Combination of policy measures: Linearity, synergy and substitution effects on road safety

Transcription

1 Combination of policy measures: Linearity, synergy and substitution effects on road safety RA-MOW B.B. Nambuusi, E. Hermans, T. Brijs Onderzoekslijn Beleidsorganisatie en -monitoring DIEPENBEEK, STEUNPUNT MOBILITEIT & OPENBARE WERKEN SPOOR VERKEERSVEILIGHEID

2 Documentbeschrijving Rapportnummer: Titel: RA-MOW Combination of policy measures Ondertitel: Linearity, synergy and substitution effects on road safety Auteur(s): B.B. Nambuusi, E. Hermans, T. Brijs Promotor: G. Wets Onderzoekslijn: Beleidsorganisatie en -monitoring Partner: Universiteit Hasselt Aantal pagina s: 24 Projectnummer Steunpunt: 7.3 Projectinhoud: Ontwikkeling van een rekenmodel voor de verkeersveiligheidseffecten van maatregelen in Vlaanderen. Uitgave: Steunpunt Mobiliteit & Openbare Werken, december Steunpunt Mobiliteit & Openbare Werken Wetenschapspark 5 B 3590 Diepenbeek T F E info@steunpuntmowverkeersveiligheid.be I

3 Samenvatting Er bestaan talrijke verkeersveiligheidsplannen die een verzameling van maatregelen voorstellen. Om de effecten van zulke plannen op verkeersveiligheid te schatten, zijn methodes vereist die rekening houden met het gecombineerde effect van verkeersveiligheidsmaatregelen. Dit rapport stelt drie methodes voor om de gecombineerde effecten te kwantificeren van verkeersveiligheidsmaatregelen die rond dezelfde tijd geïntroduceerd worden: de accident modification factor methode (Smeed, 1949), de dominant common residuals methode (Elvik, 2009) en de synergiemethode (voorgesteld in dit rapport). Op basis van een aantal studies die de effecten van een set van verkeersveiligheidsmaatregelen hebben onderzocht, wordt de kwaliteit van de methodes bepaald. Alle methodes bleken de data met voldoende precisie te beschrijven. De methode van accident modification factor is de meest voorkomende manier om het effect van meerdere maatregelen te modelleren. De term accident modification factor verwijst naar het aandeel resterende ongevallen nadat een maatregel is doorgevoerd. Deze methode schat dat het eerste orde effect van een maatregel onafhankelijk is van de eerste orde effecten van alle andere maatregelen en onveranderd blijft wanneer andere maatregelen worden doorgevoerd. (Het eerste orde effect is het effect dat een maatregel heeft wanneer het de enige maatregel met een effect is en al het overige onveranderd blijft.) Deze methode veronderstelt dat maatregelen onafhankelijk zijn en berekent het lineaire effect ervan. Het resultaat van deze methode wordt vergeleken met de resultaten geschat op basis van de dominant common residuals methode en van de synergiemethode. Als het gecombineerde effect van maatregelen groter of kleiner is dan de som van hun individuele effecten, is er niet langer sprake van lineariteit. Een groter effect wijst op synergie terwijl een kleiner effect substitutie inhoudt. In de echte wereld zijn effecten van maatregelen die gelijktijdig geïmplementeerd worden niet altijd volledig onafhankelijk. Maatregelen kunnen bepaalde risicofactoren beïnvloeden waar andere maatregelen ook op gericht zijn en dus hun mogelijke impact reduceren. Zo blijkt bijvoorbeeld reflecterend materiaal voor voetgangers minder effectief te zijn op goed verlichte wegen dan op onverlichte wegen; of maken systemen die wijzen op het gebruik van de gordel zodra de auto start, andere maatregelen gericht op een hogere gordeldracht minder effectief (Elvik, 2009). Om dit in rekening te brengen, wordt de dominant common residuals methode voorgesteld. Het basisprincipe van deze methode is dat de meest effectieve maatregel in een set, de andere maatregels in bepaalde mate domineert, door gedeeltelijk of geheel dezelfde groep van ongevallen of dezelfde risicofactoren te beïnvloeden. De berekening in deze methode gelijkt op die in de accident modification factor methode behalve dat het product van de accident modification factors verheven wordt tot de macht van de accident modification factor van de meest effectieve maatregel in de set. Deze methode resulteert in een kleinere schatting van het gecombineerde effect vergeleken met de accident modification factor methode en geeft het substitutie-effect aan. Anderzijds bestaan er maatregelen die elkaar versterken. Vaa et al. (2009) bijvoorbeeld concludeerden dat verkeersveiligheidscampagnes in combinatie met extra handhaving kon geassocieerd worden met sterker verminderde ongevallenaantallen. Dit wordt in rekening gebracht in de synergiemethode. In dit geval wordt het product van de accident modification factors verheven tot de inverse van de accident modification factor van de meest effectieve maatregel in de set. Het gecombineerde effect dat op die manier geschat wordt, is groter dan het effect berekend aan de hand van de accident modification factor methode en wijst op synergie. Naast het voorstellen van de drie methodes, bevat dit rapport een case study. Door middel van de case study worden de verschillende fases van het rekenmodel geïllustreerd. Meer informatie over het rekenmodel werd gegeven in Nambuusi et al. (2009). Dit model vertrekt van de regionale verkeersveiligheidsverkenner ontwikkeld Steunpunt Mobiliteit & Openbare Werken 3 RA-MOW

