%) for FS accidents. It is also interesting to note that the accident changing factor for FS accidents is less than that for FSS when the speed limit is relaxed from 50 to 70 km/h, whereas the reserve is observed when the speed limit is relaxed from 70 to 80 km/h. This is probably because in the former case a more homogeneous speed distribution could be achieved and in the latter case it encouraged a much higher travel speed. Notwithstanding the large variances of the pooled accident changing factors, it is quite clear that the probability of increase in accident count is noticeably greater than that of decrease at the treatment sites when their speed limits are relaxed. This provides useful evidence to argue that the relaxation of speed limit does have an adverse impact on road safety. However, whether this was due to a shift in accident occurrences from other lower speed roads to the treatment sites as traffic was attracted by their higher speeds – the [Lave](#page-11-0) [and Elias \(1994\)](#page-11-0) contention about the US experience – is yet to be explored. Nevertheless, Hong Kong did witness a drop in overall accident counts within this period despite the speed limit changes ([Wong et al., 2004\)](#page-11-0). An investigation of this would be an interesting extension to this present study. Moreover, the analyses of the accident rates (e.g., killed/million veh-km) and accident severity (e.g., killed/100 person injury accidents) are worth exploring. # **5. Conclusion** This study took advantage of the recent speed limit relaxation on 19 road sections in Hong Kong, and analyzed its impact on accident counts. By using the comparison group method, we estimated the accident counts that would have occurred had treatment not been applied, and determined the corresponding accident changing factors. We took great care in ensuring the validity of the comparison groups that were chosen by subjecting them to both the Hauer and the modified Allsop qualification tests on the odds ratios. Only sites that passed both tests were used in the analysis. The results show that after the relaxation of speed limits the accident counts went up by about 20–30% after all other possible factors were neutralized by the comparison group method, which is consistent with the European experience. Judging from the statistical results, there is useful evidence to argue that the relaxation of speed limit does have an adverse impact on road safety. ## **Acknowledgements** We gratefully acknowledge the Transport Department of the Hong Kong Special Administrative Region (HKSAR) Government for providing the traffic accident data for the research work that is reported in this paper. We would also like to thank Mr. T.F. Leung, Mr. Macro Lo and Mr. Dominic Wong of the Transport Department for their help on this research. The views expressed in this paper are those of the authors and do not represent those of the HKSAR Government. The research was supported by an Outstanding Young Researcher Award 2000 from the University of Hong Kong. #### **References** - Allsop, R.E., 1995. Road Safety Engineering. Notes for a Short Course, Department of Civil Engineering, The University of Hong Kong. - Allsop, R.E., 2005. Some traffic safety implications of movement of goods by road. 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