helmet effectiveness in preventing motorcycle driver and passenger fatalities

Accid. Anal. & Prey. Vol. 20, No. 6, pp. 447-458, 1988 0001-4575/88 $3.00+ .00 Printed in Great Britain. © 1988 Pergamon Press plc

H E L M E T E F F E C T I V E N E S S IN P R E V E N T I N G M O T O R C Y C L E D R I V E R A N D

P A S S E N G E R F A T A L I T I E S *

LEONARD EVANS a n d MICHAEL C. FRICK Operating Sciences Department, General Motors Research Laboratories,

Warren, MI 48090, U.S.A.

(Received 20 September 1987)

Abstract--Helmet effectiveness in preventing fatalities to motorcycle drivers and passengers was determined by applying the double pair comparison method to the Fatal Accident Reporting System (FARS) data for 1975 through 1986. Motorcycles with a driver and a passenger, at least one of whom was killed, were used. In order to reduce as much as possible potentially confounding effects due to the dependence of survivability on sex and age, the analysis is confined to male drivers (there were insufficient female driver data), and to cases in which the driver and passenger age do not differ by more than three years. Motorcycle helmet effectiveness estimates are found to be relatively unaffected by performing the analyses in a number of ways different from that indicated above. It was found that helmets are (28 +- 8)% effective in preventing fatalities to motorcycle riders (the error is one standard error), the effectiveness being similar for male and female passengers, and similar for drivers and passengers. An additional result found was that the fatality risk in the driver seat exceeds that in the passenger seat by (26 --- 2)%. The 28% effectiveness found generates calculated fatality increases from repeal of mandatory helmet- wearing laws that are compatible with observed increases.

I N T R O D U C T I O N

More than 4000 motorcycle riders die in traffic crashes annually in the United States [National Highway Traffic Administration, 1987]; less than half of these are wearing helmets at the time of the crash [Hedlund, 1985]. A number of investigations report that increases in fatalities followed repeal of mandatory helmet-wearing laws [Chenier and Evans, 1987; Graham and Lee, 1986; Hartunian, Smart, Willemain, and Zador, 1983]; more recently de Wolf [1986] reports an increase in fatalities per crash following repeal.

Although various data indicate that helmets prevent specific types of injuries, there is no previous paper focussing exclusively on the overall average effectiveness of motorcycle helmets in preventing a fatality in crashes. As well as being important in itself, the question of overall effectiveness is additionally important because it provides another example of the magnitude of fatality reductions obtainable by occupant protection devices in crashes. Such information may be helpful in providing insights about potential effectiveness of devices not yet made, or in guiding thinking about the likely effectiveness of already existing devices for which there are insufficient in-use data to make empirical estimates [Evans, 1987a]. Overall effectiveness estimates also allow more effective examination of the effect on motorcyclist fatalities of passing and repealing mandatory helmet-wearing laws. This provides additional information on how users might change their behavior in response to laws requiring the use of crash protection equipment in general.

In this paper, the effectiveness of motorcycle helmets in preventing fatalities is estimated using the double pair comparison method [Evans, 1986a]. A related problem of the relative safety of the driver and passenger seating positions is also discussed.

*An earlier version of this paper, which used FARS data through 1984. rather than through 1986, was presented to the 31st Annual Conference of the American Association for Automotive Medicine, New Orleans, September 1987, and appears in the Proceedings of the meeting.

447

448 L. EVANS and M. C. FRICK

PROCEDURE

The double pair comparison method The double pair comparison method used previously to determine safety belt ef-

fectiveness [Evans, 1986b; 1988a; Evans and Frick, 1986] is here applied to determine motorcycle helmet effectiveness. As the method and the assumptions on which it is based are described fully in [Evans, 1986a], only sufficient details are provided to make this paper self-contained. The method focuses on vehicles containing two occupants, referred to as a "subject" occupant and a "control" occupant, at least one of whom is killed. We here use the term "control" occupant, as used by Dalmotas and Krzyzewski [1987], in preference to the term " o t h e r " occupant used in earlier papers cited. The probabilities of a fatality to the subject occupant under two conditions, helmeted and unhelmeted, are compared. The control occupant serves essentially a normalizing, or exposure estimating, role. Using matched data to make inferences about protection device effectiveness has also been discussed by Hutchinson [1980;1982].

