Amid. Anal. & Prev. Vol. 20. No. 3. pp. 215-218. 1988 OKI-4575188 $3.00 + .Kl

Printed in Great Britain. Q 1988 Pergamon Press plc

EXAMINATION OF SOME POSSIBLE BIASES IN DOUBLE PAIR COMPARISON ESTIMATES OF

SAFETY BELT EFFECTIVENESS

LEONARD EVANS Operating Sciences Department, General Motors Research Laboratories, Warren, MI 48090,

U.S.A.

(Received 18 July 1986; in revised form 26 June 1987)

Abstract-Biases in double pair comparison estimates of safety belt effectiveness due to two effects (noncoding of some surviving passengers, and driver/passenger impact during crashes) are investigated by calculating effectiveness from fatality frequencies assumed altered by the biases. Noncoding surviving right-front passengers does not affect estimates for drivers, but does overestimate slightly passenger effectiveness. Two biasing driver/passenger contact effects occur for right-side impacfs-a “cushioning” effect (risk to unbelted driver is reduced by striking passenger rather than the vehicle interior) and a “missile” effect (passenger risk is increased by being struck by unrestrained driver). Cushioning and missile effects both reduce estimates; their combined effects could cause right-side impact effectiveness to be underestimated by as much as 20% (probably much less). Correcting for all effects increases the overall estimate from 42.6% to 43.2%. Thus, to the nearest percent, the result is still that if all presently unbelted drivers and right-front-seat passengers were to become wearers, fatalities to this group would decline by (43 2 3)%.

INTRODUCTION

In this paper we examine how two types of potential biases might affect safety belt effectiveness estimates obtained using the double pair comparison method [Evans, 1986a]. These are: (1) noncoding of surviving occupants in the Fatal Accident Reporting System (FARS) data, and (2) changes in fatality risk due to physical contact between drivers and passengers during crashes. One example is worked out in detail in the paper; for other cases results only are given. For complete derivations the reader is referred to Evans [ 1986b].

The double pair comparison method (hereafter called the method) uses data coded in the FARS [1987]. It is possible that, especially in the early FARS years, some surviving occupants may not have been coded. This could have arisen because the main focus of the data is fatally injured occupants. In addition, the police officers on the scene, who provide the source data, would naturally devote most of their attention to the most seriously injured occupants. The problem was most likely to occur for those few cases in which, although one occupant was fatally injured, another occupant departed the vehicle unassisted. Cars containing a driver and a right-front passenger (hereafter called simply “passenger”) which are involved in crashes killing the driver but not the passenger are central to the method. However, if the surviving passenger is not coded, this crash would appear as a single-occupant crash, which therefore cannot be used. Here we calculate how such noncoded surviving passengers might change safety belt effectiveness estimates.

Evans [1986c] estimated the overall effectiveness of safety belts in preventing fa- talities to drivers and right-front passengers of cars as (43 +3)%. Part of the calculation involved assuming that effectiveness estimated using the method, which intrinsically requires more than one occupant in the vehicle, also applies to drivers traveling alone. This is a good assumption for most crashes, because the drivers’ survivability should not be affected by the presence of other occupants. An exception is side crashes. In a right- side impact crash, a lone unbelted driver might strike the right-vehicle-interior, whereas when an accompanying passenger is present, the impact forces would be reduced by the cushioning effect of the passenger. In such crashes, the passenger would be at greater risk, due to being struck by the driver, such increased risk not being present when the

215

216 L. EVANS

driver is belted. These effects, which flow from physical contact between occupants, will be called “cushioning” and “missile” effects.

TERMINOLOGY AND APPROACH

In order to determine how noncoded surviving occupants and physical contact be- tween occupants might change safety belt effectiveness estimates, we expand on the earlier terminology [Evans, 1986a]. Fatality frequency counts which would be coded in FARS are represented by lower case letters a, b, c, j, k, and 1; the definitions are as in the earlier papers (for convenience, definitions are again given in Fig. 1). We refer to these as “observed” frequencies, indicating that they include influences reflecting the effects discussed here.

The hypothetical frequencies which would be observed in the absence of the biases are denoted by the corresponding uppercase letters. These, and quantities derived from them, will be referred to as “true,” indicating that they are free of the biases present in the “observed” quantities.

The observed safety belt effectiveness, E, is given in Evans [1986a] as

E = lOO(1 - R),

where R is the observed belted to unbelted fatality ratio, defined by

R = (a + c)(k + 4 (b + c)o’ + 1)’

(1)

The true safety belt effectiveness, E, is here correspondingly defined by

E = lOO(1 - p),

where p is the true belted to unbelted fatality ratio, defined by

(A + C)(K + L)

p = (B + C)(J + L)

(2)

(3)

(4)

FIRST

COMPARISON

SECOND

COMPARISON

‘x 0’ D* Pl

A = pJ

a = (l-$)A

‘x 0’

D p2

J

j = (1-))J

‘0 x’ D* Pl

B = K+(l-p)L

b B =

‘0 x’ D

p2

K

k K =

‘x x’ D+ Pl

c = pL

c=c

‘x x’

D p2

L

I L =

Fig. 1, Influence of driver safety belt effectiveness estimates of not coding in FARS a fraction, 9, of surviving passengers. The actual numbers of fatalities are represented by uppercase letters, and these coded in FARS by lowercase. X = killed, 0 = not killed, D = unbelted driver, D* = belted driver,

P = passenger (unbelted) and p = actual belted to unbelted driver fatality ratio.