4 door Reurings en Wijnen (2008). Het aantal letselongevallen dat bespaard wordt wanneer een bepaalde set van maatregelen wordt doorgevoerd en daarbij andere beïnvloedende factoren in rekening brengende (bijvoorbeeld de groei in blootstelling) wordt berekend. Voor illustratiedoeleinden worden een aantal mogelijke maatregelen uit de literatuur doorgerekend. In het huidige rapport wordt het rekenmodel aangepast om het gecombineerde effect van een set van maatregelen die mogelijk afhankelijk zijn van elkaar, te kunnen berekenen. Met andere woorden, naast het toepassen van de accident modification factor methode (en de veronderstelling dat alle maatregelen onafhankelijk zijn), worden de dominant common residuals methode en de synergiemethode geïntegreerd in het rekenmodel. Meer bepaald wordt in de case study, de dominant common residuals methode toegepast in 2004, de synergiemethode in 2006 en de accident modification factor methode in Aan de hand van de case study wordt het uitgebreide rekenmodel geïllustreerd. Dit rapport bepaalt waardevolle methodes die gebruikt kunnen worden om het gecombineerde effect van verkeersveiligheidsmaatregelen te schatten. Welke methode er dient toegepast te worden op een bepaalde set van maatregelen hangt af van het type relatie tussen hen. Met andere woorden, voorafgaande kennis over welke maatregelen elkaar versterken, verzwakken of onafhankelijk zijn, is nodig alvorens de methodes toe te passen. In de toekomst zullen de drie methodes (de accident modification factor methode, de dominant common residuals methode en de synergiemethode) gebruikt worden om de impact op verkeersveiligheid van maatregelen uit het Verkeersveiligheidsplan Vlaanderen in te schatten. Steunpunt Mobiliteit & Openbare Werken 4 RA-MOW

5 English summary Road safety plans comprising several road safety measures have been developed throughout the world. To estimate the effects of such plans on road safety, methods that consider the combined effect of road safety measures are required. This report presents three methods for quantifying the combined effects of several road safety measures introduced around the same time: the accident modification factor method (Smeed, 1949), the dominant common residuals method (Elvik, 2009) and the synergy model (suggested in this report). Based on a few studies that investigated the effects of a set of road safety measures, the goodness of fit of the methods is assessed. All methods are found to describe the data with sufficient precision. The method of accident modification factor is the most common one for modelling the effect of a set of measures. The term accident modification factor refers to the proportion of accidents that remain after a measure has taken place. This method assumes that the first order effect of a measure is independent of the first order effects of any other measures and remains unchanged when introducing other measures. (The first order effect is the effect that each measure has when it is the only measure having an effect and everything else is unchanged.) This method assumes measures to be independent and computes their linear effect. The result gained from this method will be compared to the results estimated by means of the dominant common residuals method and the synergy model. If the combined effect of measures is larger or smaller than the sum of their individual effects, there is departure from linearity. A larger effect reflects synergy while a smaller one exhibits substitution. In the real world, effects of measures implemented simultaneously are not always entirely independent. Measures are likely to influence some of the risk factors at which other measures also aim, thus reducing their likely effects. For instance, pedestrian reflective devices will be less effective on well lit roads than on unlit roads; seat belt ignition interlocks will render any other measure designed to increase seat belt wearing less effective (Elvik, 2009). To account for this, the dominant common residuals method is proposed. The basic idea underlying this method is that the most effective measure in a set dominates the others to some extent, by partly or fully influencing the same group of accidents or the same risk factors. The computation in this method resembles that in the accident modification factor method, except that the product of the accident modification factors is raised to the power of the accident modification factor for the most effective measure included in the set. This method results into a smaller estimate of the combined effects compared to the accident modification factor method and depicts the substitution effect. On the other hand, some measures reinforce each other. For example, Vaa et al. (2009) found that a combination of road safety campaigns and increased enforcement could be associated with more reduced accident counts. This is taken into account using the synergy model. In this case, the product of the accident modification factors is raised to the inverse of the accident modification factor of the most effective measure in the set. The combined effect estimated then is larger than the effect computed using the accident modification factor method and depicts synergy. Apart from presenting the three methods, a case study is carried out in this report. By means of the case study, the different stages of the computational model are illustrated. More information on the computational model can be found in Nambuusi et al. (2009). This model starts from the regional road safety explorer (RRSE) model developed by Reurings and Wijnen (2008). The number of injury accidents saved when applying a particular set of measures, and taking into account other factors influencing road safety (e.g. the growth in traffic performance) is computed. For means of illustration, possible measures from literature are used. Steunpunt Mobiliteit & Openbare Werken 5 RA-MOW

