# The Health Impact of Mandatory Bicycle Helmet Laws

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3 The Health Impact of Mandatory Bicycle Helmet Laws 3 exercise is only sustainable if it is integrated into daily routine such as shopping errands or traveling to and from work. In any case, in the analysis below, substitution effects can be accommodated by lowering the assumed health benefit of each km of cycling. Third, the health impacts calculated below do not reflect the possibly negative health or economic impacts associated with shifts to other modes of transportation such as cars. Fourth, the discussion below is in terms of statistical averages and sets off gains and losses across different individuals. The analysis is based on a representative bicyclist and does not distinguish between different groups of bicycle riders. Different groups may have different parameters and a targeted helmet law may be warranted. Further, groups of riders may have different parameter configurations making for a misleading average analysis. This is further discussed in 6. Relation (1) is based on assumptions detailed, discussed and analyzed in subsuent sections. The next section presents the key expressions for evaluating the net health impact of a helmet law. The key parameters and their values in these expressions are discussed in 3. Section 4 uses figures from European countries and the US to compute potential net health impacts. Section 5 displays further sensitivity calculations. Substitution and environmental effects are considered in 6. Conclusions are presented in THE NET HEALTH IMPACT OF A HELMET LAW This section shows (1) is a necessary condition for there to be a net health benefit to a mandatory bicycle helmet law. The argument is based on a representative cyclist model. The cyclist accrues a gross health benefit v from each accident free km of cycling. The gross health benefit v is denominated in an appropriate unit such as dollars, increased life expectancy, reduced mortality risk, or other. Representative riders are assumed to suffer bicycling accidents according to a Poisson process with expected accident rate of λ per km. (12) If there is an accident, the expected health cost if no helmet is worn is c, reducing to c if a helmet is worn. Accident costs are denominated in the same units as health v. Here and below quantities with an asterisk indicate values when a helmet is worn. Thus v λc is the expected health benefit of 1 km of helmetless cycling and v λc is the expected health benefit of cycling 1 km with a helmet. A mandatory helmet law effects only cyclists who do not wear helmet before the law and who either start wearing a helmet or choose to give up cycling. This group is called the behavior changing group. Thus suppose those who already wear a helmet prior to the law and those unhelmeted riders who choose to ignore the law do not change behavior 4. Suppose there are m km ridden by the behavior changing group before the law of which proportion p is given up as a result of the law. Then the health benefit of cycling for the group is m(v λc) before the law, and (1 p)m(v λc ) after. The net health impact of the law, expressed as a fraction of helmet preventable health costs is net health impact of helmet law Ψ helmet preventable health cost = (1 p)m(v λc ) m(v λc) mλ(c c ) = (1 p)λ(c c ) p(v λc) = (1 p) λ(c c ) ) ( 1 µβ (2) (3) = (1 p) pβ, (4) where the ualities follow from direct manipulation and the fact that helmets are only useful in preventing head injuries: c c = c qc (1 e)qc c =. The advantage of the expressions in (3) or (4) is that Ψ is stated in terms of testable and readily estimated, intelligible constructs and does not explicitly involve the units of measurement of v. Note Ψ 1 with Ψ > 0 indicating benefits exceed costs while Ψ < 0 indicates an unintended net health cost. Further Ψ > 0 if and only if > µβ as in (1). The ratio µβ = pm(v λc) (1 p)mλ(c c ), (5) is the cost to benefit ratio of a helmet law with p = 0 implying the cost is zero and the helmet law effectiveness Ψ = 1. 4 The number of riders who ignore the law and hence the size of the behavior changing group will depend on the degree to which the law is enforced.

