Speed and road accidents - trg.dk

1 TOI report740/2004 Speed and road accidents An evaluation of the Power Model Rune Elvik, Peter Christensen, Astrid Amundsen The Institute of Transport Economics (TOI) holds the exclusive rights to the use of the entire report and its individual sections. Contents of the report may be used for referencing or as a source of information. Quotations or references must be attributed to TOI as the source with specific mention made to the author and report number. Contents must not be altered. For other use, advance permission must be provided by TOI. The report is covered by the terms and conditions specified by the Norwegian Copyright Act. ISSN 0802-0175 ISBN 82-480-0451-1 Oslo, December 2004 * Preface The relationship between Speed and road safety is a highly controversial and emotionally charged subject.

2 This report investigates the effects of changes in Speed on the number of road accidents or road accident victims. It is found that the relationship between Speed and accidents or accident victims can be represented by a set of power functions, as postulated in the so called Power Model of the relationship between Speed and road safety. The study was funded by the Swedish National road Administration and the Norwegian Public Roads Administration. Project manager at the Swedish National road Administration was first Jan Ifver, then Thomas Lekander. Project manager at the Norwegian Public Roads Administration was Finn Harald Amundsen. The principal author of this report is chief researcher Rune Elvik, who was project manager at the Insti-tute of Transport Economics. Senior research statistician Peter Christensen performed the meta-analyses presented in the report.

3 Research geographer Astrid Amundsen retrieved the studies used in the report and coded the data used in the study. Comments to drafts of this report have been given by professor (emeritus) Ezra Hauer, University of Toronto, professor Richard Allsop, University College London, professor Christer Hyd n, Lund Institute of Technology, and colleagues at the Institute of Transport Economics. Head of department Marika Kol-benstvedt has been responsible for formal quality assurance. Secretary Trude R mming did the final editing of the manuscript. Oslo, December 2004 Institute of Transport Economics S nneve lnes Marika Kolbenstvedt Acting managing director Head of department Contents Summary Sammendrag 1 Background and Background.

4 1 Recent reviews of Speed and Research problems addressed in this 2 The Power Model ..4 The Power Model as presented by G ran The algebra of Powers ..6 3 Theoretical perspectives on Speed and accidents ..7 An elementary model of the relationship between Speed and The relationship between Speed and injury The relationship between Speed variance and road Speed in context: the role of confounding factors ..14 4 Threats to validity in studies of the impacts of Speed on road Types of validity and threats to validity ..17 Threats to validity in studies evaluating the relationship between Speed and road Errors and bias in Speed data .. 19 Incomplete accident reporting and changes in the level of accident reporting 20 20 Long term trends in accident 22 Major changes in traffic volume.

5 22 Inadequate control of risk factors influencing accident occurrence .. 23 Control for threats to validity in various study designs ..26 Commonly employed study 26 Ways of introducing Speed -influencing 27 5 Study retrieval, data extraction and study quality assessment ..29 Literature search ..29 Study inclusion criteria ..29 Data extracted and coded for meta-analysis ..30 Case illustrations of data Case 1: Upchurch 1989 .. 32 Case 2: Nilsson 2004A .. 33 Study quality assessment ..34 Control for regression-to-the-mean .. 35 Long term trends in accident 35 Changes in traffic volume .. 36 Other risk factors influencing accident occurrence or injury 36 6 Studies included in Studies not providing information for inclusion in Studies that have been excluded from meta-analysis.

6 44 Overview of evidence from studies included in meta-analysis ..45 Exploratory meta-analysis ..47 Two ways of representing data concerning Speed and road 47 The consistency of the relationship between Speed and road safety .. 48 Analysis of funnel 50 Testing for publication bias .. 54 Main analysis ..55 Statistical weighting of estimates of 55 Models 57 Results of conventional 58 Results of meta-regression analyses .. 60 Assessing the consistency of the findings with the Power 61 Sensitivity analysis ..62 The cumulative and non-cumulative formulations of the Power Model .. 63 Choosing the best estimates of the exponents .. 67 The effects of contextual 72 Other analytic choices .. 72 7 Discussion of findings ..74 A general note on the interpretation of the results of research.

7 74 Limitations of the analyses ..74 The possibility of study inclusion bias .. 75 Effects of other road safety measures residual confounding .. 76 Effects of Speed on various types of accident or groups of road 77 The reliability of Speed data .. 78 Alternative models of the relationship between Speed and road 78 Statistical dependency between multiple results of the same study .. 81 Criteria of causality in non-experimental research ..82 Presence, strength and consistency of statistical relationship .. 83 Direction of causality .. 83 Control for confounding factors .. 84 Dose-response 84 Specificity of 84 Causal mechanisms .. 85 Consistency with theory .. 86 8 Practical implications ..87 The importance of Speed as a risk factor ..87 The need for regulating The controllability of Speed by means of road safety measures.

8 93 Principles for setting Speed limits ..94 The enforcement of Speed 9 Main 10 Appendix 1: Data Recorded For Each Study ..117 Appendix 2: Residual Plots ..128 T I report 740/2004 Authors: Rune Elvik, Peter Christensen, Astrid Amundsen Oslo 2004, 134 pages English language The report can be ordered from: Institute of Transport Economics, PO Box 6110 Etterstad, N-0602 Oslo, Norway Telephone: +47 22 57 38 00 Telefax: +47 22 57 02 90 i Summary: Speed and road accidents : an evaluation of the Power Model The relationship between Speed and road safety is a controversial topic. In this report, the relationship between Speed and road safety has been evaluated by means of a meta-analysis of studies that provide estimates of how changes in Speed affect the number of road accidents and the number and severity of injuries to road users.

9 The Power Model This study was designed to evaluate the Power Model of the relationship between Speed and road safety. This model has been proposed by the Swedish road safety researcher G ran Nilsson. According to the Power Model, the effects of changes in Speed on the number of accidents and the severity of injuries can be estimated by means of a set of power functions. A power function is a mathematical function that relates two variables to each other by raising values of one of the variables to a power in order to obtain values for the other variable. Any function in which a variable is raised to a certain exponent is called a power function (not to be mixed up with an exponential function, which is e (e = ) raised to an exponent). The Power Model describes the relationship between Speed and road safety in terms of six equations.

10 As an example, the equation referring to fatal accidents is: 4 Fatal accidents afterSpeed afterSpeed beforeFatal accidents before = If Speed is reduced from 100 km/h to 90 km/h, the ratio Speed after/ Speed before equals 90/100 = Raising to a power of 4 gives ( ) This means that the number of fatal accidents is estimated to go down to times the initial number, corresponding to a reduction of percent. The Power Model consists of one equation for fatalities, one for fatal and serious injuries and one for all injured road users. Moreover, there is one equation for fatal accidents , one for accidents involving fatal or serious injury, and one for all injury accidents . An exponent of 4 is proposed for fatal accidents , an exponent of 3 for accidents involving fatal or serious injury, and an exponent of 2 for all injury accidents .