All "occupants" in this study are riders of motorcycles (minibikes, mopeds, etc. are excluded)- -e i ther drivers, or passengers seated behind the driver. The study is confined to motorcycles carrying both riders; helmet effectiveness in preventing fatalities to each is determined using the other to estimate exposure. The method is described below for one of these two cases, namely, when the driver is the subject occupant and the passenger is the control occupant.

The method uses two sets of fatal crashes. The first set consists of crashes involving motorcycles carrying a helmeted driver and an unhelmeted passenger, at least one of whom is killed. From the numbers of driver and passenger fatalities, a helmeted driver to unhelmeted passenger fatality ratio is calculated. From a second set of crashes involving motorcycles containing unhelmeted drivers and unhelmeted passengers, an unhelmeted driver to unhelmeted passenger fatality ratio is similarly estimated. Under assumptions discussed in Evans [1986a], dividing the first fatality ratio by the second gives the probability that a helmeted driver is killed compared to the corresponding probability that an unhelmeted driver is killed, averaged over the distribution of motorcycle crashes that occur in actual traffic; this is the measure of safety helmet effectiveness sought.

The control occupant, the unhelmeted passenger, does not enter directly into the result, so that a number of separate estimates can be calculated by choosing a variety of control occupants. In the present investigation eight estimates are obtained.

In the result section, all the required calculations to determine individual estimates of effectiveness and to combine many estimates together to generate a more precise overall estimate are given in terms of one specific numerical example.

Data Fatal Accident Reporting System (FARS) data for 1975 through 1986 are used;

FARS is a computerized data file maintained by the National Highway Traffic Safety Administration containing detailed information on all traffic crashes occurring in the United States since January 1, 1975 in which anyone was killed. The narrowness of the distributions of the riders by age (Fig. 1) allows us to perform the analysis in a manner somewhat different from the earlier safety belt effectiveness investigations [Evans, 1986b; 1988a; Evans and Frick, 1986]. The present study focuses on cases in which driver age does not differ from passenger age by more than a small, arbitrarily chosen, amount. By ensuring that subject and control occupant are essentially the same age, potential biases due to different survivability as a function of age [Evans, 1988b] are largely removed.

Potential biases due to different survivability as a function of sex [Evans, 1988b] are removed by disaggregating passengers by sex (see Table 1). Drivers could not be so disaggregated because of insufficient data for female drivers. Instead, the study uses only male driver data, so that the term "driver" hereafter implies "male driver."

The analysis is based on the data shown in Table 1, for which the chosen age

Helmet effectiveness in motorcycle fatalities 449

700

6 0 0

5O0

C ° 400 == O" 0) 300

,,=-

200

100

0

i 1 i t i t

• l

• Driver Age

• _P_a_ _a_a_e_ _n_Q 9_r_ _A_ g ~

I t

0 10 20 30 40 50 60 70

Age Fig. 1. Numbers of motorcycle drivers and passengers distributed by age (in one year age cells). Only data from motorcycles with driver and a passenger (at least one of whom was killed) are included. The FARS data, 1975 through 1986, had 7,584 such motorcycles coded, so that the area under each of the

two curves is also equal to 7,584.

difference is three years. The analysis was repeated using other values, and also per- formed using other approaches such as those of the earlier safety belt investigations, in which data were divided into three categories of subject age, or used without any re- strictions. As discussed later, these various choices have minimal effect on the effectiveness estimates.

Confining the study to cases in which driver and passenger age are closely similar (and including only male drivers) requires discarding a portion of the data. Clearly, the more nearly identical we require the ages to be, the more data will be discarded. Re- quiring driver and passenger age to be within three years of each other was chosen as a compromise between keeping sufficient data to perform the study and removing as

Table 1. Data from FARS, 1975-1986, for motorcycles with drivers and passengers aged 16 years or older. Only cases in which driver and passenger age differ by three or less years were retained for the analysis. In addition,

the cases with female drivers were eliminated

Total Used in Fatalities Study

Helmeted 1,862 1,094 Male Unhelmeted 2,336 1,371

Drivers Helmeted 25 0

Female Unhelmeted 46 0 Helmeted 620 426

Male Unhelmeted 1,109 725 Passengers Helmeted 894 468

Female Unhelmeted 1,214 630 TOTALS 8,106 4,714


much as possible potentially biasing age effects. This choice (see Table 1) led to discarding 42% of the data.

