Estimating the Lives Saved by Safety Belts and Air Bags

Transcription

1 0. Introducton Estmatng the Lves Saved by Safety s and Ar Bags Donna Glassbrenner, Ph. D. Natonal Hghway Traffc Safety Admnstraton, 400 Seventh St SW, Washngton DC donna.glassbrenner@nhtsa.dot.gov Safety belts and ar bags are among the most mportant safety devces n socety today, together savng thousands of lves each year. The Natonal Hghway Traffc Safety Admnstraton (NHTSA) estmates the number saved each year, as well as the number that would have been saved f more occupants had buckled up. These estmates are not determned by examnng crashes on a case by case bass, but rather are estmated from the number of occupants who ded, the restrants they used, and the effectveness of the restrants n preventng fatalty. Specfcally, NHTSA estmates on an annual bass: the passenger vehcle occupants over 4 years old saved by safety belts, the passenger vehcle occupants over 12 years old saved by frontal ar bags, and the passenger vehcle occupants over 4 years old that would have been saved by safety belts f more of them had buckled up. Note that these do not nclude the relatvely small numbers of occupants of large trucks saved by belts, chldren under fve saved by belts, chldren under 13 saved by frontal ar bags, and occupants saved by sde ar bags. Sde ar bags have not yet been rated for effectveness, and so the lves that they save 12,000 10,000 Chart 1: Passenger Vehcle Occupants Saved by Safety s and Ar Bags, and Lost from not Usng s cannot currently be estmated. The current data do not support relable ar bag effectveness ratngs for chldren under 13. NHTSA recommends that these chldren not be n front of an ar bag, unless no other seatng poston s avalable. Lves saved and savable are used n calculatng the economc mpact of belt use and nonuse. (Blncoe, Seay, et al, 2002) Ths paper presents mprovements made the calculatons of lves saved and savable. More detaled nformaton can be found n (Glassbrenner, 2003). In the rest of ths paper, ar bag wll mean frontal ar bag, although we occasonally wrte frontal ar bag for emphass. Lves saved by belts wll mean passenger vehcle occupants over 4 years old saved by belts, and lves saved by bags wll mean passenger vehcle occupants over 12 years old saved by (frontal) ar bags. 1. Input to the Lves Saved Calculatons: Effectveness Ratngs, Restrant Confguratons, and atalty Counts 8,000 6,000 4,000 2,000 Source: Natonal Center for Statstcs and Analyss, NHTSA, ARS Occupants 5 and Older Saved by Safety s Occupants 13 and Older Saved by rontal Ar Bags Occupants 5 and Older Who Ded Because of Not Usng s 1.1 Effectveness Ratngs NHTSA rates the effectveness of belts and bags n preventng fatalty, fndng for nstance the followng ratngs for the drver s seat of passenger cars: 1. Three-pont belts are 48% effectve for occupants over 4 years old. 2. Ar bags are 14% effectve for occupants over 12 years old. 3. Ar bags are 11% effectve for belted occupants over 12 years old who are not saved by thr belt. 4. Three-pont belts n conjuncton wth ar bags are 53.72% effectve for occupants over 12 years old. The frst ratng means that 48% of the drvers (over 4 years old) of passenger cars n crashes severe enough that they would de f they were unbuckled and any ar bag n thr poston were removed, would lve f they buckled up. The second means that 14% of the passenger car drvers over 12 who would de wthout a belt and bag would lve wth the bag. The thrd means that 11% of the passenger car drvers over 12 who would de wth a belt but no bag, would lve wth a belt and bag. The fourth means that 53.72% of the drvers over 12 years old who would de wthout a belt and bag would lve f they buckled Page 132

2 and had an arbag. Ths ratng and can be derved from 1 and 3. (Report to Congress, 2001; Glassbrenner, 2003) Note that the belt and bag ratngs are specfed for dfferent age ranges. Of course, there wll be few drvers under 12 years old. Three pont belts are the manual lap/shoulder belts n today s vehcles and the automatc lap/shoulder belts that appeared prmarly n vehcles made by General Motors. Two-pont belts consst of ther a) an automatc shoulder belt combned wth a manual lap belt, a confguraton that appeared n some passenger cars n the 1980 s and nto the 1990 s, or b) an automatc or manual shoulder belt together wth a knee bolster under the dashboard, a less common confguraton. Defnng ratngs ths way follows standard practce for two devces, A