6 6 Piet de Jong 4. NET HEALTH IMPACTS FOR SELECTED COUNTRIES This section estimates the net health benefit of mandatory cycle helmet laws for the different countries listed in Table II. The countries span a range of cycling cultures. (25) Cross country comparisons are used throw light on the likely size of the benefit cost ratio of bicycling β in different jurisdictions and in turn the likely values of the standardized health impact Ψ. The likely size of β in different countries is established using two reference points: the country specific per km death rate from bicycling injuries and the reference value β = 20 suggested in Hillman report to the British Medical Association. (18) Values for the bicycling death rate d i per km of bicyclin for different countries i are displayed in Table II. Suppose the accident rate λ in country i is proportional to the bicycling death rate d i per km: λ i = κd i where κ is a constant, independent of the country. Then if the gross health benefit v and expected cost c per accident are the same for all countries β i v λ ic λ i c = v κd i c 1 = α d i 1, (6) where α v/(κc) does not depend on i. Equation (6) can be used to determine α from the death rate d i and β i for a particular country. Given α and the death rates permits the determination of β i for all other countries. Hillman (18) suggests β i = 20 for the UK, a not particularly safe bicycling country as indicated by the bicycling mortality rates d i in Table II. Assume β i = 20 applies to the Netherlands, the safest bicycling nation listed in Table II. This is clearly a pessimistic view of the benefit cost ratio of cycling. Given d i = 1.6 for the Netherlands then α = d i (1 + β i ) = = Hence 25 < α < 50 appears a pessimistic range for α. The two extreme values for α yield, when substituted into (6), the two β i values for each country listed in Table II. The resulting β i values range from a low of 1 in Italy, to a high of 30 in the Netherlands. The resulting β i values for Great Britain are 3 and 7, very pessimistic given the assessment of Hillman (18). The overall range of pessimistic β i values for different countries i gives a reasonable range which may be used in a variety of other jurisdictions say Austin, Texas or Melbourne, Victoria or Kyoto, Japan. The β i for each country i in Table II is combined with two reductions in cycling: p = 0.10 and p = These relatively modest reductions should be compared to the range 20% to 40% reported in the studies cited in 3.3. In all cases it is assumed the preventable fraction = 0.5 corresponding to an optimistic view of helmet effectiveness, achieved for example with e = 0.67 and q = The Ψ figures given in Table II have a maximum of 1. The figures are positive whenever > µβ i or β i < 1/(2µ), ual to 5 and 2.5, if p = 0.1 and p = 0.2, respectively. That is, for a net health benefit, cycling must be very dangerous as occurs for example in Italy for both β scenarios or Great Britain for the worse β scenario. With p = 0.2 and the more optimistic β scenario, only Italy displays a net health benefit. If a helmet law is strictly enforced then all pre law unhelmeted cycling is sensitive to a helmet law in the sense that either it is lost or converted to a helmeted km. The annual per capita net health impact of a strictly enforced mandatory helmet law in units v is thus Φ (1 φ)mλ(c c ) nv Ψ = (1 φ)m n(1 + β) Ψ, (7) where n is the population of the country and (1 φ)m is the annual per capita rate of unhelmeted bicycling. Daily cycling rates m/(365n) and helmet wearing rates φ for different countries are displayed in Table II together with resulting estimates for Φ. For example for the USA, with β = 5.7 and p = 0.1 then Φ = 1, indicating a per capita per annum health cost uivalent to the health benefit of 1 km of accident free cycling. For Great Britain using β = 7.3 and p = 0.20, the net health cost of a mandatory helmet law is 3.6v per person per annum. For countries where cycling is very safe and popular, such as the Netherlands, Denmark and Sweden, the net health costs of a mandatory bicycle helmet law are large. Table II shows that for most countries, under assumptions favorable to the helmet legislation case, the unintended health costs cancel out the direct health benefit. Note these are not costs to solve the head injury problem but figures showing the extent to which the problem is compounded. The rates in Table II provide evidence on the relationship between the bicycling death rate d i, the bicycling rate b i and helmet usage φ i. In particular suppose ln d i α + δ ln b i + γφ i. Then δ models the safety in numbers effect. (26) Further, 1 e γ is the reduction in the relative risk of death due to helmets. Least squares estimation leads to estimates