The crucial information for this study is provided by cases in which helmet use of driver and passenger differ. There is a strong tendency for both riders to be either helmeted or not helmeted. Hence, sample sizes in the really important cells are smaller than would arise if helmet use were distributed randomly among riders; helmet use by motorcyclists in fatal crashes is about 42%, considerably higher than the 5% belt use by car occupants in fatal crashes [National Highway Traffic Administration, 1987]. The sample sizes are different for each subject and control occupant pair and are given in the tables (which present all the raw data used in the study) for the specific pairs in the results section.

R E S U L T S

All the equations required in this report are given in terms of a specific numerical example; for derivations, justifications, proofs and discussion of these equations, see Evans [1986a], in which the equations are developed in terminology identical to that used here.

The specific example chosen uses the driver as the subject occupant, and the unhelmeted male passenger as the control occupant. The raw fatality data for this case are given as the first of the four cases in Table 2. These data show that a = 70 helmeted drivers were killed travelling with unhelmeted male passengers who were not killed, b = 84 unhelmeted male passengers were killed travelling with helmeted drivers who were not killed, and there were c = 37 cases in which helmeted drivers and unhelmeted male passengers travelling together were both killed. From these values we compute the helmeted driver to unhelmeted passenger ratio

r 1 = (a + c ) / ( b + c) = d / e = 107/121 = 0.884. (1)

Similarly, the unhelmeted driver to unhelmeted male passenger ratio is given by

r2 = ( j + l ) / ( k + l) = m / n = 772/604 = 1.278, (2)

where j, k, and l are defined as a, b, and c, except that the driver is unhelmeted. The helmeted to unhelmeted fatality ratio for drivers is then given by

R = n d / m e = r~/r2 = 0.692, (3)

Table 2. Calculation of the effectiveness of helmets in preventing fatalities to d r i v e r s . For each datum, driver and passenger age do not differ by more than three years. The fatality frequencies a, b, c, j, k, and l are defined in the text and extracted from the FARS data; all the other quantities are functions

of these, as explained in the text

First (upper) and Second (lower) Comparison Data

Control Occupant (passenger) a b c d e rt Error Range

Characteristics j k I m n r, R E(%) (%)

Unhelmeted 70 84 37 107 121 0.884 0.692 30.8 18 to 42 male 546 378 226 772 604 1.278

Unhelmeted 27 36 10 37 46 0.804 0.916 8.4 - 18 to 29 female 342 413 171 513 584 0.878

Helmeted 360 259 152 512 411 1.246 0.456 54.4 37 to 67 male 34 8 7 41 15 2.733

Helmeted 279 270 159 438 429 1.021 0.885 11.5 - 14 to 31

female 39 33 6 45 39 1.154 Weighted average values 0.735 26.5 17 to 35

Average effectiveness in preventing driver fatalities = (26.5 -+ 8.5)%.

Helmet effectiveness in motorcycle fatalities

or, expressed as a helmet effectiveness in percent, E, given by

451

E = 100(1 - R) = 30.8%. (4)

Effectiveness, as defined as eqn (4), is the percent reduction in fatalities that would occur in a population of unhelmeted motorcyclists if all were to adopt helmet use, with nothing else changing; this is essentially the same as the fatality risk reduction a random motorcyclist obtains by changing from helmet nonuse to helmet use. The standard error in the estimate of R, AR, is given by

AR = RX/cr 2 + 1/n + 1/d + l / m + 1/e, (5)

where % is an estimate of the intrinsic uncertainty. This is analogous to a random instrumental error. It reflects that, even if we had very large sample sizes, we would still not know the effectiveness of helmets in preventing fatalities to unlimited precision because of unidentifiable inadequacies in the method. As before [Evans, 1986b; 1988a; Evans and Frick, 1986], we take or, = 0.1; that is, we assume that even in the limit of very large samples, unknown confounding effects limit the accuracy that can be obtained by an individual determination to about ---10%. Sample sizes are sufficiently small that this choice, rather than zero, for cry, has a negligible effect on results.