6 In the current report, the computational model is adjusted in order to be able to assess the combined effect of a set of measures which might be dependent of one another. In other words, apart from only applying the accident modification factor method (and assuming all measures to be independent), the dominant common residuals method and the synergy model are integrated in the computational model. More specifically, in the case study, the dominant common residuals method is applied in 2004, the synergy model in 2006 and the accident modification factor method in Through this case study, the extended computational model is illustrated. This report identifies valuable methods that can be used to estimate the combined effect of road safety measures. Which method to apply on a particular combination of measures will depend on the kind of relationship between them. In other words, prior knowledge of whether the measures reinforce each other, weaken each other or be independent of each other is necessary before applying the methods. In the future, the three methods (the accident modification factor method, the dominant common residuals method and the synergy model) will be utilized to assess the road safety impact of measures listed in the road safety plan for Flanders. Steunpunt Mobiliteit & Openbare Werken 6 RA-MOW

7 Table of contents 1. INTRODUCTION Objective of the report Organization of the report 9 2. METHODS ESTIMATING THE COMBINED EFFECTS OF ROAD SAFETY MEASURES The accident modification factor method The dominant common residuals method The synergy model Goodness of fit of the methods CASE STUDY The reference year Baseline prognosis Baseline risk for injury accidents Baseline traffic performance Baseline injury accidents Measure prognosis Computing the effectiveness of measures The assessed measures NUMBER OF INJURY ACCIDENTS SAVED Computing the effectiveness of a single measure Computing the effectiveness of more than one measure Overview of injury accidents saved DISCUSSION, CONCLUSION AND FUTURE RESEARCH REFERENCES Steunpunt Mobiliteit & Openbare Werken 7 RA-MOW

8 1. I N T R O DUCTION Road safety policy is frequently associated with several road safety measures implemented around the same time, causing potential interactions between them. Interaction refers to a situation where the effect of one independent variable on the dependent one depends on the levels of the other independent variable (Kutner et al., 2005). If the effect of the interaction of the measures is larger or smaller than the sum of their individual effects, there is interaction on a linear scale or departure from linearity (Kutner et al., 2005; Knol et al., 2007; Rothman, 2002; Hosmer and Lemeshow, 1992). In this research, the independent variables are the road safety measures while the dependent one is an indicator of road safety, that is, the number of injury accidents. Given the occurrence of sets of measures, it is practical to evaluate the interaction effects of measures as opposed to the often assumed independent nature of their contributions to road safety. In general, the combined effect of road safety measures is estimated by multiplying the accident modification factors. The term accident modification factors refers to the proportion of accidents that remain after a measure has taken place. This method has been proposed by Smeed (1949). This method assumes that the effectiveness of one road safety measure is independent of the effectiveness of any other measure it is combined with and remains unchanged when other road safety measures are introduced. In reality, effects will not be entirely independent. One would expect interactions between some measures when implemented simultaneously (e.g. Elvik, 2009). For instance, pedestrian reflective devices will be less effective on well lit roads than on unlit roads; seat belt ignition interlocks will render any other measure designed to increase seat belt wearing less effective (Elvik, 2009). In a study assessing policy instruments in injury accidents, Eger III (2006) demonstrated that increasing law enforcement personnel and alcohol prohibition enforce each other to reduce the number of injury accidents. Besides, Vaa et al. (2009) found that a combination of road safety campaigns and increased enforcement with respect to seatbelt usage is associated with more reduced accident counts. Furthermore, the longterm campaign to wear safety belts and issuing tickets to violators in North Carolina resulted in an improved seat belt usage rate and a measurable decline in motor vehicle injuries (Solomon et al., 2004). Such interactions are not taken into account by most current models, and only the individual effects of the measures are considered. The hypothesis is that measures affect road safety independently. To address this research gap, interactions will be taken into account in the computational model presented in Nambuusi et al. (2009). Specifically, emphasis will be focussed on: synergism (the total effect exceeding the sum of the individual effects), substitution (the total effect being less than the sum of the individual effects) and linearity (the total effect being equal to the sum of the individual effects). Linearity will be taken into account using the independent accident modification factors (Smeed, 1949). Substitution will be modelled using the dominant common residuals method (Elvik, 2009). Synergism will be estimated using a modified version of the dominant common residuals method, termed the synergy model (suggested in this report). 1.1 Objective of the report The objective of this report is to present and discuss some appropriate methods for estimating the combined effects of several road safety measures introduced around the same time. Further, the goodness of fit of the three methods for estimating the combined effects of measures the accident modification factor method, the dominant common residuals method and the synergy model is evaluated empirically. Finally, a case study is carried out in which the extended computational model (incorporating all three possible methods for assessing the combined effect of a set of measures) is applied to obtain valuable estimates of road safety impacts. Steunpunt Mobiliteit & Openbare Werken 8 RA-MOW

9 1.2 Organization of the report First, each method estimating the combined effects of road safety measures is demonstrated using an example in Section 2. Also, the goodness of fit of the methods is compared in this section. Second, a case study is carried out in Section 3. In this case study, the independence of two measures is taken into account using the accident modification factor method in 2009; the interaction of measures is accounted for by means of the dominant common residuals method in 2004 and the synergy model in The outcomes in terms of the number of injury accidents saved are discussed in Section 4. Finally, the Discussion, Conclusion and Future research are presented in Section 5. Steunpunt Mobiliteit & Openbare Werken 9 RA-MOW