and B, that act n conjuncton. In general, defnng potental fataltes as those who would de wth nther A nor B, the effectveness of A s the percent of potental fataltes who would lve f they used A but not B, the effectveness of B s the percent who would lve f they used B but not A, and the resdual effectveness of B s the percent who would lve f they used A and B but A dd not save them. We wll call the effectveness n 2 the effectveness of bags and that n 3 the resdual effectveness of bags, snce t s the remanng effectveness after belts are appled. These are the only two ratngs of ar bags. s are rated for thr performance as they are used, so the rates reflect both proper and mproper use (such as not bucklng the manual lap belt f the shoulder belt s automatc). Also note that the ar bags are rated for the lfe-savng capablty of thr presence, not thr deployment. However the deployment ratngs would be the same as those for presence. Vehcle technology s constantly mprovng and the types of potentally fatal crashes may change over tme. or nstance the ncreasng popularty of SUVs has been accompaned by an ncrease n rollover crashes. Consequently NHTSA perodcally updates ts ratngs to reflect changng condtons. The most recent belt effectveness ratngs are n (Kahane, 2000) and (Morgan, 1999), and the most recent bag ratngs n (Report to Congress, 2001). Kahane and Morgan were computed usng data from and respectvely, and the Report to Congress used Restrant Confguratons and atalty Counts We defne a restrant confguraton to be a 6-tuple consstng of the coordnates n Table 1. Note that ths ncludes nformaton on the vehcle and occupant as well as the restrant. The coordnate ar bag? s to take the value yes f the occupant s the drver or rght front passenger and there s an ar bag n thr seatng poston, and no otherwse. The effectveness of belts and bags n (Kahane, 2000), (Morgan, 1999), and (Report to Congress, 2001) are specfed n terms of the restrant confguratons. Table 1: Restrant Confguratons Coordnate Values vehcle type passenger car; lght truck or van seatng poston drver, rght front passenger, front center, rear outboard, rear center belt type 3-pont, 2-pont, lap belt used? yes, no ar bag? yes, no age 5-12, 13 or older NHTSA comples a census of all motor vehcle fataltes n the U.S. from polce reports, hosptal records and other state documents called the atalty Analyss Reportng System (ARS). atal crashes are defned as polce-reported crashes nvolvng a motor vehcle n transport on a publc road, street, or hghway n whch at least one person, called a fatalty, ded wthn 30 days of the crash. rom ARS, we produce counts of occupant fataltes n passenger vehcles, called the fatalty counts, who are ages 5 or older and had access to a belt, for the varous restrant confguratons. or nstance, the fatalty counts for drvers of passenger cars wth 3-pont belts n 2001 are gven n Table 2. We wll refer to ths as Example 1. Note that belted chldren under 13 have the same effectveness ratng, whether or not they had an ar bag. 1.3 Notaton Table 3 defnes the notaton used n the remander of ths paper. or nstance, the second restrant confguraton n Table 2 s =(passenger car, drver, 3-pont belt, no, yes, 13 or older), = 3,354, belt()=0, bag()=1, e (belt)= 48%, e (used) = e(bag) = 14%, e (system)=53.72%, and e (belt bag)=46.19%, whch s the resdual effectveness of these belts. Table 2: 2001 atalty Counts Ratngs for Drvers of Passenger Cars wth 3-Pont s Age Ar Bag Effectveness atalty 5- n Seatng of Restrant Used? Count Poston? Used No Yes Yes 53.72% 3,555 No No Yes 14% 3,354 No Yes No 48% 1,989 No No No 0% 2,873 Yes Yes NA 48% 0 Yes No NA 0% 2 Source: Natonal Center for Statstcs and Analyss, NHTSA, ARS, 2001 Page 133

3 2. The Total Lves that Were Saved by a or a Bag It s a relatvely straghtforward matter to estmate the lves saved by both restrants combned. If x people de usng a safety devce that has an effectveness e (.e. that reduces fataltes n settngs n whch people would otherwse de by e 100%), then one can nfer that a total of x/(1-e) used the devce n a settng n whch they would otherwse de (the potental fataltes), ex/(1-e) of whch were saved by the devce. Applyng ths to Example 1 gves that 6,508 drvers n passenger cars equpped wth 3-pont belts were saved n (See Table 4.) ormulacally, R (used) people were saved. Of course Example 1 only comprses drvers of passenger cars wth three-pont belts whle the natonal calculaton uses all passenger vehcles and all