The author gives advance notice that he expects to publish further data in cooperation with Professor Elliot Levine of the Philosophy Department, University of Winnipeg.(January 2003).

The following Tables were prepared as indicated in  Table notes.

    TABLE 1 NOTES

1. The data is taken from NOPUS (Refs 2, 8, 12, 13 at bottom of page)
2. NOPUS studies were made in 1994 & 1996. Asterisk  *  values were obtained by linear interpolation, Hash   #  values are "best guess".
3. Values in brackets are 95% confidence limits.
4. The "Urban Value" column is my guesstimate of the weighted average & is derived from the Moving Traffic, Intersection City & Intersection Suburbs data.
5. The Rural data for 1997 of 64.3% was chosen because it gave smooth results.

        TABLES 2, 3, 4a, 4b, 5a & 5b  - NOTES.

1. Tables 2, 3, 4a, 4b, 5a & 5b were prepared using FARS (which can be found at http://www-fars.nhtsa.gov/www/query.html.)
2. Reason for the removal of the alcoholic affected driver stream are given here
3. The "nonalcoholic fatalities unbelted" and "nonalcoholic fatalities belted" and "alcoholic fatalities unbelted" and "alcoholic fatalities belted" columns are fatalities counts compiled from FARS data. Click here for sample compilation.
4. The "(fn) nonalcoholic fatalities belted" is the rate of belt wearing among nonalcaholic fatalities, fn = nb/(nu + nb).
5. The "(fa) alcoholic fatalities belted" is the rate of belt wearing among alcohol using fatalities, fa = ab/(au + ab).
6. The "(fc) combined fatalities belted" is the rate of belt wearing among all fatalities, fc = (ab+nb)/(au+ab+nu+nb).
7. Observed belt wearing probability is from the NOPUS reports summarized in Table 1 & Table 1 Notes.
8. "Raw Effectiveness" is an empirical calculation of the effectiveness ratio "E" of a seat belt based on a negligible delinquent group size.  The raw empirical calculation is made using the uncorrected NOPUS data.  A corrected empirical calculation of E requires an estimate of the delinquent group size (see Table 6a and Table 6b).   If the raw effectiveness is negative, then it is hazardous to wear a seat belt.  [See below, "empirical effectiveness ratio" = "raw effectiveness"  = E = 1-(nb/nu)*(1-nopus)/(nopus) ]
9. In preparing the above Tables information had to be discarded.  Consider Table 4a.  In about 14% of fatality reports the wearing or failure to wear a seat belt was not reported.  There seems to be no reason to assume that this failure to report was not random.    In about 10% of cases the presence of alcohol was "unknown", and in about 17% of cases the presence of alcohol was "not reported".    It is possible that the presence of alcohol is entered as "unknown" when relatives refuse permission for postmortem examination.   It seems likely that an entry of "unreported" occurs because there is no jurisdictional requirement for a report of the presence of alcohol.   The seat belt wearing rate when the alcohol status was unreported was 63.5%, which is barely distinguishable from the wearing rate in the general population (63.9%) and so likely to be random.    In the cases where the presence of alcohol was "unknown", the belt wearing rate averaged about 46.7%, which is significantly lower would be expected if there was no bias.  The inference is that there might have been a disproportionate number of alcoholic fatalities (who wear belts on only 35.8% of fatal occasions) included in the stream.  If a disproportionate number of alcoholics had been included in the "unreported" stream, the lethal effects of seat belts would have been (apparently) reduced.

TABLE 6a & 6b - NOTES.