10 2. M E T H O D S E ST I M A T I N G T H E C O M B I N E D E F F E C T S O F R O A D SAFETY MEASURES Suppose automatic warnings of queues with variable signs and congestion warning signals are introduced. Automatic warnings of queues with variable signs reduce injury accidents involving rear-end collisions by 22% and the second measure reduces injury accidents involving rear-end collisions by 16% (Elvik and Vaa, 2004). What is the combined effect on injury accidents involving rear-end collisions after introducing the two measures? In theory, a number of methods can be imagined for estimating the combined effects of road safety measures. In practice, the most commonly used is the accident modification factor method described in the successive section. 2.1 The accident modification factor method This method assumes that the first order effect of a measure is independent of the first order effect of any other measure it is combined with and remains unchanged on introducing other measures. The first order effect is the effect each measure has when it is the only measure having an effect and everything else is unchanged (Elvik, 2003). The accident modification factor method is proposed by Smeed (1949) and can be illustrated as follows: Let the effect of the n th measure be denoted by E n and the number of injury accidents involving rear-end collisions before implementing the two measures by I. Then, after applying the two measures, I is reduced to I*(1-E 1 )(1-E 2 ). 1-E n is the modification factor for measure n. The modification factor is the expected proportion of the injury accidents remaining after the measure is applied. In the given example, 78% of the injury accidents involving rear-end collisions remain after the measure that reduces these accidents by 22% is implemented. 84% of the injury accidents involving rear-end collisions remain after the measure that reduces these accidents by 16% is taken. Therefore, in this example, the combined effect of the two measures is estimated as follows: Combined effect = 1 - [(1-E 1 )(1-E 2 )] = 1 - [(1-0.22)(1-0.16)] = 1 - (0.78*0.84) = = The combined effect of the two measures is an accident reduction of about 34%. Because measure effects are assumed independent, the linear effect of measures is estimated. The result of the dependence methods (i.e. the dominant common residuals method and the synergy model) will be compared with this result. If the combined effect estimated by any of the two dependence methods is larger or smaller than the linear effect, there is interaction on a linear scale or departure from linearity. A larger effect reflects synergy while a smaller one exhibits substitution (Kutner et al., 2005 and Knol et al., 2007). In practice, measure effects will often not be entirely independent. It is possible for measures to influence some of the risk factors that other measures also aim at, thus reducing their expected effects. To account for this, the product of the accident modification factors is raised to the power of the accident modification factor of the most effective measure in the measure set (Elvik, 2009). This method is referred to as the dominant common residuals method and will be illustrated in the succeeding section. Steunpunt Mobiliteit & Openbare Werken 10 RA-MOW

11 2.2 The dominant common residuals method The term residuals refers to the accidents that remain after a measure has taken effect (so this is the same as the modification factor). The basic idea underlying this method is that the most effective road safety measure in a set to some extent dominates the others, by partly or fully influencing the same group of accidents or the same risk factors. Implementing some measures reduces the effect of the others as some of the accidents are already avoided by other measures and one accident can only be avoided once. In the given example, the accident modification factor for the most effective measure is Thus, for the case of the two measures, the dominant common residuals method estimates a combined effect of: Combined effect = 1 - [(1-0.22)(1-0.16)] (1-0.22) = 1 - [(0.6552) (0.78) ] = = The combined effect of the two measures becomes 28% as compared to 34% when applying the accident modification factor method. This indicates a smaller combined effect of the two measures reflecting the substitution effect of the measures. Although various evaluation studies (Elvik, 2009; 2007) have found a number of measures weakening each other, several researchers (Vaa et al., 2009; Elvik and Vaa, 2004; Eger III, 2006; Solomon et al., 2004) indicate that some measures reinforce each other. This is taken into account using the synergy model in the following section. 2.3 The synergy model In literature, almost no research has been done to identify a method for estimating the synergy effects of road safety measures. In this study, synergy will be modelled by raising the product of the accident modification factors to the inverse of the accident modification factor of the most effective measure in the set. Various functions were tested and this one fitted the data best. The synergy model has no theoretical rationale; its plausibility is empirically based. Using the example of the two measures, the synergy model estimates a combined effect of: Combined effect = 1 - [(1-0.22)(1-0.16)] (1/1-0.22) = 1 - [(0.6552) (1/0.78) ] = = The combined effect of measures estimated using the synergy model is larger than the linear effect. This condition depicts the synergy effect of measures. Even though the methods are demonstrated using two measures, they can be extended to as many measures as possible. It should be noted that none of the three methods is proposed here for estimating the combined effect of automatic warnings of queues with variable signs and congestion warning signals. The two measures are used for the purpose of demonstrating the methods. Next, the goodness of fit of each of the methods is determined. 2.4 Goodness of fit of the methods Having illustrated the three methods, the next question is: how well do the three methods describe the data? The goodness of fit of the three methods is examined using the squared correlation coefficient (Kutner et al., 2005) on data taken from five studies Steunpunt Mobiliteit & Openbare Werken 11 RA-MOW

