Investigation of Fatality Probability Function Associated with Injury Severity and Age. Toshiyuki Yanaoka, Akihiko Akiyama, Yukou Takahashi

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1 Investgton of Ftlty Probblty Functon Assocted wth Injury Severty nd Age Toshyuk Ynok, Akhko Akym, Yukou Tkhsh Abstrct The gol of ths study s to develop ftlty probblty functon ssocted wth njury severty nd ge, whch could provde useful method to estmte the ftlty rte ccurtely. Seven types of logstc regresson models were tken nto consderton. The results of the estmtons from the 7 logstc regresson models were compred to select the best ft regresson model by usng the dt from US ccdent sttstcs (NASS CDS: Ntonl Automotve Smplng System Crshworthness Dt System) n yer 001. In ddton, the constnt coeffcents of the model best ft to the yer 001 dt were replced by regresson functons s functon of yer to develop model ncorportng the effect of the yer chnge. The followng results were found: 1) the best ft regresson model ws functon of mxmum AIS (Abbrevted Injury Scle) of ech body regon nd ge; ) the ccurcy of the regresson model ws mproved by pplyng regresson functons of the coeffcents s functon of the yer; nd 3) the regresson functons of the coeffcents show tht the ftlty rte decreses wth ech progressng yer. Keywords Agng, Ftlty Probblty Functon, Frlty, Injury Severty, Regresson Model I. INTRODUCTION In order to estmte the ftlty rte n trffc ccdents ccurtely, t s necessry to tke nto ccount not only the frglty, whch mens the probblty of njury n gven exposure, but lso the frlty, whch mens the probblty of ftlty for gven njury. For exmple, the Sttstcl Dtbse for rod trffc ccdents from UNECE (Unted Ntons Economc Commsson for Europe) [1] showed tht the ftlty rte defned s the rto of ftltes to the sum of ftltes nd njures n the elderly older thn 65 yers ws 5.4%, whle tht of persons from 5 to 64 yers old ws.6%. Addtonlly, elderly people tend to result n hgher probblty of njury n gven exposure compred to younger people []. Furthermore, elderly people tend to result n hgher probblty of ftlty for gven njury compred to younger people [3 4]. From these stutons, t s crucl to estblsh methodology to ccurtely predct probblty of ftlty tht tkes nto ccount the ge of vctms. One wy to predct probblty of njures for gven exposure s computer smulton usng model for vctm of trffc ccdent subjected to gven crsh envronment. Although t s useful tool to study the njury mechnsm n nvestgtng the effect of pssve nd ctve sfety technology to reduce ftltes n trffc ccdents, t cn only predct the probblty of njury bsed on the frglty of the vctm. Therefore, estmton of ftlty rte bsed on the estmted probblty of njures from the computer smulton requres clrfcton of the probblty of ftlty for gven njures sustned by vctm when clcultng the ftlty rte usng the result of the computer smulton. Whle there hve been mny studes focusng on the mechnsm nd probblty of njury (e.g. Pettjen et l. [] nd Tkhsh et l. [5]), only few hve focused on method to predct the probblty of ftlty wth gven njury to be used wth the results of the computer smulton. In order to predct the probblty of ftlty for gven njures usng the result of computer smulton, the nformton relted to the njury severty, njured body regon nd ge re needed. Erler studes hve nvestgted the probblty of ftlty for gven njures. Goertz et l. [6] showed the reltonshp between the probblty of ftlty nd known mxmum AIS (Abbrevted Injury Scle), but they dd not consder ge nd the body regon n whch the njury wth the mxmum AIS occurred. Bker et l. [3] showed the reltonshp between the probblty of ftlty nd ISS (Injury Severty Score) for ech ge group (0 to 4 yers, 50 to 6 T. Ynok s ssstnt chef engneer (tel: , e ml: Toshyuk_Ynok@n.t.rd.hond.co.jp), A. Akym s ssstnt chef engneer nd Y. Tkhsh s chef engneer, ll t Hond R&D Co., Ltd. Automoble R&D center n Jpn. - -