1. The "Raw Effectiveness" in Tables 4a, 4b, 5a & 5b is based on the notion that a group of negligible size has been removed from the population.  Tables 6a & 6b show the adjustments to the "Raw Effectiveness" score where Alcohol Group sizes of Table 4a and 4b are expressed as a (non negligible) percentage of the relevant car driver population.
2. Fatality belt wearing proportions "ns" (sober) & "na" (alcohol affected) from Tables 4a & 4b were adjusted by the formula

        Ai = (ni + ni*E/(1-E))/(1 + ni*E/(1-E)) ....................{1}[i=a,s]
To give the actual (live) proportional belt use rates As & Aa of each group for a selected value of E.
3. The actual proportions thus obtained for each group were combined to give the NOPUS observed safety belt use data for urban car drivers "o" from Table 1 with "X" being the proportion of alcohol affected drivers:

        X = (As-o)/(As-Aa) ..................................................{2}
4. Different trials for E with the output of equation {1} as input as equation {2} gave the rows on TABLE 6.

NOPUS. The restraint rates observed in a 1994 National Occupant Protection User Survey of 50,000 car passengers & in a 1996 NOPUS of 176,651 car passengers have been compiled to give Table 1.

SPEEDING AND ALCOHOL.  Speeding (defined as exceeding the local speed limit) and alcohol use by drivers are identified as high risk behaviors.  It seems reasonable to assume that those who are speeding or affected by alcohol might also be less likely to wear a seat belt.  That is the opinion of the NHTSA.  In Reference (10) is the statement: Among drivers in fatal crashes in 1996, those who were not speeding were twice as likely to be wearing safety belts as those who were speeding at the time of the crash. In Reference (5) is the statement: Safety belts were used by only 18.5% of the fatally injured intoxicated drivers, compared to 30.2% of fatally injured (alcohol) impaired drivers.   Tables 4a & 4b provide support for the statement that alcoholics wear safety belts less frequently.  That is also the basis of the "Selective Recruitment" theory of Evans.L.

Since speeders and drinkers appear to be high-risk sub-groups that wear seat belts at a lesser rate than the general population, then proper accounting requires that they should be sorted into streams with lower belt use.  A sample calculation demonstrates that in the circumstances, if a stream is of negligible size, then that stream can be excised without significantly changing the calculated effectiveness.  The size of the speeder stream is unknown.  It might be as high as 5% of drivers.

FARS. The restrained-v-unrestrained car driver fatalities on urban-v-rural roads in the USA for the years 1994, 1995, 1996 & 1997 as reported by police were extracted using the Fatality Analysis Reporting System, and are reported on Tables 3, 4, 5a & 5b. The data was homogenized by removal of negligible sized groups that had been using alcohol and separation in to urban and rural groups.

The conclusion from the resulting table is that wearing seat belts is associated with extra fatalities numbered in the thousands each year on urban roads in the USA (and numbered in the hundreds each year on Australian urban roads).

THEORY  &  CALCULATIONS

The FARS (Fatality Analysis Reporting System) engine was set to extract fatalities for each year for a person type driver of a vehicle body type motor car, and this subset was then set to extract road function classes of rural or urban roads. The FARS engine was set to select seat belt usage cross tabulated with alcohol involvement (See explanatory page) In this manner the seat belt use rate for non-alcohol-affected urban car drivers was calculated. Since the sample size is in the thousands, the 95% confidence limits will be at most a few percentage points. This data was combined with the NOPUS observations to empirically estimate the seat belt effectiveness ratio on rural or urban roads.

The data was sorted into urban & rural crashes because NOPUS found that those roads had different wearing rates and they seemed to offer environments that might require separate "effectiveness ratios". A seat belt may effectively reduce fatalities in the (mostly) high speed head-on or rollover crashes that occur on rural roads.  Urban fatalities result from a greater proportion of low-speed right-angle crashes.  Further sorting by regions could probably be done with profit.  No significant relationship between the time of day and seat belt wearing was found.