12 (Bali et al., 1978; Brüde and Larsson, 1985; Bach and Jørgensen, 1986; Kulmala, 1995; Gitelman et al., 2001). The study by Bali et al. (1978) is about the effects of various road markings. This study was cross-sectional and compared accident rates at locations that had different combinations of road marking treatments. The second was a before-after study which controlled for regression to the mean and long term trends. In this study, Brüde and Larsson (1985) assessed 10 different treatments at each junction. The study by Bach and Jørgensen (1986) refers to treatments taken at signalized junctions and allows comparison of the effects of 1 and 2 treatments. It was a before- after study controlling for long-term trends. The study by Kulmala (1995) evaluated a number of treatments at junctions. The empirical Bayes method was used to control for regression to the mean and long term trends. Finally, the study of Gitelman et al. (2001) was a before-after design utilizing the empirical Bayes technique to evaluate a number of treatments at junctions. The study controlled for regression to the mean and long term trends. Additional information about the studies can be found in Elvik (2009). In Elvik (2009) these five studies were used to estimate the combined effect of measures based on the accident modification factor method and the dominant common residuals method. In order to fairly assess the fit of the synergy model we use the same data set here. Additionally, studies that have empirically evaluated the combined effect of introducing more than one road safety measure (influencing the same group of accidents) are rare. When assessing how good a model is in describing the data, the use of correlations is very common. The methods are compared by means of the squared correlation coefficients between the weighted measure effects and the measure effects estimated using the methods. The estimates of the effect are weighted in inverse proportion to the sampling variance of the individual estimates; such weights ensure that the variance of the weighted mean estimate is minimized. Table 1 contains the results on the fit of the three methods. The results indicate that all methods fit the data almost equally well. Table 1: Squared correlation coefficients of the accident modification factor method, the dominant common residuals method and the synergy model Method Squared correlation coefficients Accident modification factor 0.64 Dominant common residuals 0.62 Synergy model 0.67 The results imply that in case the measures are independent of each other, weaken each other or reinforce each other, the corresponding method describes their fit well. In other words, the correlation is used as a test of goodness of fit. It is the correlation between the predicted measure effects by the method (accident modification factor method, dominant common residuals method or the synergy model) and the measure effects estimated from the observed number of accidents. It is shown that for example the accident modification factor method explains 64% of the variation in the observed number of accidents. Steunpunt Mobiliteit & Openbare Werken 12 RA-MOW

13 3. C A SE STUDY This section discusses the three methods in a case study using the computational model described in Nambuusi et al. (2009). This model based on the regional road safety explorer (RRSE) model developed by Reurings and Wijnen (2008) assists regions in assessing the road safety effects of a set of measures on a broader area and in selecting measures resulting in the most efficient cost-benefit ratios. The model consists of five stages: the reference situation, the baseline prognosis, the measure prognosis, the number of saved injury accidents (and/or casualties) and the cost-benefit analysis. The reference situation (see Section 3.1) describes the traffic performance (exposure) and the road safety situation in the region in the reference year. The model considers a long time perspective and therefore, the main future evolutions in exposure and autonomous risk are taken into account in the baseline prognosis (Section 3.2). The measure prognosis (Section 3.3) relates to the situation after applying and estimating the effectiveness of measures on road safety. The main outputs of the model are the number of saved injury accidents (and/or casualties) (see Section 4) and the cost-benefit ratios of the measures taken (not within the scope of the current report which is about estimating the effect of the combination of policy measures on road safety outcomes). The computational model extended with methods that are able to take dependence between measures into account is illustrated using possible measures from literature and assuming (in)dependence relationships between them (more specifically, the accident modification factor method is applied in 2009, the dominant common residuals method in 2004 and the synergy model in 2006). 3.1 The reference year The reference year currently considered is The reference year describes the traffic performance (exposure) and road safety situation of Flanders in the starting year of the analysis. Due to data scarcity, only highway segments are considered. Traffic performance in this report is calculated by multiplying the length of the highway segment and the number of vehicles passing by that segment (between 6 am and 10 pm) and the total on all highway segments serves as the regional traffic performance. The regional traffic performance is expressed in thousands as 43.80km (1000s). For now, the road safety situation is only reflected in terms of the number of injury accidents. It should be noted that the number of injury accidents is in reality higher than shown in official statistics because not all accidents are reported and registered by the authorities (Elvik and Vaa, 2004). To better reflect reality, underreporting factors of the injury accidents are used. These are factors by which a registered road safety quantity is multiplied in order to obtain a better approximation of the actual road safety quantities. Different highway segments have different underreporting levels (Reurings et al., 2007). Hence, data on underreporting factors are required for the number of injury accidents per highway segment. Underreporting factors available in literature are not broken down to highway segments. In this report, it is assumed that all highway segments have the same underreporting factor. Hence, 1.75 (Elvik and Mysen, 1999) is utilized as a factor with which the registered number of injury accidents on all highways (i.e. 5117) is multiplied. Adjusting for underreporting results into 8,954 injury accidents at the regional level in the reference year. In addition to injury accidents, the road safety situation in the reference year can be reflected by the accident risk. By dividing the adjusted injury accidents by the traffic performance in the region, the accident risk is computed as 204,43. It should be noted that the aim of the gathered traffic performance and road safety data is to develop and illustrate the methodology rather than reflecting the true (risk) situation on highways in Flanders. Subsequent to the reference year is the baseline prognosis in which changes in traffic performance and autonomous risk are taken into account. Steunpunt Mobiliteit & Openbare Werken 13 RA-MOW