The error bounds are then given as

and

E, . . . . = 10011 - exp(log(R) + o-)] (6)

Eupp~ = 10011 - exp(log(R) - cr)], (7)

where cr is defined as AR/R. Equations (6) and (7) are used in preference to the simpler assumption of a sym-

metric error, AE, in the effectiveness, given by

AE = IOOR~r. (8)

This error estimate, which was used in the prior work [Evans, 1986b; 1988a; Evans and Frick, 1986], is derived by assuming that cr is small compared to unity [Evans, 1986a]. This assumption was used only to present errors in convenient fo rm-- i t is not contained in any derivations. Equations (6) and (7), which reflect that errors are in fact symmetric around the logarithm of R, rather than around R, is more appropriate when ~ becomes large due to few data. The numerical values in the present example substituted into eqns (6) and (7) give lower and upper error limits of 17.6% and 41.9%, respectively. Applying eqn (8) gives E = (30.8 --- 12.1)%.

The weighted average of the four values of R in Table 2, R, is obtained as

-R = exp [ ~ wX l o g ( R ) / ~ w] (9)

where the weight, w, is given by

w = (R /AR) 2 (10)

m

and the summation is over the four values of R. For the data in Table 2, R has the value 0.735, or an average helmet effectiveness of 26.5%.

The error in the average value of R, AR, is given by

(11)


which, for the present case is 0.085, or 8.5%. For convenience, this, rather than the upper and lower bound estimates (also shown in Table 2), will be used. For small errors, the difference is immaterial.

Thus, the data in Table 2 give the following estimate of helmet effectiveness for drivers:

(26.5 ± 8.5)%. (12)

Table 3 shows data for passengers as subject occupants. Although it is in this case possible to disaggregate the subject by sex, the control occupant (the driver) cannot be so disaggregated because of too few female drivers (see Table 1). The data in Table 3 can be used to obtain separate effectiveness estimates for male and female passengers; these are (35.6 -+ 10.1)% for males and (22.6 ± 13.7)% for females. As these estimates do not indicate any statistically significant difference between effectiveness for male and female passengers, all four values in Table 3 are combined, as was done for the Table 2 data, to give that helmet effectiveness in preventing fatalities to motorcycle passengers is

(30.2 + 8.2)%. (13)

The estimates in eqns (12) and (13) give no indication that effectiveness is different in the two seating positions. It is, therefore, appropriate to combine them to obtain a composite estimate, using eqn (9). However, because the same data organized differently are used in the driver and passenger estimates, these estimates are not independent. It would accordingly be inappropriate to combine their errors as was done for the four estimates in each of Tables 2 and 3. Instead, we make the conservative choice of taking the overall error as the one obtained for the passenger, without reducing it further to reflect the additional information from the driver analysis.

Thus we estimate that the effectiveness of helmets in preventing fatalities to motorcycle riders is

(28.4 _+ 8.2)%. (14)

Effect of performing the analysis in different ways Equation (14), which gives that helmets are (28 + 8)% effective in preventing

fatalities, was obtained by an analysis in which data were disaggregated by passenger sex, and driver and passenger age agreed to within three years. The study was repeated applying a variety of different analysis approaches, with the results shown in Table 4.

Table 3. Calculation of the effectiveness of helmets in preventing fatalities to passengers. Male and female passengers are considered separately. Drivers (in all cases, male) serve as control occupants. The fatality frequencies a, b, c, j, k, and ! are defined in the text and extracted from the FARS data; all the other quantit ies

are functions of these, as explained in the text.

Occupant Characteristics First (upper) and Second (lower)

Compar ison Data Error

Subject = Control = a b c d e r~ Range passenger driver j k l m n r2 R E (%) (%)

8 34 7 15 41 0.366 Male Not helmeted 0.468 53.2 35 to 66

378 546 226 604 772 0.782 259 360 152 411 512 0.803

Male Helmeted 0.710 29.0 15 to 41 84 70 37 121 107 1.131 33 39 6 39 45 0.867

Female Not helmeted 0.761 23.9 2 to 41 413 342 171 584 513 1.138 270 279 159 429 438 0.979

Female Helmeted 0.788 21.2 - 1 to 39 36 27 10 46 37 1.243

Weighted average values 0.698 30.2 22 to 38

Average effectiveness in preventing passenger fatalities = (30.2 -+ 8.2)%.

