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Rear lap/shoulder belt effectiveness estimated using data with miscoded belt use

Leonard Evans

Dated mid 1999.  This project was never  completed as I was preoccupied with other matters as I prepared to leave GM.  However, as I have been often asked about the reliability of belt coding,  I am making this near final draft available in the hope it might be helpful.  I am not in a position to pursue this research further -- but consider it well worth pursuing if resources are available.  It could provide the basis for a valuable thesis topic.



NHTSA recently used FARS data for 1988 through the first half of 1997 to estimate effectiveness of rear-seat belts. Their results include a finding that car rear-seat lap/shoulder belts reduce fatality risk by 36%. The purpose of this research is to estimate how much of this effectiveness estimate is attributable to the belt, and how much of it is attributable to miscoding unbelted occupants as belt wearers. Such miscoding, which biases effectiveness estimates towards higher values, has become an increasing problem since mandatory wearing laws were passed in the mid to late 1980s.


The NHTSA analysis also estimates the effectiveness of car rear-seat lap-only belts as 27%. Earlier GM and NHTSA research using 1975-1986 data estimated 18%. Assuming that the 18% estimate is unaffected by miscoding, the 27% estimate is used to show that about 10% of surviving occupants coded as belted were likely unbelted. By assuming that this same proportion applies to the lap/shoulder belt case, the effectiveness for lap/shoulder belts is computed with biasing influences due to miscoding reduced.


The following estimates of effectiveness for car rear-seat restraints are suggested: 

Lap belt only 18%

Lap/shoulder belt 29%

These are markedly different from the recent NHTSA estimates of 27% and 36%, respectively (higher values of 32% and 44% are reported when these plus additional estimates are averaged).


Safety belt effectiveness is usually estimated by analyzing data sets such as the Fatality Analysis Reporting System (FARS) (National Highway Traffic Administration, 1998) that document large numbers of crashes. A crucial assumption is that occupants coded as belted were belted. We use "miscoding" to indicate that a occupant coded as belted was in fact not belted. We assume that an occupant coded as unbelted was indeed unbelted. 

Since the advent of mandatory wearing laws in the mid to late 1980s, the possibility of miscoding has become a serious problem in FARS data. One factor generating miscoding is that an occupant at the crash scene who admits non-use of a belt to a police officer is likely admitting to a law violation. This should, formally at least, invite some actions on the part of the officer. In the context of a fatal-crash, the officer has good cause to not want to devote time to dispute claims of belt use. As such considerations do not apply to fatally injured occupants, we assume no miscoding for these. When unbelted occupants who survive are miscoded as belted, their survival will falsely be attributed to the belt, so miscoding biases observed belt effectiveness to be higher than true belt effectiveness.

The purpose of this paper is to present a method to estimate the fraction of occupants miscoded in FARS, and to use the results to modify an estimate of rear-seat lap/shoulder belt effectiveness in reducing fatality risk contained in a recent NHTSA report (Morgan 1999). The author stresses the formidable difficulties of estimating effectiveness in a "Caveats" section (p. 51). The present work aims at decreasing the magnitude of bias in estimates in the face of difficulties that have been a major problem for researchers trying to determine restraint effectiveness.

Based on one of a number of analyses using FARS data from 1988 through the first half of 1997, Morgan (1999) reports that rear-seat lap/shoulder belts reduce fatality risk by 36%. The double pair comparison method (Evans 1986) was used to infer effectiveness from FARS data.


Let us apply the same terminology as Evans (1996) to a vehicle containing a subject occupant and a control occupant, at least one being killed in the crash (a typical combination is driver as subject, right-front-passenger as control). The following quantities are extracted from FARS data.

A = number of crashes in which belted subject was killed but control survived

B = number of crashes in which belted subject survived but control  was killed

C = number of crashes in which belted subject and control  were both killed

J = number of crashes in which unbelted subject  was killed but control survive

K = number of crashes in which unbelted subject  survived but control was killed

L = number of crashes in which unbelted subject  and control  were both killed

The quantities A, B and C refer to subjects coded as belted, while J, K, and L refer to subjects coded as unbelted. The control occupant must have the same belt use in all six cases, but can be either belted or unbelted.

The observed percent belt effectiveness is estimated as EObserved = 100(1-RObserved) where

RObserved = {(K + L)(A + C) } / {(J + L)(B + C }         (Eqn 1)                                                                                                            


When controls are coded as unbelted, the question of control-induced biases does not arise because we assume that all occupants coded as unbelted are indeed unbelted. If controls are belted, then miscoding will cause to A and J to be larger than they would be in the absence of miscoding. If C/A = L/J, which tends to approximately so in real data, then RObserved will be unaffected by equal proportionate miscoding errors in A and J. So, miscoding of control occupants can have at most a minimal influence on estimates.