14 3.2 Baseline prognosis In this section, baseline prognoses on highways in Flanders are discussed. First, with respect to the baseline risk for injury accidents, followed by the baseline for traffic performance and lastly the baseline for injury accidents. In this report, interest is in evaluating road safety measures upto Therefore, eight baseline years are considered ( ) Baseline risk for injury accidents The baseline risk for injury accidents, br t on highways in year t is determined by the injury accident risk in the reference year, r c, and the autonomous risk change in that year, f t as: br t = f 1 * f 2... f t * rc. The autonomous risk refers to the collective learning process caused by the growing knowledge of the road safety problem, the constant improvement of the safety performance of the road transport system, better equipped motor vehicles and roads, improvement of road safety education and, increasing legislation and enforcement (COST329, 2004). The effect of the autonomous risk was quantified as (see Section in Nambuusi et al., 2009 for computations) using time series data of the number of casualties ( ) in Belgium (FOD Economie, 2008). This decrease is assumed constant during the years following the reference year. In other words, the baseline risk for injury accidents is expected to decrease by 4.49% (( )*100) each year due to the collective learning process. Starting from 2003 to 2010, the baseline risk for injury accidents is obtained as , , , , , , and respectively Baseline traffic performance Traffic performance changes over time. This change is incorporated into the model assuming that all highway segments have the same growth rate in traffic performance each year. The data used to compute the growth factor in traffic performance on highways (1.0176) (see Section in Nambuusi et al., 2009 for computations) relate to the period (FOD MV, 2008). In other words, traffic performance on highways is expected to grow by 1.76% each year. The traffic performance, TP t in year t is given by: TPt = g 1 * g 2 *...* g t * TP with TP and g t being the regional traffic performance on highways in the reference year and the growth factor in traffic performance in year t. The traffic performance is respectively calculated as 44.57, 45.36, 46.15, 46.97, 47.79, 48.64, and (1000s km) for the period 2003, Baseline injury accidents Based on the baseline risk for injury accidents and traffic performance obtained in Sections and respectively, the model predicts the baseline for injury accidents in various baseline years at the regional level. These represent the amount of injury accidents if no new regional or locational measures are taken. The baseline for the number of injury accidents, b_ias t in year t is given by: b _ IAst = br t * TPt. This results in 8,702; 8,458; 8,220; 7,990; 7,766; 7,549; 7,337 and 7,132 in the period 2003, respectively. A decreasing trend is observed over time. Based on the predicted baseline injury accidents, it is deduced that if no new regional or locational measures are applied, the baseline injury accidents decrease at an approximate rate of 2.81% per year. These results depend on the growth in traffic performance on the one hand and the autonomous risk change on the other hand. If the growth in traffic performance outweighs the decline in the autonomous risk per year, an increase in injury accidents is realized and vice versa. In this case, the decline in autonomous risk (- 4.49%) is higher than the growth in traffic performance (1.76%) per year for the period Steunpunt Mobiliteit & Openbare Werken 14 RA-MOW

15 causing a decreasing trend in injury accidents. Apart from the regional figure, the baseline for the number of injury accidents in year t at a location can be obtained by multiplying the regional baseline risk for injury accidents and the traffic performance at that location in that year. 3.3 Measure prognosis In this phase of the model, the effectiveness of measures on the number of injury accidents is assessed. Two types of measures are distinguished in the model: regional and locational measures. Regional measures have an effect on road safety in the entire region. However, certain measures can only be implemented at locations as it may be very expensive and inappropriate to be applied in the entire region. Such measures are termed locational measures and only have an effect at the location(s) they are applied. The procedure used to calculate the effectiveness of measures on injury accidents is described in the next section Computing the effectiveness of measures To determine the effectiveness of a measure, its modification factor for injury accidents is required. The methods used to estimate the effectiveness of one or several measures are illustrated. Here, the computation for the effectiveness of a single measure is described. For the combined effects of measures, the methods explained in Section 2 are utilized: the accident modification factor method, the dominant common residuals method and the synergy model. The illustration is made using regional measures. The effectiveness of locational measures can be obtained by replacing the regional quantities with locational ones Effectiveness of a single measure Let E IAs denote the effectiveness of a regional measure applied on injury accidents. This implies a modification factor of 1-E IAs. Starting from the number of injury accidents computed in the baseline, the remaining injury accidents, IAs t in year t after applying a regional measure are obtained as:. The number of injury accidents saved in year t is obtained as: The assessed measures IAs = b _ *( 1 ) t IAs t E IAs b _ IAs t IAs. In this report, nine measures obtained from international and regional sources (Elvik and Vaa, 2004; Ministerie van de Vlaamse Gemeenschap, 2007) are examined for the period Their selection is based on availability of required information. The year in which they are implemented as well as on which segments and the kind of relationship between combinations of measures (independent, reinforcing or substituting) are arbitrarily chosen for illustration purposes. The set of measures comprises one regional measure and eight locational ones. The regional measure is alcohol or drugs checks (measure 1) applied in 2003 and the locational ones include a combination of automatic warnings of queues with variable signs (measure 2) and congestion warning signals (measure 3) applied at 17 highway segments in 2004; a combination of signs showing recommended speed in curves (measure 4) and new guardrails along embankments (measure 5) taken at 21 highway segments in 2006; fog warning signals (measure 6) applied in 2007 at eight highway segments; more stringent road works warnings on twolane roads (measure 7) in 2008 at 11 highway segments; and a combination of scent signals to frighten game (measure 8) and directional markings in curves (measure 9) in 2009 at 10 highway segments. A measure is applied on the proportion of injury accidents related to it. For example, alcohol or drug checks are applied on injury accidents related to alcohol or drugs. Table 2 lists the measures with the respective years of implementation and the effectiveness in terms of a specific category of accidents Steunpunt Mobiliteit & Openbare Werken 15 RA-MOW t