seatng postons. Table 3: Notaton Notaton Defnton e(bag) the effectveness of ar bags,.e. 14% e(bag belt) the resdual effectveness of ar bags,.e. 11% R the set of all restrant confguratons In the remanng defntons, denotes a restrant confguraton. the fatalty count for belt() 1 f a belt s used n, and 0 otherwse bag() 1 f a bag s present and the occupant s over 12 n, 0 otherwse e (belt) the effectveness of the belt n I e (system) e (belt) f bag()=0, otherwse the effectveness of the belt-bag system n e (used) the effectveness of the restrant (belt, bag, or belt-bag) used n e (belt bag) e (system) - e(bag) 1- e(bag) when bag()=1, otherwse undefned Table 4: Lves Saved n 2001 Among Drvers of Passenger Cars wth 3-Pont s Effectveness of atal- Potental Lves Vehcle Has Age 5- Used Drver s Sde Restrant tes ataltes Saved? Ar Bag? Used No Yes Yes 53.72% 3,555 7,682 4,127 No No Yes 14% 3,354 3, No Yes No 48% 1,989 3,824 1,836 No No No 0% 2,873 2,873 0 Yes Yes NA 48% Yes No NA 0% Totals* 11,774 18,282 6,508 *Row entres may not sum to totals due to roundng. Source: Natonal Center for Statstcs and Analyss, NHTSA, ARS, Attrbutng the Lves Saved to s and Bags To quantfy the benefts of belts and bags separately, NHTSA wshes to partton the total lves saved from the prevous secton nto those that were saved by belts and those that were saved by bags. Unfortunately, there s no clear way to determne such a partton. One can determne the maxmum number that could have been saved by ther restrant, but ths only places lmts on the attrbuton, wthout determnng t. (Logcally there should also be occupants for whom both restrants were necessary for thr survval, but there s no clear way to calculate ths number.) We llustrate on Example 1. Obvously the 1,836 drvers that were saved but dd not have an ar bag must have been saved by the belt. Had any chldren under 13 been saved, they would have also been saved by the belt, snce we do not have a bag effectveness ratng n ths age range. Smlarly the 546 people who were unbelted were saved by the ar bag. The only ssue s how to attrbute the 4,127 that were saved whle bng protected by both restrants. Snce thr belts are 48% effectve, belts could only have saved at most 3,687 of the 4,127 occupants (0.48 3,555/( ) = 3,687), leavng 439 saved by bags. Smlarly, bags could have saved at most 1,075 of these occupants, leavng 3,051 for belts. We call these two attrbuton methods the belt-maxmzng and bag-maxmzng methods, respectvely. Note that we do not mean to suggest by these names that the methods were contrved to favor belts or bags. There are smply the bounds set by logc. NHTSA consdered these attrbutons and a mddle ground that attrbutes the 4,127 lves saved usng both restrants to belts and bags n proporton to the effectveness of belts and bags separately. Ths method, whch we call restrant-neutral, attrbutes 3,195 of the 4,127 occupants to belts (.e. 4,127.48/( )= 3,195), and the remanng 932 to bags. Combnng these calculatons wth the 1,836 occupants who were saved usng only a belt and the 546 saved usng only a bag yelds the three attrbutons for Example 1 n Table 5. Table 6 gves the formulas for the three attrbuton methods. Page 134

4 Each method has merts. The belt-maxmzng method s used n classcal benefts analyss. Classcally, the safety devce that s nsttuted frst (n ths case, belts) s attrbuted the maxmal benefts possble, and subsequent safety devces (n ths case, bags) are attrbuted only the resdual benefts. Also one can vew ar bags as restrants that supplement belts, and from ths vew, bags should only be attrbuted the resdual benefts. In comparson, the restrant-neutral attrbuton does not gve preference to ther restrant. nally, snce bags actvate automatcally, belts can be vewed as restrants that supplement ar bags. rom ths pont of vew, belts should only recve the resdual savngs, supportng the bag-maxmzng attrbuton. Table 5: Attrbutons Consdered for the Lves Saved n 2001 Among Drvers of Passenger Cars wth 3-Pont s Attrbuton Method Lves Saved s Bags -maxmzng 5, Restrant-neutral 5,030 1,478 Bag-maxmzng 4,887 1,621 Source: Natonal Center for Statstcs and Analyss, NHTSA, ARS, 2001 Snce each method, and n fact any method that falls wthn the lmts set by the beltmaxmzng and bagmaxmzng attrbutons, s scentfcally vald, choosng among them s a polcy decson. NHTSA chose to use the belt-maxmzng attrbuton, whch s the method t has used n the past. The formulas for ths attrbuton n Table 6 are mprovements over the