Helmet effectiveness in motorcycle fatalities

Table 4. Results of performing the analysis in a number of different ways. In all cases, the data are disaggregated by helmet use of the control occupant. The effectiveness estimate is the weighted average for drivers and passengers combined; the error is the standard error of driver or passenger estimate (whichever is smaller). The main result

of the study, as presented in eqn (14), is in bold type

Disaggregation Scheme Used in Analysis Effectiveness

No disaggregation (apart from helmet use) Into three age categories (16-20; 21-25; ->26) By sex, into three age categories By sex, driver, and passenger age within 2 years By sex, driver, and passenger age within 3 years By sex, driver, and passenger age within 5 years By sex, driver, and passenger age not restricted

(29 4- 7)% (27 _+ 6)% (28 +- 6)% (28 _+ 9)% (28 ± 8)% (33 4- 7)% (31 4- 6)%

453

Table 4 shows tha t the resul t is re la t ive ly robus t , be ing not much a f fec ted by the choice of d i saggrega t ion scheme. This i l lus t ra tes the s t rong t e n d e n c y of b iases f rom even large con found ing in te rac t ions to be r e m o v e d by the doub le pa i r c o m p a r i s o n m e t h o d . F o r e x a m p l e , a l though females have lower survivabi l i ty to physical t r a u m a than males [Evans , 1988b], this does no t affect ef fec t iveness es t ima tes if h e l m e t e d and u n h e l m e t e d dr ivers a re a c c o m p a n i e d by passengers s imi lar ly d i s t r ibu ted by sex ( the inf luence of some poss ib le sys temat ic b iases , which would not be au tomat i ca l ly r e m o v e d by d i saggrega t ing da ta , a re d iscussed in Evans [1988c D. F r o m Tab le 4, no te in pa r t i cu la r tha t the resul t wi thou t any d i saggrega t ion is in close a g r e e m e n t with the resul t [eqn (14)] in which the ca tegor ica l va r iab le sex is con t ro l l ed , and the con t inuous var iab le age is con t ro l l ed wi thin na r row limits. Such a f inding al lows more conf iden t in ferences to be m a d e in cases where there a re so few da t a tha t the on ly feas ible analysis is the s imple one wi thou t d isaggre- ga t ion , as was the case in Evans [1988a] and Evans and Fr ick [1986].

Relative safety of driver and passenger seating positions The a b o v e ana lyses p rov ide no ind ica t ion tha t he lme t ef fec t iveness is d i f fe ren t for

dr ivers and passenger s [see eqns (12) and (13)]; howeve r , this does not p rov ide infor- ma t ion on the re la t ive safety of dr iver and passenge r sea t ing pos i t ions , which is the sub jec t of this sect ion.

Table 5 gives the n u m b e r s of mo to rcyc le dr iver and pas senge r fa ta l i t ies for cases in which he lme t use was the same for each , and (as be fo re ) age of pas senge r and dr iver d id not differ by m o r e than th ree years . The ra t ios shown are s imply counts of d r iver to pa s senge r dea ths for c rashes by moto rcyc l e s with a dr iver and a pas senge r , at least one of w h o m is ki l led. The ra t ios do not involve the doub le pa i r c o m p a r i s o n m e t h o d .

Table 5. Relative fatality risk for drivers and passengers with same helmet use and similar age (to within three years). For the male passengers, the ratio reflects only differences due to the seating position; for the female passengers, the ratio reflects a combination of effects due to seating position

and lower survivability of females compared to males

Male Passengers Female Passengers

Fatalities Fatalities

Age, Years Helmet Use Driver Passenger Ratio Driver Passenger Ratio

16-20 No 374 280 1.336 161 192 0.839 Yes 271 224 1.210 106 122 0.869

21-25 No 294 237 1.241 195 212 0.920 Yes 178 138 1.290 171 146 1.17l No 104 87 1.195 157 180 0.872 ->26 Yes 63 49 1.286 161 161 1.000

Average values of ratio 1.260 0.945 Standard deviation 0.054 0.124 Standard error of mean 0.022 0.051

454 L. EVANS and M, C. FRICK

Sample sizes are consequently larger, because cases in which driver and passenger helmet use agree provide all the information, whereas in double pair comparison, the rarer cases in which driver helmet use is different from passenger helmet use provide crucial information. Note that passenger age is not necessarily in the same category as the indicated driver category, because, for example, a 20-year-old driver will be included in the first category if accompanied by a passenger aged 17 through 23.

The ratio of driver to passenger fatalities measures the relative fatality risk to these drivers averaged over the motorcycle crashes which occur in traffic. This ratio is presented separately for male and female passengers.