16 (average and confidence interval) obtained from literature. In the years 2005 and 2010, only the effect of the growth in traffic performance and the change in autonomous risk is to be taken into account. Table 2: Measures and effectiveness Measure; Year of implementation Alcohol or drug checks; 2003 Automatic warnings of queues with variable signs and congestion warning signals (Dominant common residuals method); 2004 Effectiveness (Confidence interval) Reduce IAs related to alcohol or drugs by 25% (-0.32,-0.18) Automatic warnings reduce IAs involving rear-end collisions by 22% (-29,-13) Congestion warning signals reduce IAs involving rear-end collisions by 16% (-23,- 11) Signs showing recommended speed in curves and new guardrails along embankments (Synergy model); 2006 Signs reduce IAs in curves by 13% (-22,-2) New guard rails reduce IAs in the event of running off the road by 47% (-52,-41) Fog warning signals; 2007 Reduce IAs related to fog by 84% (-93,-63) More stringent road works warnings on two-lane roads; 2008 Reduce IAs at road works by 40% (-65,-5) Scent signals to frighten game and directional markings in curves (Accident modification factor method); 2009 Scent signals reduce IAs involving game by 70% (-90,-5) Directional markings reduce IAs in curves by 39% (-52,-22) IAs = Injury accidents Steunpunt Mobiliteit & Openbare Werken 16 RA-MOW

17 4. N U M B E R O F I N J U R Y ACCIDENTS SAVED This section demonstrates the evaluation of the measures. The procedure for computing the effectiveness of a single measure is illustrated using alcohol or drug checks in 2003 and, a combination of automatic warnings of queues with variable signs and congestion warning signals is used to illustrate the process for obtaining the effectiveness of more than one measure. The same procedures apply to the other measures. The total number of injury accidents saved by 2010 results from the sum of injury accidents saved in the previous years ( ). 4.1 Computing the effectiveness of a single measure Before implementing measures in 2003, the effect of the change in autonomous risk and growth in traffic performance on the number of injury accidents in the region is taken into account. The total number of injury accidents in the region in the reference year is 8,954 (Section 3.1 ). The change in autonomous risk and growth in traffic performance in 2003 are applied on 8,954 and the injury accidents in the region reduce to 8,702 (Section ). The injury accidents saved due to the change in autonomous risk and growth in traffic performance is calculated as 252 (8,954-8,702). Alcohol or drug checks are then evaluated at the regional level in 2003 and reduce injury accidents related to alcohol or drugs by 25% (Table 2). The proportion of injury accidents related to alcohol or drugs is obtained from literature as 7.69% (National Highway Traffic Safety Administration, 2005). The number of injury accidents related to alcohol or drugs in 2003 is 669=7.69%*8,702. The number 502 (669*0.75) represents the remaining injury accidents after applying alcohol or drug checks (Section ). In other words, 167 ( ) injury accidents are saved due to this measure. In total, 419 ( ) injury accidents are saved due to the change in autonomous risk, growth in traffic performance and the regional measure. By deducting 419 from the number of injury accidents in the region in the reference year (8,954) 8,535 injury accidents remain. This figure is used as starting point for the year 2004 in which a combination of automatic warnings of queues with variable signs and congestion warning signals is implemented. 4.2 Computing the effectiveness of more than one measure The combination of the two measures, automatic warnings of queues with variable signs and congestion warning signals, is applied at 17 highway segments in 2004 and reduces injury accidents involving rear-end collisions by 28% (Section 2.2 ). Of the total injury accidents, 19.81% are related to rear-end collisions (Wang et al., 1999). Before implementing the measure, the change in autonomous risk and growth in traffic performance in 2004 are taken into account. These two factors are applied on 8,535 to yield 8,295 (Table 3). The number of injury accidents saved due to the change in autonomous risk and the growth in traffic performance is 240 (8,535-8,295). The number of injury accidents that occur as a result of rear-end collisions in the region in 2004 is then obtained as 1,643 (8,295*19.81%). To obtain the number of injury accidents (involving rear-end collisions) remaining at a particular highway segment after the change in autonomous risk and growth in traffic performance in 2004 have taken effect, the regional baseline risk for injury accidents involving rear-end collisions in 2004 is multiplied by the traffic performance at that highway segment in 2004 (see Section 3.2.3). At the 17 highway segments, a total of 399 rear-end injury accidents remains after the change in autonomous risk and growth in traffic performance in 2004 are accounted for. Following this, the combination of measures is applied at each of the highway segments and the rear-end injury accidents reduce from 399 to 287. The number of rear-end injury accidents saved due to the measures is 112 ( ), reducing the total number of rear-end injury accidents to 1,531 (1, ). The total Steunpunt Mobiliteit & Openbare Werken 17 RA-MOW