formulas prevously used that better reflect the contrbutons of ar bags. 4. The Lves that Would Have Been Saved f Use Had Been Hgher Table 6: ormulas for the Attrbuton Methods Method Restrant Lves Saved (belt) -maxmzng Restrant-neutral Bagmaxmzng Bag Bag Bag e(bag belt) 1- e(bag belt) belt() =1 NHTSA estmates the number bag() =1 of lves that would have been saved n a gven year f front seat daytme belt use had been at varous hgher rates, such as one percentage pont hgher, 90%, or 100%. ront seat daytme s used because our best measurements of belt use arse from an observatonal survey that employs ths restrcton for practcal reasons. (Glassbrenner, 2002) However, the resultng estmates are frequently referred to as the lves saved f belt use had been, e.g. 90% or 100%, nstead of front seat daytme use bng 90% or 100%, as wll we. The calculatons utlze a belt use model developed by NHTSA. The most recent verson of ths model s UP(x) = x x, where x denotes belt use n the front seat durng daytme and UP(x) denotes the belt use among potental fataltes when daytme front seat use s x. (Wang and Blncoe, 2003) We wll refer to belt use among potental fataltes as UP. As wth the total lves saved, t s a relatvely straghtforward matter to estmate the number of lves that would have been saved f belt use had been hgher. We llustrate wth Example 1, calculatng the addtonal lves that would have been saved f (daytme front seat) belt use had been 90% n The UP model from (Wang and Blncoe, 2002) estmates that UP would have been 21 percentage ponts hgher n 2001, when front seat occupants buckled up durng 73% of thr daylght drvng tme (.e = UP(0.9) UP(0.73)). That s, the model predcts that 21% more of the potental fataltes would have buckled up. Applyng ths to the 18,282 potental fataltes gves 3,753 addtonal potental fataltes that would have buckled up. We would expect 2,160 of them to be over 12 and have an ar bag, snce 3,900 of the 6,776 orgnal unbelted potental fataltes ft ths descrpton (.e. 2,160=3,753 3,900 / 6,776). belt() = 1, bag() = 0 e(bag) 1- e(bag) belt() = 1, bag() = 1 (belt) + 1- e (belt) belt() = 0, bag() = 1 belt() = 1, bag() = 1 belt() = 1, bag() = 1 + belt() = 1, bag() = 1 (belt bag) + 1- e (belt bag) e(bag) e(bag) + 1- e(bag) belt() = 0, bag() = 1 (belt) (system) e (belt) + e(bag) 1- e (system) e(bag) (system) e (belt) + e(bag) 1- e (system) belt() = 1, bag() = 0 (belt) 1- e (belt) Page 135

5 That s, the addtonal lves that would have been saved n a gven tme perod (e.g. a gven year) had belt use been x hypoth s (UP(x hypoth ) UP(x current )) e(system unbelted) e(bag). R, bag() 1, belt() 0 = = belt() = 0 where x current s the belt use n the tme perod consdered, and e(system unbelted) s average value of e (system) among the (system) unbelted potental fataltes, whch s and was 53% n If one magnes belt() = 0 1- (used) belt() = 0 1- (used) choosng a random subset from the potental fataltes equal to the number you wsh to addtonally buckle, the formula takes the number saved f you buckle all of them and subtracts the number that were already saved by thr bag. Note that we are not computng the addtonal lves saved by estmatng the total lves saved n the natural way from the UP model and subtractng the current lves saved. Ths would have resulted n a dscontnuty, snce the UP model does not precsely predct the use rate that actually occurred among the potental fataltes when nputted the actual daytme front seat use. The addtonal lves saved were prevously calculated usng a varety of formulas for varous hypotheszed use rates, whch produced nconsstent estmates. or nstance, the estmated lves saved at 100% use had been precsely ths, whch resulted n a large gap between the estmate at 99% use, whch hypotheszed 99% daytme front seat use, and the 100% estmate, whch hypotheszed 100% use. In addton to producng consstent estmates, the new calculaton also uses an updated belt use model from (Wang and Blncoe, 2002). Ths model s better than that prevously used, whch predcted daytme front seat use among potental fataltes. 