2 yers, 70+ yers), but dd not consder the body regon n whch the njury wth the mxmum AIS occurred. Addtonlly, ther results my not be relevnt to the current stuton of trffc ccdents becuse they conducted the study 40 yers go. Boyd et l. [7] developed the regresson functon for the probblty of survvl ssocted wth RTS (Revsed Trum Score) [8], ISS nd ge. However, most humn computer smulton models (e.g. Tkhsh et l. [5] nd Dokko et l. []) cnnot predct vtl sgns, such s blood pressure nd resprton rte, whch re necessry for determnng RTS. Therefore, methodology for estmtng the probblty of ftlty bsed on the njury severty nd ge to be used wth the result of computer smulton s stll lckng. The objectve of ths study s to develop ftlty probblty functon ssocted wth njury severty nd ge, whch could estmte the ftlty rte ccurtely. Seven types of logstc regresson models ssocted wth njury severty nd ge were tken nto consderton to fnd the best ft regresson model by usng the dt from US ccdent sttstcs (NASS CDS: Ntonl Automotve Smplng System Crshworthness Dt System) [10] n yer 001. The numbers of ftltes n other yers were then estmted by pplyng the best ft regresson model nd ts coeffcents determned gnst the dt for 001 to ech of the dtsets from yer 00 to 010, nd were compred to the ctul numbers of ftltes for the correspondng yers, to clrfy the pplcblty of the model to the dtset n dfferent yers. In ddton, the constnt coeffcents of the model best ft to the yer 001 dt were replced by regresson functons s functon of yer to develop model ncorportng the effect of the yer chnge. Vrbles for Regresson Model II. METHODS In order to nvestgte ftlty probblty functons s functon of njury severty nd ge, thrteen vrbles were defned bsed on the relevnt vrbles from NASS CDS [11] nd body regon code (frst dgt of AIS code [1]). Tble 1 summrzes the thrteen vrbles (summry of thrteen vrbles cn be found n the APPENDIX). The dt ncludng unknown were excluded from ths study. TABLE 1 DEFINITION OF THIRTEEN VARIABLES Vrbles Rnge Defnton DEATH 0 or 1 0: Tme to Deth defned n [11] ws equl to 0, 1: other AGE 0 to Age of Occupnt defned n [11] ISS 1 to 75 Injury Severty Score defned n [11] MAIS 1 to 6 Mxmum Known Occupnt AIS defned n [11] MAIS 0 to 6 Mxmum AIS n body regon 1 (frst dgt of AIS code [1]) 1 MAIS 0 to 6 Mxmum AIS n body regon (frst dgt of AIS code [1]) MAIS 0 to 6 Mxmum AIS n body regon 3 (frst dgt of AIS code [1]) 3 MAIS 0 to 6 Mxmum AIS n body regon 4 (frst dgt of AIS code [1]) 4 MAIS 0 to 6 Mxmum AIS n body regon 5 (frst dgt of AIS code [1]) 5 MAIS 0 to 6 Mxmum AIS n body regon 6 (frst dgt of AIS code [1]) 6 MAIS 0 to 6 Mxmum AIS n body regon 7 (frst dgt of AIS code [1]) 7 MAIS 0 to 6 Mxmum AIS n body regon 8 (frst dgt of AIS code [1]) 8 MAIS 0 to 6 Mxmum AIS n body regon (frst dgt of AIS code [1]) Investgton of the Best Ft Regresson Model Fgure 1 nd Fgure show the ftlty rte from NASS CDS s functon of the ge group nd the body regon for ech MAIS (Mxmum AIS), respectvely. From these two grphs, the followng were found: 1) the ftlty rtes for MAIS 6 nd MAIS 1 re lmost constnt n ll ge groups nd body regons; ) lthough the

3 ftlty rte for MAIS n the thorx s hgh compred to tht for other body regons, t s lmost constnt n ll ge groups; 3) the ftlty rtes for MAIS 5 nd MAIS 3 ncrese wth ge nd re dfferent between body regons; nd 4) lthough the ftlty rte for MAIS 4 s lmost constnt n ll body regons, t does not ncrese contnuously wth ge. In ths study, therefore, 7 types of logstc regresson models were tken nto consderton n order to confrm the effect of the nformton bout ge nd njured body regon, respectvely. They were: 1) types of smplfed regresson models, whch only nclude MAIS or ISS; ) 1 type of regresson model, whch only ncludes the nformton bout the njured body regon for MAIS; 3) types of regresson models, whch only nclude the nformton bout ge wth MAIS nd ISS, respectvely; nd 4) types of regresson models, whch nclude the nformton bout ge nd njured body regon for MAIS. Tble shows the 7 types of logstc regresson models. Fg. 1. Ftlty rte for ech MAIS by ge group (dt from NASS CDS from yer 001 to 007). Fg.. Ftlty rte for ech MAIS by body regon (dt from NASS CDS from yer 001 to 007). ID A B C D E F G TABLE CANDIDATE FOR THE BEST FIT REGRESSION MODEL Regresson Model MAIS b) p 1 MAIS b) ISS b) p 1 ISS b) p 1 1 MAIS 1 MAIS b) b) MAIS bage c) p 1 MAIS bage c) ISS bage c) p 1 ISS bage c) p 1 p MAIS 1 1 MAIS MAIS MAIS where p s probblty of ftlty, nd, b, c nd the regresson model. bage c) bage c) bage bage c) c) re the coeffcents of The coeffcents of ech regresson model were optmzed to the dt from NASS CDS n yer 001 by the mxmum lkelhood estmton. The regresson model wth the best ft ws chosen, bsed on the Akke