18 number of injury accidents saved in 2004 (due to the change in autonomous risk, growth in traffic performance and the measures) is = 352. In the end, 8,183 (8, ) injury accidents remain in the region; this figure serves as the starting point of the year The procedures are repeated for the other years and Table 3 presents all results. Steunpunt Mobiliteit & Openbare Werken 18 RA-MOW

19 4.3 Overview of injury accidents saved Table 3: Summary of injury accidents saved Measure; Year of implementation Regional IAs in previous year Regional IAs after AR, GTP Regional savings (%) after AR,GTP Number of IAs related to measure Remaining IAs after applying measures Measure Savings Total Remaining IAs in region after AR,GTP, measures Alcohol or drug checks; 2003 Automatic warnings of queues with variable signs and congestion warning signals; 2004 (Dominant common resid.) No regional or locational measures; ,954 8,702 8,535 8,295 8,183 7, (2.81) 240 (2.81) ,535 1,643 1, ,183 (2.81) NA NA NA 230 7,953 Signs showing recommended speed in curves and new guardrails along embankments; 2006 (Synergy model) 7,953 7, (2.81) 1,681 1, ,449 Fog warning signals; 2007 More stringent road works warnings on twolane roads; 2008 Scent signals to frighten game and directional markings in curves; 2009 (Accident modification factor method) No regional or locational measures; ,449 7,240 7,235 7,032 7,024 6,827 6,772 6, (2.81) 203 (2.81) 197 (2.81) 189 (2.81) , , ,772 NA NA NA 189 6,583 Savings by , ,371 IAs = Injury accidents; AR = Autonomous risk change; GTP = Growth in traffic performance Steunpunt Mobiliteit & Openbare Werken 19 RA-MOW

20 To conclude, the results in Table 3 indicate that for the current case study 2,371 injury accidents are saved by Of these, the nine measures contributed 629 while 1,742 were avoided due to the autonomous risk change and the growth in traffic performance. Steunpunt Mobiliteit & Openbare Werken 20 RA-MOW

21 5. D I SCUSSION, C O N C L U S I O N AND FUTURE RESEARCH Estimating the combined effects of a set of road safety measures is a difficulty encountered by many researchers. Given its impact, for example in terms of the estimated effectiveness of road safety plans, it is essential to identify the best methods for assessing the combined effects of various road safety measures. This was the main objective of this report. Three methods were described: the accident modification factor method, the dominant common residuals method and the synergy model. At present, the method of accident modification factor by Smeed (1949) is the most widespread. This method assumes that the first order effect of a measure is independent of the first order effects of any other measures it is combined with and remains unchanged when introducing other measures. With this method, the combined effects of several road safety measures are obtained by multiplying the accident modification factors of the measures. This method estimates the linear effect of measures. However, effects of measures implemented simultaneously are not always completely independent. Some measures influence risk factors that are the targets of other measures, thus reducing their likely effects. Such interdependences are not taken into account by the accident modification factor method. To address this, a modified version of this method, termed the dominant common residuals method (Elvik, 2009) was suggested. This method is identical to the accident modification factor method, except that the product of the accident modification factors is raised to the power of the accident modification factor of the most effective measure included in the set. This method assumes that the most effective measure in a set dominates the others to some extent, by partly or fully influencing the same group of accidents or the same risk factors. Using the example in Section 2, the combined effect approximated by this method was smaller as compared to the combined effect when the accident modification factor method was applied. This is because measures influence the same group of accidents and since an accident can only be prevented once, the effect of other measures is weakened. On the other hand, literature (see e.g. Vaa et al., 2009; Solomon et al., 2004) reveals that some measures reinforce each other. This is not tackled by either method mentioned before. This is addressed using the synergy model suggested in this report. Synergy is estimated by raising the product of the accident modification factors to the inverse of the accident modification factor of the most effective measure in the set. The combined effect estimated using this method is larger than the effect computed using the accident modification factor method. After quantifying the goodness of fit of the three methods using several studies, it could be concluded that all methods adequately described the data. In other words, the results implied that in case the measures are independent of each other, weaken each other or reinforce each other, the corresponding method described their fit well. However, in order to decide which method to apply on a particular set of measures, knowledge on the kind of relationship between them is needed. In the future, the combined effect of measures obtained from the road safety plan for Flanders will be assessed using the methods discussed in this report. In the meantime, the application of the methods has been illustrated by means of a case study in which the different stages of the computational model were discussed and the three possible methods for assessing the effect of a combination of measures were shown. From now on, possible interdependence between measures (which is a critical aspect) can be accounted for by the model. That way, the combined effect of road safety plans comprising several measures can be assessed more realistically. A limitation of the current report is the data set used. A more up-to-date reference year, other data sources, more Flemish related measures (and their effectiveness) would increase the policy value of the report. Nevertheless, the development of an appropriate Steunpunt Mobiliteit & Openbare Werken 21 RA-MOW