7 The Health Impact of Mandatory Bicycle Helmet Laws 7 of δ and γ of and -0.40, respectively. The δ estimate is highly significant (p value 0.01) while the helmet effect is insignificant (p value 0.76). Hence the reduction in death risk on account of helmets is estimated as 1 e 0.40 = 0.33 with a wide margin of error. In comparison the δ estimate suggests a halving in cycling increases the death rate by about 1 (0.5) 0.54 = With a behavioral response of p, an enforced helmet law reduces bicycling from b i to φ i b i + (1 p)(1 φ i )b i = b i {1 p(1 φ i )}. The net effect of a strictly enforced helmet law is thus to reduce the death rate by proportion 1 e γ(1 φi)+δ ln{1 p(1 φi)} (1 φ i )(pδ γ). Using the estimates, the proportionate reduction γ = 0.40 is, on account of safety in numbers, modified to p, which in turn is multiplied by the fraction of unhelmeted riders before the law. With p = 0.10 or p = 0.20, as used in Table II, the modification has a marginal effect. 5. SENSITIVITY ANALYSIS Figure 1 plots Ψ versus preventable fraction for a variety of parameter combinations. In each panel it is assumed no helmets are worn pre helmet law and there is proper 100% post law compliance. Different panels correspond to different values of p. Note if helmets are 67% effective and 75% of injury costs are due to head injuries then = Different β correspond to the different lines. Figure 1 indicates a net health benefits is difficult to achieve except in extreme circumstances: a small behavioral response (p or µ is small), helmets highly effective ( near 1), and a low health benefit of cycling (β small), indicating either minimal exercise benefits or a dangerous bicycling environment. 6. NON HEALTH COSTS, SUBSTITUTION AND GROUPING The analysis of the previous sections focuses solely on health costs. This is inappropriate in an overall appraisal of a mandatory bicycle helmet law, given that bicycling is often substituted for by more costly and less environmentally benign modes of transport. Bicycles, on average, pose small risks to others, especially when compared to say cars. Suppose reducing cycling by 1 km leads to, on average, an increase in environmental costs of ɛ(v λc). Hence the environmental cost is denominated in terms of the expected health benefit of 1 km of cycling. Then the standardized health impact combined with the environmental cost is Ψ pɛ(v λc) λ(c c ) { = (1 p) 1 } µβ(1 + ɛ). (8) Thus factoring in environmental costs is uivalent to increasing β by 100ɛ percent. For example if the environmental cost of 1 km of lost cycling uals the expected health benefit of 1 km of cycling, then ɛ = 1 and factoring in environmental costs is uivalent to increasing β by 100%. Using the lower β values in Table II as a starting point and ɛ = 1 than factoring in environmental costs is uivalent to approximately moving from the lower β to the higher β. Hence even with a 10% reduction in cycling and very pessimistic assumptions about β, factoring in environmental costs of ɛ = 1, suggests no benefit for any country except for Italy. Substitution effects can be handled similarly. Suppose ɛ is the proportion of lost km substituted with other forms of ually healthy exercise. Then the net health impact is similar to (8) except that ɛ replaces ɛ. Hence substitution effects of ɛ are accommodated by reducing β. Environmental and substitution, can be incorporated via a joint calculation. For example if 70% of lost cycling is substituted and the environmental costs of each km of lost cycling is 2(v λc) then ɛ = = 1.3 and hence for purposes of computing Ψ, β is increased by 130%. Finally consider the situation where bicyclists are grouped into distinct groups i with group i cycling m i km, having accident rate λ i, behavioral response p i, and bicycling benefit cost ratio β i. Then the overall net health impact is, assuming helmets confer a common per accident benefit c c, Ψ = i i m iλ i {(1 p i )(c c ) p i (v i λ i c)} i m iλ i (c c ) w i Ψ i, where Ψ i is the standardized health impact for group i and w i = m i λ i / i m iλ i is the proportion of accidents arising from group i. An analysis, based on population average values of β, µ, e and q, may suggest Ψ < 0 even though some or even all Ψ i > 0 or vice versa. This again argues for a detailed appraisal of the four key parameters, this time at a group level.

8 8 Piet de Jong Table II. Helmet law net impact and annual per capita health benefit death cycling helmet p = 0.10 p = 0.20 rate rate rate β Ψ Φ Ψ Φ Austria Denmark Finland Germany Great Britain Italy Netherlands Norway Sweden Switzerland United States Notes: Death rate is deaths per hundred million km of cycling. Cycling rate is km per person per day. (7,27) The helmet rate is the proportion of cyclists wearing helmets. (28) Bicycling benefit cost ratio β i derived from death rate as discussed in text. Ψ and Φ assume = CONCLUSIONS Using elementary mathematical modeling and parameter estimates from previous studies, leads to reasonable bounds for the net health impact of a mandatory bicycle helmet law. The model highlights the importance of four parameters in any evaluation: helmet efficiency, the behavioural response of riders to the law, the benefit cost ratio of cycling, and the proportion of injuries in cycling due to head injuries. These key parameters offer critical testable points for assessing the net impact. A (positive) net health benefit emerges only in dangerous bicycling environments under optimistic assumptions as to the efficacy of helmets and a minor behavioral response. Resolution of the issue for any particular jurisdiction ruires detailed information on the four key parameters. The calculations are based on a representative bicyclist model. It may be the case that those giving up cycling are not representative: they may be more accident prone, less susceptible to the health stimulus or more inclined to substitute cycling with other exercise activities. A disaggregated model can be used to address such issues which in turn ruires a detailed appraisal of the four key parameters at a disaggregated group level. REFERENCES 1. Thompson RS, Rivara FP, Thompson DC. A case control study of the effectiveness of bicycle safety helmets. New England Journal of Medicine. 1989;320(21): Robinson DL. Head injuries and bicycle helmet laws. Accident Analysis & Prevention. 1996;28(4): BMJ; Robinson DL. Do enforced bicycle helmet laws improve public health? British Medical Journal. 2006;332(7543): Wardlaw MJ. Three lessons for a better cycling future. British Medical Journal. 2000;321(7276): Wardlaw MJ. Assessing the actual risks faced by cyclists. Traffic engineering & control. 2002;43(11): Hurst R. The Art of Urban Cycling: Lessons from the Street. Guilford, CT. Globe Puot Press; Towner E, Dowswell T, Burkes M, Dickinson H, Towner J, Hayes M. Bicycle Helmets: Review of Effectiveness. Road Safety Research Reports. 2002; DeMarco TJ. Butting heads over bicycle helmets. Canadian Medical Association Journal. 2002;167(4): Lutter R, Morrall JF. Health-health analysis: A new way to evaluate health and safety regulation. Journal of Risk