4 Informton Crteron (AIC) nd Root Men Squre Error (RMSE). The AIC ssesses the lkelhood of the model nd tkes nto ccount the number of vrbles used n the model. The lowest AIC nd RMSE ndcte the best ft model. The AIC nd RMSE re defned by the followng equtons: AIC LogLklhood Number of Vrbles, (1) ( DEATH Probblty RMSE n () of Ftlty), where n s the number of occupnts n the dtset of NASS CDS. Addtonlly, ch squre test ws conducted only for the best ft regresson model to confrm the conformty degree of the predcton. Furthermore, the numbers of ftltes estmted by pplyng the best ft regresson model determned from the yer 001 dt to ech dtset from yer 00 to 010 were compred to those of ctul ftltes to clrfy the pplcblty of the model to the dtset n dfferent yers. Investgton of Coeffcents of Regresson Model Snce the result of the comprson between the ctul nd estmted ftltes showed the low pplcblty of the model to the dtset n dfferent yers, regresson functons for replcng the constnt coeffcents of the model best ft to the yer 001 dt were nvestgted. The constnt coeffcents of the best ft regresson model determned from the yer 001 dt were optmzed for ech dtset of NASS CDS from yer 00 to 010. Regresson functons s functon of the yer for replcng ech constnt coeffcent were then determned by usng the coeffcents optmzed for ech yer. Furthermore, RMSE nd the number of ftltes were compred between estmtons. One ws estmted from the regresson model best ft to the yer 001 wth the coeffcents from the yer 001 dt by pplyng the regresson model best ft to the yer 001 to the yer 011 dt. The other ws estmted from the regresson model best ft to the yer 001 wth the coeffcents clculted from the regresson functons for replcng the constnt coeffcents by pplyng the regresson model best ft to the yer 001 to the yer 011 dt. Investgton of the Best Ft Regresson Model III. RESULTS Fgure 3 shows the comprson of AIC nd RMSE for ech regresson model from the result of optmzton. AIC nd RMSE of the regresson model G were lowest mong ll of the regresson models (AIC: nd RMSE: 0.177). From the results, the best ft regresson model s G. Addtonlly, Fgure 4 shows the comprson of the ctul ftltes nd the estmted ftltes by regresson model G whch confrms tht the dstrbuton of the estmted ftltes s smlr to tht of the ctul ftltes. Furthermore, s result of ch squre test, there ws no sgnfcnt dfference between the dstrbuton of the ctul ftltes nd tht of the estmted ftltes clculted from the best ft regresson model G (p=0.67), whch mens the conformty degree of dstrbuton of ftltes by the best ft regresson model s hgh

5 Fg. 3. Comprson of AIC nd RMSE mong regresson models Fg. 4. Comprson of ctul ftltes nd ftltes estmted by regresson model G Tble 3 nd Fgure 5 show the comprson of the ctul ftltes nd the ftltes estmted by pplyng the best ft regresson model determned from the yer 001 dt to ech dtset from yer 00 to 010. From Fgure 5, the degree of overestmton of the estmted ftltes to the ctul ftltes ncresed wth ech progressng yer. TABLE 3 COMPARISON OF ACTUAL FATALITIES AND FATALITIES ESTIMATED BY APPLYING THE REGRESSION MODEL G TO EACH OF DATASET FROM YEAR 00 TO 010 Yer Actul Estmted Estmted/ Actul