The safety belt effectiveness ratio "E" is a concept developed by the NHTSA and represents an estimate of the reduction of fatalities if occupants had worn safety belts. {E = ratio of lives saved if everyone wore a seat belt instead of being unbelted}.  The effectiveness ratio "E" substitutes into the formula (from Ref 3).
        (LIVES SAVED)     LS = b * E /(1 – E)    {Where "b" is the number of belted casualties.}
In theory E can have values from negative infinity (always fatal when occupant uses belt) up to <+1.0 (at +1.0 there would be no fatalities if buckled up, i.e. the numerator factor b=0 and the denominator (1-E) would be zero, and the equation would fail.{Thanks to Matt Bobrowski for that observation}).
Working backwards from an actual belt wearing rate (p = proportion of people observed wearing seat belts from the NOPUS study) and the counts of belted (b) and unbelted (u) fatalities, it is possible to empirically calculate the NHTSA defined effectiveness ratio. As a practical example, suppose that for a homogeneous population an observation study has shown that 45% of people do not wear seat belts (p = 0.55). Suppose also that of 1000 occupant fatalities in a period of 12 months, it was found that 630 were unrestrained (u = 630, b = 1000-630 = 370). We can calculate that, if both belted and unbelted people are equally likely to be involved in a potentially fatal accident, then the 55% of belted people would, (if not wearing belts) have suffered 630*55/45 = 770 fatalities. Since there were only 370 fatalities in this group, then the number of lives saved by belts was 770 – 370 = 400, and the empirical effectiveness ratio is 400/770 ~ 52%.
On reducing this empirical calculation to a formula, we obtain
        (EMPIRICAL EFFECTIVENESS RATIO)     E = 1 - (b/u) * (1-p)/p
Where "p" is the proportion of people wearing belts, "u" is count of unbelted fatalities, and "b" is the count of belted fatalities.

Following is a summary of the data extracted from FARS.

Table 2 shows fatalities among all car drivers that were wearing a seat belt.  This group has not had alcoholic or speeding drivers removed.

Table 3 is a subset of Table 2.   Table 2 fatalities were subdivided into fatalities where alcohol was reported as not involved and fatalities where alcohol was reported as involved.  Quite a number of police fatality reports did not report alcohol status.  Abandoning these records did not significantly alter the average rate of belt wearing in the remaining fatality population.

Tables 4a and 4b are subsets of Table 3.  The fatalities were subdivided into urban road fatalities Vs rural road fatalities.  The column labeled "raw E" shows the empirically derived effectiveness ratio.  It is noted that values are strongly negative on urban roads, and negative on rural roads.

Tables 5a and 5b derived from Tables 4a and 4b by removal of speeder fatalities.  Since the proportion of drinkers and/or speeders in the live population were unknown, the results have uncertain confidence limits.  However, if the proportion of speeders is less than 5%, the estimates have reasonable accuracy.

Tables 6a & 6b are subsets of Tables 4a and 4b.  The concept "Raw Effectiveness" was devised to describe the effectiveness of a seat belt based on a negligible size for the delinquent group.  Tables 6a & 6b shows how the value of effectiveness "E" varies as the size of the delinquent group assumes significant values.  Only by assuming a negative effectiveness ratio is the proportion of alcohol affected drivers in the population less than the fatality rate for alcohol affected drivers. This leads to the conclusion either that alcohol reduces the probability that one will be involved in an accident, or that seat belts are killing their wearers.

CONCLUSION

A more detailed study should be made.  There should be a comparison of the fatality belt wearing rate against the wearing rate in small regions, taking into account population density, environment, road quality and relevant legislation.  It is the nature of statistics that the tendencies hinted at in a more general study become much starker as the relevant streams are isolated.

It could be asked, might not isolation of other groups reverse these conclusions?  The details of a group that would reverse these conclusions can be characterized.  We would need to isolate a group of drivers that was fatal-accident prone, and that characteristically wore seatbelts more frequently than average.  Or alternatively, a quite large group of drivers that rarely had fatal accidents and characteristically wore seatbelts at a lower-than-average rate.  So far I have searched for but not found any group that might meet those criteria.

One possible source of error not detailed was the null data.  (null data occurs where some of the details, such as whether a seat belt was worn, or whether alcohol was involved are not noted on the input form to FARS).  Although I have not published details, I was able to discount those sources of error by a matrix technique.

Present evidence is that seat belt effectiveness on urban roads is more negative than -100%.  This means that when a car driver straps up in a seat belt on an urban road, he more than doubles the probability that he will become a fatality.  When a car driver straps up in a seat belt on a rural road, he increases by more than a third the probability that he will be a fatality.