Biases in estimates of safety belt effectiveness 217

The approach is to consider very general, but hypothetical, scenarios which would generate the uppercase fatality frequency counts, and explore how each of the effects would modify these to produce the observed (lowercase) frequencies that would be coded in FARS. If we find, for example, that R is larger than p (which implies that E is smaller than E), we will say that the observed estimate of effectiveness is decreased, meaning that the method underestimates the true benefits of safety belt wearing.

RESULTS

As noncoding of surviving passengers influences effectiveness estimates for drivers and passengers in different ways, let us first estimate in detail the effect for drivers, referring to Fig. 1 [which corresponds to Fig. 1 of Evans, 1986a]. Let us focus first on the second comparison data. In order to obtain the first comparison frequency counts, we “replicate” the second comparison crashes, with all factors the same except one. The factor we change is that, in the replication, the driver is belted. Assuming that the true belted to unbelted driver fatality ratio is p, we can write the first comparison true fatality frequencies as follows:

and

A = pJ, (5)

c = pL, (6)

B = K + (1 - p)L. (7)

The second term in eqn 7 reflects that, due to driver safety belt use, some former cases in which both driver and passenger were killed become cases in which only the passenger is killed. Substituting these frequency counts into eqn 4 readily reproduces the definition of p.

Now let us assume that a fraction, $, of surviving passengers are uncoded in the FARS data. That is, the observed count, a, is given by

a = (1 - +)A. (8)

Let us assume that the fraction of surviving passengers uncoded is independent of whether or not the driver wears a safety belt. This then gives

j = (1 - +)J. (9)

We assume that there are no cases in which the vehicle is coded as not having a driver. Therefore, all the other frequency counts in FARS reflect correctly the actual frequencies (that is b = B, c = C, k = K, and 1 = L). The above definitions and simple derivations are reproduced in Fig. 1.

Substituting eqns 5-9 into eqn 2 gives:

R = P, (10)

Hence, the noncoding of surviving passengers has zero effect on the estimate of safety belt effectiveness for drivers, provided such noncoding is not itself a function of driver safety belt use.

Applying similar reasoning [Evans, 1986131 to determining belt effectiveness for the passenger using the driver as the other occupant gives that missing survivor data cause the method to systematically overestimate safety belt effectiveness, but by small amounts. For example, 10% missing data leads to a 0.8% overestimate.

As effects due to contact between occupants during crashes influence primarily side- impact crashes, the algebraic derivations are necessarily more complicated than for the

218 L. EVANS

case of missing data. Based on estimates [Park, 1987; Mackay, 19851 of the increase in fatality risk to front-seat occupants from being struck by rear-seat occupants in frontal crashes, I assume [Evans 1986b] that in a side-impact crash a near-side occupant’s fatality risk is increased by 8% by being struck by a far-side occupant. I similarly assume that the striking occupant’s fatality risk is reduced by the same 8% due to cushioning provided by the other occupant. These missile and cushioning effects both reduce estimates; their combined effects could cause right-side impact effectiveness to be underestimated by as much as 20% (probably much less). Although these effects can be relatively large in side impacts, such crashes generate a small fraction of all fatal crashes.

When all the biases are combined, weighted by driver and passenger occupancy, and by the fraction of side impacts, the revised estimate of effectiveness is (43.2 ? 3.0)%, compared to the former estimate [Evans, 1986~1 of (42.6 + 3.0)%. Thus, when rounded to the nearest percent the revised result of 43% is the same as previously reported.

Acknowledgments-Brian O’Neill, President, Insurance Institute for Highway Safety, raised the question of how noncoding of surviving passengers might affect estimates. Ian Jones, Director, Engineering Research and Support, at the same organization, brought up the question of cushioning benefits to drivers striking passengers in right-side impacts. I thank both for their insightful inputs and the obvious care. thoughtfulness, and attention to detail with which they read the earlier papers.

REFERENCES

Evans L., Double pair comparison-a new method to determine how occupant characteristics affect fatality risk in traffic crashes. Accid. Anal. Prev. 18, 217-227, 1986a.

Evans L., Examination of some possible biases in double pair comparison estimates of safety belt effectiveness. General Morors Research Publication GMR-5485, July 11, 1986b.

Evans L., The effectiveness of safety belts in preventing fatalities. Accid. Anal. Prev. 18, 229-241, 1986~. FARS (Fatal Accident Reporting System), National Highway Traffic Safety Administration, Fatal Accident

Reporting System 1985, Document DOT HS-807-071, February 1987. Mackay M., Two years’ experience with the seat belt law in Britain. SAE paper 851234. Society of Automotive

Engineers, May 1985. Park S., The influence of rear-seat occupants on front-seat occupant fatalities: The unbelted cast. General

Motors Research Laboratories Research Publication GMR-5664, January 8, 1987. Wilson R.A. and Savage C.M., Restraint system effectiveness-a study of fatal accidents. Proceedings of

Aufomofive Safety Engineering Seminar, sponsored by Automotive Safety Engineering, Environmental Activities Staff, General Motors Corporation. June 20-21, 1973.