For male passengers, driver and passenger are the same in helmet use and sex and similar in age. Hence, the only obvious major difference between them is seating position. The six values of the ratio of driver to passenger fatalities show drivers consistently at higher fatality risk, the increased fatality risk being in a narrow range of 20.0% to 34.0%. From the six values, we conclude that when driver and passenger are present, other factors being equal, fatality risk to the driver is (26 - 2)% greater than that to the passenger; the error is one standard error, obtained by dividing the standard deviation by the square root of the number of values (six). This value is lower than the (31 -+ 2)% we found [Evans and Frick, 1987b] using 1975-1984 FARS data; the difference implies that, for the additional 1985 and 1986 data, the driver fatality risk did not exceed that for the passenger nearly as much as found in the overall data.

The corresponding information for female passengers indicates that a female passenger is 100(1 - 0.945) = 5.5% less likely to be killed than a male driver. However, this result reflects differences due to sex as well as seating position. Indeed, the ratio of the two ratios, 1.260/0.945 = 1.333 indicates that female passengers are 33.3% more likely to be killed than are male passengers of the same age, which agrees well with the results in Evans [1988b]. Basically, the reduced fatality risk associated with the passenger seat is similar in magnitude to the increased fatality risk associated with being female, so that female passengers and male drivers of similar age have similar fatality risk.

The consistency of the estimates and consequent precision of the composite results from Table 5 suggests that the method of disaggregating occupant sex, and confining ages to agree within specified limits, might be a powerful method for comparing relative fatality risk as a function of seating position for other vehicles. Indeed, Evans and Frick [1987a] applied this same approach to determine the relative fatality risk to car occupants as a function of seating position.

It is beyond the scope of the present investigation to explore in detail the mechanisms by which the driver is (26 --- 2)% more likely to be killed than is the passenger. However , as the explanation may be related to physical interaction between the occupants during the crash, it seems appropriate to examine the influence of impact direction.

Table 6 shows data for frontal and for nonfrontal crashes, defined in terms of the principal impact variable in FARS. Frontal crashes are restricted to principal impact direction 12 o'clock; all other principal impacts are considered nonfrontal. The data of Table 6, in contrast to those in Table 5, are not disaggregated into age categories, nor

Table 6. Relative fatality risk for drivers and passengers with same helmet use for frontal crashes (12 o'clock) and nonfrontal crashes

Male Passengers Female Passengers

Fatalities Average -+ Fatalities Principal Helmet Standard Impact Use Dry. Pass. Ratio Error Drv. Pass. Ratio

Average ± Standard

Error

No 756 567 1.333 645 636 1.014 12 o'clock 1.395 ± 0.062

Yes 520 357 1.457 578 454 1.273 No 381 364 1.047 397 466 0.852

Not l2 o'clock 1.008 ± 0.039 Yes 217 224 0.969 317 378 0.839 No 1137 931 1.221 1042 1 1 0 2 0.946

All 1.245 ± 0.024 Yes 737 581 1.269 895 832 1.076

1.144 --- 0.130

0.846 -+ 0.007

1.011 +- 0.065


are they restricted to drivers and passengers of similar age. For the following reasons, this probably has no more than a small effect. The average ratio for males for all principal impacts, 1.245 -+ 0.024 is close to the corresponding value, 1.262 -+ 0.017, inferred from the data in Table 5 by summing the raw data for all age categories; this in turn is close to the value, 1.260 -+ 0.022, obtained by including age disaggregation. The corresponding values for females are 1.011 +- 0.065, 0.950 -+ 0.071, and 0.945 -+ 0.049, respectively.

The data in Table 6 indicate clearly that in frontal crashes drivers have a substantially higher, (40 -+ 6)%, risk of fatality than passengers of the same sex and, by implication, using the reasoning in the last paragraph, also of similar age. For nonfrontal crashes (clock points 1, 2, 3 . . . through 11, and including noncrashes such as falling off skidding motorcycle) the difference, (1 -+ 4)%, is close to zero. These findings are consistent with the driver being at increased risk due to loading from the passenger, or with the passenger being at reduced risk due to being cushioned by the driver (see also a discussion of similar possible effects in car side impacts in Evans [1988c]). However, the magnitude of the effects found suggest the possibility of other contributing mechanisms. For example, the passenger's trajectory might be beneficially influenced by the presence of the driver; perhaps, in some approximate sense, the passenger has a "second" collision with the driver that consequently reduces the kinetic energy that must be absorbed in collisions with objects external to the motorcycle. Understanding of the elevated risk to drivers compared to passengers will require understanding of occupant kinematics during the crash.