4. Attrbutng to the Total Lves Savable at Hgher Use to s and Bags Table 8 apples the three attrbuton methods to the 1,925 people that would have been saved among the newly belted n Example 1 f belt use had been 90%. Recall that 302 of these occupants were saved by thr ar bags when they were unbelted. The bag-maxmzng attrbuton contnues to attrbute all 302 to bags, whle the belt-maxmzng and restrantneutral attrbutons revse the attrbuton for some of them to belts. Namely under the beltmaxmzng attrbuton, 178 unbelted occupants saved by bags would have been saved by belts f they had buckled up, whle the restrant neutral method would have reattrbuted 40 occupants. Table 9 contans the formulas for these attrbuton methods. Note that all methods attrbute the addtonal lves saved (e.g. the 1,623 people n Example 1) to belts. Table 7: The Newly Buckled Potental ataltes Among Drvers of Passenger Cars wth 3- Pont s f Use Had Been 90% n 2001 Lves Saved Lves Prevously Saved by Bags Net Lves Saved No Yes Yes 54% 2,160 1, No Yes No 48% 1, Yes Yes NA 48% Totals* 3,753 1, ,623 *Row entres do not necessarly sum to totals due to roundng. Source: Natonal Center for Statstcs and Analyss, NHTSA, ARS, 2001 Table 8: Attrbutng the Lves Saved Among the Newly Buckled Potentally atal Drvers of Passenger Cars wth 3-Pont s f Use Had Been 90% n 2001 Age 5- Arbag Present Used?? Lves Saved Table 7 computes that a total of 1,925 of the 3,753 newly belted would be saved. However not all of the newly belted ded when they were unbelted. One would expect that 302 of them were saved by thr ar bags when they were unbelted snce 302 = ,160. Subtractng these from the 1,925 that would have been saved f belted, Age 5- Used? Arbag Present? Effectveness Potental ataltes we fnd that 1,623 addtonal occupants would have been saved f belt use had been 90%. - Maxmzng Attrbuton Restrant- Neutral Attrbuton Bag- Maxmzng Attrbuton Bag Bag Bag No Yes Yes 1,160 1, No Yes No Yes Yes NA Totals 1,925 1, , , Source: Natonal Center for Statstcs and Analyss, NHTSA, ARS, 2001 Page 136

6 Table 9: Reattrbuton ormulas When Use s Hypotheszed to Be x hypoth Attrbuton maxmzng Restrantneutral Bagmaxmzng (UP(x e(bag) Newly ed Occupants Prevously Saved by Bags Who Are Reattrbuted to s (UP(x ) UP(x )) hypoth e(bag) ) UP(x hypoth R current )) e(bag belt) 1- e(bag belt) current e(bag belt) 1- e(bag belt) R bag() = 1 belt() bag() = = 1, 1 0 belt() = 1, bag() = 1 belt() = 0, bag() = 1 (used) 1- (used) (belt) (belt) + e(bag) - e e (belt) + e(bag) (used) Revsng attrbutons for the 302 prevously saved by bags makes perfect sense from the belt-maxmzng and restrantneutral ponts of vew. Bucklng the 302 prevously unbelted occupants poses a new scenaro, n whch these occupants would now be restraned by both a bag and a belt. Ether restrant mght save them. The bag-maxmzng perspectve doesn t revse the attrbuton for these 302 occupants because they were saved by bags when they were unbelted. Agan each method s justfable. NHTSA had prevously used the bag-maxmzng approach for ths computaton. The other attrbutons would obvously cause much confuson among many of the people who use the estmates, many of whom are lay readers. Consequently t was decded to contnue usng the bag maxmzng attrbuton. 5. Summary In addton to the correcton of oversghts, we made three major mprovements to the calculatons of lves saved and savable by belts and bags. ormulas were mproved to better reflect the contrbutons of ar bags. The varous calculatons of savable lves were made consstent. In partcular, the lves that would have been saved at 100% use was changed to be consstent wth other estmates. nally, updated effectveness ratngs and a better UP model were ncorporated. The mprovements have a substantal mpact on the estmates. Under the new calculatons, the lves saved by belts ncreases by about 10% and that for bags by 6%. The lves that would have been saved f belt use had been one percentage pont hgher drops by 10%, that for 90% belt use drops by 25%, and that for 100% drops by 19%. References 1. Blncoe, L., Seay, A., Zaloshnja, E., Mller, T., Romano, E., Luchter, S., Spcer, R., The Economc Impact of Motor Vehcle Crashes, 2000, NHTSA Techncal Report, DOT HS , May fth / Sxth Report to Congress, Effectveness of Occupant Protecton Systems and Thr Use, DOT HS , November Glassbrenner, D., Safety and Helmet Use n 2002 Overall Results, NHTSA Techncal Report, DOT HS , August Glassbrenner, D., Improvng the Calculatons of the Lves Saved by Safety s and Ar Bags, NHTSA Techncal Report, DOT HS 809, August Kahane, C., atalty Reducton by Safety s for ront-seat Occupants of Cars and Lght Trucks, NHTSA Techncal Report, DOT HS , December Morgan, C., Effectveness of Lap/Shoulder s n the Back Outboard Seatng Postons, NHTSA Techncal Report, DOT HS , June Wang, J. and Blncoe, L., Regresson Model Update, NHTSA Research Note, DOT HS 809, May 2003 Page 137