The only quantity subject to miscoding that directly affects B. Let us write

BTrue = (1-Λ)B ,                                                          (Eqn 2)

where Λ is the fraction miscoded. The number of occupants miscoded is ΛB. These should have been classified as unbelted, and therefore added to the observed quantity K, giving

KTrue = K + ΛB                                                            (Eqn 3)

The true percent belt effectiveness is estimated as ETrue = 100(1-RTrue) where


RTrue =  {(K + ΛB + L)(A + C)} / {(J + L)(B - ΛB + C)}         (Eqn 4)


Combining Eqns 1 and 4 allows us to solve for Λ as


Λ = { (ρ - 1)(K + L) }/ { B(ρα +1) }           (Eqn 5)


ρ = RTrue/RObserved                                 (Eqn 6)


α =   (K + L) /(B + C)                                    (Eqn 7)

If we knew the true effectiveness, then Eqn 5 estimates miscoding. 


Morgan (1999) estimates effectiveness of outboard car rear seat lap only belts and lap/shoulder belts using five different control occupants, and computes weighted averages of 32% and 44% respectively. This report uses only the estimates based on one control occupant, namely, belted front seat occupants. It is only for this case, which contributes by far the largest samples, that the raw data necessary for this study are given. The estimates using belted front occupants as controls are 27% for lap only belts and 36% for lap/shoulder belts.

The estimate for lap-only belts is calculated using (in the above terminology) A = 860, B = 804; C = 275, and J = 2312, K = 1382, L = 716. Substituting these values into Eqn 1 gives RObserved = 0.7288, equivalent to EObserved = 27%, as reported by Morgan (1999). This is higher than the value of about 18% estimated by applying the double pair comparison method to 1975-1986 FARS data (Evans 1987,1988; Kahane 1987). Let us assume that the true value is 18%, and that the 27% value is inflated due to miscoding. Substituting into Eqn 5 gives

Λ = 0.1024 .

That is, 10.2% of surviving rear seat occupants coded as belted were in fact unbelted.

Estimates are also given for the effectiveness of lap/shoulder belts, using A= 601, B= 674; C=206. The same values of J, K, and L as above are assumed (a reasonable assumption, but hardly necessary when the actual data are available in FARS). Substituting into Eqn 1 gives RObserved = 0.6354, equivalent to EObserved = 36%, as reported by Morgan (1999).

If we now assume that miscoding for lap/shoulder belts was the same as miscoding for lap only belts, then we can substitute Λ = 0.1024 into Eqn 4, and obtain ETrue = 28.78%.

There is considerable uncertainty in effectiveness estimates for rear seat restraints. The estimate identified as ETrue = 18% for lap only belts is reported by Evans (1986) as (18 9)%, where 9% is one standard error. Kahane (1987) finds a similar estimate and error. Despite the uncertainty, the following values are suggested as the best currently available for rear seat restraint effectiveness in reducing fatality risk.

Lap belt only 18%

Lap/shoulder belt 29%


The above application was to car rear-seat belts using published hard copy data. There seems to be no reason why the same procedure could not be applied to the other rear seat cases in Morgan (1999), namely different controls for car occupants, and estimates for vans and sports utility vehicles.

The method is expected to produce important information if applied to the much larger numbers of front seat occupants coded in FARS. The following procedure is suggested.

Select a cohort, of vehicles, say model years 1974, 1975 and 1976. Measure belt effectiveness for these vehicles using 1975 through 1986 calendar year FARS data. Assume that the result gives ETrue. Then obtain fatalities in this same cohort of vehicles in later calendar years of FARS. Substituting these into Eqn 5 will give Λ as a function of calendar year. A finding that EObserved has increased in time is more plausibly interpreted as increase in miscoding rather than an increase in the effectiveness of the same safety belts as they become older. Observed belt effectiveness for a given set of belts could increase if users started to fasten them in ways that enhanced their protection, but no such changes have been reported in large populations.

Understanding the dependence of Λ on time and on other factors (type of vehicle, age and sex of driver, etc.) might supply an important links in estimating the effectiveness of restraint systems for which the only available data contains miscoding.


Evans, L. Double pair comparison -- a new method to determine how occupant characteristics affect fatality risk in traffic crashes. Accident Analysis and Prevention 18:217-227; 1986

Evans, L. Rear compared to front seat restraint system effectiveness in preventing fatalities. Society of Automobile Engineers, Paper No. 870485, Detroit, February 1987. Included in SAE Special Publication SP-691, 39-43.

Evans, L. Rear seat restraint system effectiveness in preventing fatalities. Accident Analysis and Prevention 20: 129-136; 1988.

Kahane, C.J. Fatality and injury reducing effectiveness of lap belts for back seat occupants. Society of Automobile Engineers, Paper No. 870486, Detroit, February 1987. Included in SAE Special Publication SP-691, 45-52.

Morgan, C. Effectiveness of lap/shoulder belts in the back outboard seating positions. U.S. Department of Transportation, National Highway Traffic Safety Administration, Washington, DC. NHTSA Technical Report DOT HS 808 945, June 1999.

National Highway Traffic Safety Administration. Fatality Analysis Reporting System, formatted fatal injury traffic data; 1990-1996. <>