DISCUSSION

This study finds three factors to be associated with lower fatality risk to motorcycle riders, in all three cases the reduction in fatality risk being about 30%: (1) wearing a helmet compared to not wearing one, (2) being a passenger rather than being a driver, and (3) being male rather than female. The last finding confirms previously reported work [Evans, 1988b].

The main finding of the study is that helmet use reduces fatality risk to motorcycle drivers and passengers by (28 -+ 8)%. The result depends on the assumptions on which the double pair comparison method [Evans, 1986a] rests; in particular, on the assumption that the effectiveness of helmets for drivers travelling accompanied by passengers is sufficiently similar to the effectiveness for drivers travelling alone. This assumption could be violated through two distinct mechanisms. First, the presence of the passenger might affect the biomechanical and kinematic experience of the driver to render the outcome importantly different than if the passenger had not been present. Second, the distribution of crashes in various types (single vehicle, into car, etc.) might be different for motorcycles with two occupants than with one occupant. Note that both mechanisms relate only to the determination of effectiveness for the driver--the passenger always rides with a driver present,

Basically, given that we need both occupants to make an effectiveness estimate using the double pair comparison method, it is not possible to obtain estimates for the driver alone to examine such effects quantitatively. The difference in fatality risk to driver and passenger does not, in itself, require that the driver risk be influenced by the presence of the passenger; even if the driver risk is so influenced, this changes helmet effectiveness only if it influences driver risk differently in the helmeted and unhelmeted cases. The most likely mechanism is that the driver is loaded in a frontal crash by the presence of the passenger, although one cannot rule out that the presence of the passenger would influence the trajectory of the driver. If loading by the passenger on the driver increased driver fatalities due to nonhead injuries, then, other factors being equal, this would decrease helmet effectiveness. Similarly, if cushioning decreased fatalities due to nonhead injuries for the passenger, this would increase the effectiveness estimate for passengers. Indeed, the nominally higher effectiveness for the passenger is consistent with such an interpretation. If the loading and cushioning have similar quantitative effects on effectiveness, then taking the average for driver and passenger would remove any systematic


bias from such effects. We consider any net bias, whose sign cannot be predicted, to be small relative to the uncertainty in the estimate.

The data do not permit a fruitful analysis of effectiveness versus crash type. There- fore, any differences in distributions by crash type for motorcycles containing one or two occupants cannot be used to imply differences in helmet effectiveness for accompanied compared to unaccompanied drivers. For the case of lap/shoulder belts in cars [Evans and Frick, 1986], we found effectiveness reasonably similar over a variety of crash types, so that different distributions of crash types are unlikely to make much difference in overall effectiveness. We consider it likely that helmet effectiveness would be even less variable over different crash types than was so for lap/shoulder belts, given that the impact suffered by the occupant is generally external to the vehicle in the motorcycle case. We thus consider the assumption that the effectiveness estimates determined for drivers accompanied by passengers applies also to lone drivers to be ade- quately correct, especially in the light of the uncertainty implicit in any determination of helmet effectiveness.

The main result of the study that effectiveness is (28 _+ 8)% differs from our earlier published estimate (Evans and Frick, 1987b; Evans 1987d] of (27 _+ 9)%. This was based on FARS data for 1975-1984, unlike the present study which used data for 1975-1986. Our main result is within the 10.4% to 33.3% range reported by de Wolf [1986], where the range indicates two standard errors (95% confidence) in contrast to the one standard error we use; no estimate of the central value, or most likely value was given. Watson, Zador , and Wilks [1981] report that helmets are 52% effective in reducing fatalities due to head injuries and that 66% of unhelmeted driver fatalities are due to head injuries, so that the product of these therefore implies that helmets are 34% effective in preventing fatalities, in good agreement with the present estimate.

A recent study [Goldstein, 1986] addressed whether helmets reduced fatality risk in crashes by applying multivariate analyses to 644 cases (of which, apparently, under 3% involved fatality). Although no quantitative estimates are given, the following conclusion is not only stated, but is claimed to be important: "Helmets have no statistically significant effect on the probability of fatality." This conclusion illuminates two important points. First, the frailty of multivariate analyses using ten or so variables, especially if these are selected after examining the data; different choices of variables, t ransforma- tions, etc. can often generate just about any conclusion. Second, the inappropriate use and interpretation of hypothesis testing. For sufficiently small samples, no effect, no matter how large, is statistically significant. For sufficiently large samples, every effect, no matter how small or unimportant , becomes statistically significant. Quantitat ive estimates with error limits, say 20 + 30 or 0.003 -+ 0.001, convey crucial information immediately. In contrast, statements, in isolation and devoid of quantitative estimate, to the effect that the first difference is not statistically significant whereas the second one is, although true, are rarely useful.