BIBLIOGRAPHY

JOURNALS

Adams J.G.U.  "The Efficiency of Seat Belt Legislation". SAE Technical Paper 820819. Passenger Car Meeting, 1982.
Andreassend D.C. "Victoria & the Seat Belt Law 1971 on".  Human Factors 1976 18(6) 593-600
Evans Leonard "Double Pair Comparison - A new method to determine how occupant characteristics affect Fatality Risk in Traffic Crashes" Accident Analysis & Prevention, Vol 18 No 3; pp217-227. 1986.
Evans Leonard."The Effectiveness of Safety Belts in preventing fatalities." Accident Analysis & Prevention, Vol 18 No 3; pp229-241. 1986.
Grush E.S, Marsh J.C. & South N.E. "Comparison of High Speed Crash Test Results with Fatality Rates". 27th Annual Proc., Am.Ass for Auto Medicine, Oct 3 - 6 1983.
Hamer Mick  Report questions whether Seat Belts save Lives".  New Scientist, 7 February 1985.  p7.
Harvey A.C. & Durbin J. "The Effects of Seat Belt Legislation on British Road Casualties: A Case Study in Structural Time Series Modelling." J.Royal Statist. Soc. A. 1986, 149, Part 3, pp 187-227.
Reinfurt DW, Campbell BJ, Stewart JR Stutts JC. Evaluating the NC safety belt wearing law. Accid Anal Prev. 1990
Semmens John. "Do Seat Belt Laws Work" (online publication)
Voas R.B., Wells J, Lestina D., Williams A. & Greene M. "Drinking & Driving in the United States, the 1986 National Roadside Survey." " Accident Analysis & Prevention, Vol 30 No 2; pp267-275. 1998.

BOOKS

Adams - John Adams' "Risk" (UCL 1995)
Evans - Leonard Evans' book "Traffic Safety and the Driver" (Van Nostrand Reinhold 1991)
Wilde - Gerald J S Wilde's "Target Risk" (PDE 1994) also available online

US GOVERNMENT PUBLICATIONS (mostly available online)

NHTSA=National Highway Traffic Safety Administration, a department of USA Department of Transport. Their query engine is at http://www-fars.nhtsa.gov/www/query.html.
FARS      Fatality Analysis Reporting System at http://www-fars.nhtsa.dot.gov/
NOPUS   National Occupant Protection Use Survey
Bibliography,mostly from the National Transport Library.

Following are the numbered references eg Ref(n) from the paper above.

1. NHTSA Research Note "Trends in daily Traffic Fatalities 1975 – 1995 E.C.Cerrelli.
2. NOPUS (1994) - Controlled Intersection Study ~ US Department of Transportation.
3. NHTSA Estimating Lives saved by Restraint Use in Potentially Fatal Crashes. 1995
4. NHTSA Traffic Safety Facts 1995
5. NHTSA Alcohol Traffic Safety Facts 1996
6. NHTSA Overview Traffic Safety Facts 1996
7. NHTSA Report to Congress 1996
8. NHTSA Research Note "Observed Safety Belt Use in 1996"
9. NHTSA Rural & Urban Crashes – A Comparative Analysis. 1996
10. NHTSA Speeding Traffic Safety Facts 1996
11. NHTSA Traffic Safety Facts 1996 "Occupant Protection"
12. NOPUS 1996 - Controlled Intersection Study ~ US Department of Transportation.
13. NOPUS 1995 – Shopping Center Study ~ US Department of Transportation.
14. NHTSA "1997 Traffic Crashes, Injuries & Fatalities -  Preliminary Report.
15. NHTSA 3rd Report to Congress "Effectiveness of Occupant Protection Systems" December 1996
16. NHTSA Technical Report DOT HS 808 338 January 1996 (CODES)

Originally published 28 April 1997.
Last major upgrade between 1st & 6th December 1998.
Bibliography, conclusions revised August 2000

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