9 The Health Impact of Mandatory Bicycle Helmet Laws 9 p=0.05 p= Psi -1 Psi p=0.2 p= Psi -1 Psi Fig. 1. Ψ plotted against the preventable fraction. Different panels correspond to different assumed reductions in cycling as indicated. Lines in each panel correspond (from highest to lowest) to β = 1, 2, 5, 10, 15 and 20. and Uncertainty. 1994;8(1): Graham JD, Wiener JB. Risk versus risk: Tradeoffs in protecting health and the environment. Harvard Univ Pr; Ross SM. Introduction to Probability Models. 8th ed. San Diego, CA: Academic Press; Robinson DL. Bicycle helmet legislation: Can we reach a consensus? Accident Analysis & Prevention. 2007;39: Hunt A. Gory film aims to keep teens safe on roads. Evening Chronicle (Newcastle, England); ACTIVITY, D E O F P. Physical Activity and Public Health A Recommendation from the Centers for Disease Control and Prevention and the American College of Sports Medicine. Journal of the American Medical Association. 1995;273: Fletcher GF, Balady G, Blair SN, Blumenthal J, Caspersen C, Chaitman B, et al. Statement on exercise: benefits and recommendations for physical activity programs for all Americans: a statement for health professionals by the Committee on Exercise and Cardiac Rehabilitation of the Council on Clinical Cardiology, American Heart Association. Circulation. 1996;94(4): Dishman RK, Sallis JF, Orenstein DR. The determinants of physical activity and exercise. Public Health Reports. 1985;100(2): Hillman M. Cycling: towards health and safety. A report for the British Medical Association. Oxford University Press; Hillman M. Cycling and the promotion of health. Policy Studies. 1993;14(2): Klugman SA, Panjer HH, Willmot GE. Loss Models: From Data to Decisions. Wiley; Thompson DC, Rivara FP, Thompson RS. Helmets for preventing head and facial injuries in bicyclists. Cochrane Database Syst Rev. 2000; Attewell RG, Glase K, McFadden M. Bicycle helmet efficacy: a meta-analysis. Accident Analysis & Prevention. 2001;33(3): Ormel W. Hoofdletsels na fietsongevallen. Stichting Consument en Veiligheid, Amsterdam. 2009;. 24. Dinh MM, Roncal S, Green TC, Leonard E, Stack A, Byrne C, et al. Trends in head injuries and helmet use in cyclists at an inner city major trauma centre, The Medical Journal of Australia. 2010;193(10): Pucher J, Buehler R. Making cycling irresistible: Lessons from the Netherlands, Denmark and Germany. Transport Reviews. 2008;28(4):

10 10 Piet de Jong 26. Komanoff C. Safety in numbers? A new dimension to the bicycle helmet controversy. British Medical Journal. 2001;7(4): Wittink R. Planning for cycling supports road safety. In: Tolley R, editor. Sustainable transport: planning for walking and cycling in urban environments. Boca Raton: CRC Press LLC; p Hydèn C, Nilsson A, Risser R. WALCYNG How to enhance WALking and CycliNG instead of shorter car trips and to make these modes safer. Final Report Department of Traffic Planning and Engineering, University of Lund, Sweden & FACTUM Chaloupka, Praschl & Risser OHG, Vienna, Austria. 1998;.

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