Effect on repeal of mandatory wearing laws The results of the present study that helmet use reduces fatality risk to motorcycle

drivers and passengers by (28 _+ 8)% allows us to calculate fatality changes associated with helmet use rate changes, such as occurred when mandatory wearing laws were repealed in the mid 1970s. Based on more than 18,000 observations in 1984, the following wearing rates were calculated; in mandatory use locations, 99.7% for drivers and 98.4% for passengers; in locations with no or limited use laws, 51.3% for drivers and 34.8% for passengers.

If users and nonusers were random members of the same population, then, from eqn (3) of Evans [1987b], we would expect repeal of a mandatory wearing law to increase driver fatalities by (0.28 x 0.484)/(1 - 0.28 x 0.997) = 18.8%, assuming that the effect of repeal was to reduce use from 99.7% to 51.3%; a 24.6% increase is calculated for passengers. The FARS data give that helmeted wearers killed are 91.2% drivers and 9.8% passengers, so that the estimated increase in rider fatalities from repeal is 0.912 x 18.8 + 0.098 x 24.6% = 20%.


The use rate changes assumed above may be too large, because after repeal some users who were not initially voluntary users may continue to be users. Habi t and the already purchased helmet would contribute to such an effect, which would reduce the expected fatality increase of repeal to below the 20% calculated. On the other hand, the assumption that users and nonusers are random members of the same populat ion may generate a bias in the opposite direction. Although such effects have been quantified (and found to be relatively small) for safety belt use in cars [Evans, 1987b; 1987c; 1985], this can not be done for the helmets case because there are no data available on relative crash involvement rates of users and nonusers. Let us therefore examine how the simply calculated 20% fatality increase in rider fatalities compares with observed changes.

Watson, Zador , and Wilks [1981] report that repeal led to a 40% increase in motorcyclist fatalities. However , Adams [1983] criticized the methodology in this study, and his reanalysis of the same data led to a claim that the effect was close to zero. Recently, de Wolf [1986] reports an effect in the range of 4% to 10%; let us assume, for convenience, a point estimate is 7%. A (25 -+ 3)% increase is reported by Chenier and Evans [1987]; this is a revision of an earlier calculation [Chenier and Evans, 1985] which gave (28 +-- 3)%. Some background to this study, which, incidentally, answers some questions raised by Adams [1985], is given in [Evans, 1986c], Increases of 14% and 22% are reported by Graham and Lee [1986] in fatalities after controlling for changes in registrations; the two values reflect different calculation assumptions. A 24% increase in fatalities is repor ted in Hartunian et al. [1983]. Taken together, the estimates collec- tively indicate that the fatality increase associated with repeal may have exceeded the 20% calculated from the helmet effectiveness estimate. If true, this would suggest the human behavior interactive effects [Evans, 1985] may be a m p l i f y i n g the direct effect of the legislative change. Indeed, it has been suggested [Evans, 1987b; 1985] that obser- vational and other data indicate (weakly) that benefits of mandatory safety belt wearing laws may also exceed calculated benefits because of interactive effects. That is, it is possible that the act of fastening the restraint may act as a safety reminder, thus contributing to crash reduction as well as protection in crashes.

Any interactive effects due to repeal of helmet wearing laws appear to be small. Indeed, the finding that motorcycle helmets are (28 +- 8)% effective in preventing fatalities, and the consequent inference that repealing mandatory wearing laws would generate a 20% fatality increase, is in fairly close agreement with the four of the above estimates of actual fatality increases which were 25%, 14%, 22% and 24% (the other three estimates, 40%, 7% and 0% appear to be outside the general pattern).

Acknowledgements--This paper has benefitted greatly from valuable inputs from Drs. John D. Graham, T. Paul Hutchinson, Charles J. Kahane, Rudolf G. Mortimer, and Paul Zador.

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helmet effectiveness in preventing motorcycle driver and passenger fatalities

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