6 Fg. 5. Rto of estmted ftltes clculted from the regresson model G to ctul ftltes for ech yer Investgton of Coeffcents of Regresson Model Tble 4 shows the regresson functon relted to the yer for the coeffcents of the regresson model G, s well s the coeffcents for the yer 011 determned from the regresson functon, nd the constnt coeffcents of the regresson model G optmzed for the yer 001. Tble 4 shows tht the coeffcents 1, 5, 7, nd b hd postve correlton whle other coeffcents hd negtve correlton wth ech progressng yer. TABLE 4 REGRESSION FUNCTION FOR COEFFICIENTS OF REGRESSION MODEL G, ESTIMATED COEFFICIENTS FOR YEAR 011 FROM REGRESSION FUNCTION AND CONSTANT COEFFICIENTS OF REGRESSION MODEL G OPTIMIZED FOR YEAR 001 Coeffcents Regresson functon for replcng the constnt coeffcents Regresson functon Correlton Coeffcent Estmted for 011 from the regresson functon Constnt coeffcents optmzed for the yer E 03YEAR 3.83E E E E 03YEAR 3.76E E E E 0 YEAR 1.30E E E E 03YEAR 4.06E E E E 03YEAR 7.16E E E E 03YEAR 1.06E E 0.07E E 04 YEAR 1.10E E 0.33E E 03YEAR 3.46E E E E 03YEAR 8.55E E E 01 b 8.8E 06 YEAR 1.5E E E 04 c 5.0E 0 YEAR 1.14E E E+00 where, b, c nd re the coeffcents of the regresson model G shown n below. p MAIS MAIS bage bage Fgure 6 shows the comprson of RMSE from the estmton of the totl number of ftltes n 011 usng the regresson model G between the constnt coeffcents optmzed for the yer 001 nd the coeffcents estmted for 011 from the regresson functons (ll of the coeffcents re shown n Tble 4). Addtonlly, c) c)

7 Fgure 7 shows the comprson of the rto of the totl number of ftltes n 011 estmted by pplyng the regresson model G to the ctul totl number of ftltes n 011 between the constnt coeffcents optmzed for the yer 001 nd the coeffcents estmted for 011 from the regresson functons (ll of the coeffcents re shown n Tble 4). Furthermore, Fgure 8 shows the comprson of the ctul number of ftltes n 011, the estmted number of ftltes n 011 clculted by pplyng the regresson model G wth the constnt coeffcents optmzed for the yer 001, nd the coeffcents estmted for 011 from the regresson functons (ll of the coeffcents re shown n Tble 4) by ge group. Fgure 6 nd Fgure 7 show tht RMSE nd the rto of the estmted totl number of ftltes to the ctul totl number of ftltes were mproved from to nd from 1.0 to 0., respectvely, when the regresson functons for the coeffcents were tken nto consderton. Addtonlly, from Fgure 8, t ws found tht the representtveness of the number of ftltes mproved especlly n 0s, 30s nd 50s. Fg. 6. Comprson of RMSE for yer 011 Fg. 7. Comprson of rto of estmted to ctul totl number of ftltes n 011 Fg. 8. Comprson of number of ftltes n 011 by ge group IV. DISCUSSION As shown n Fgure 3, comprng the regresson models A nd D, B nd E, nd C nd F, the dfferences of whch were ge, AIC nd RMSE of the regresson models whch ncluded ge were lower thn those whch dd not nclude ge. Addtonlly, comprng the regresson models F nd G, the dfference of whch ws the degree of vrbles, AIC nd RMSE of the regresson model G were lower thn those of F. Furthermore, comprng the regresson models D nd F, nd E nd G, the dfferences of whch were the consderton of the njured body regon, AIC nd RMSE of the regresson models whch consdered the njured body regon were lower thn those whch dd not consder the njured body regon. These results suggest tht t s mportnt to consder the nfluence of ge, degree of vrbles nd njured body regon when estmtng the probblty of ftlty ccurtely. Ths cn expln why the best ft regresson model s the regresson model G n Tble

8 As shown n Tble 4 nd Fgures 6 through 8, the regresson model G wth the estmted coeffcents from the regresson functons for 011 shown n Tble 4 cn predct the ftltes more ccurtely thn tht wth the constnt coeffcents optmzed to the yer 001. Ths result suggests tht the coeffcents of the regresson model re sgnfcntly dependent upon ech progressng yer. From Fgure 7 nd Tble 4, t cn be sd tht the coeffcents for the regresson model G chnge wth yer progress nd tht the probblty of ftlty decreses even f njury severty nd ge do not chnge. In order to nvestgte the fctors for the chnge of the coeffcents of the regresson model, the yer chnge of the ftlty rte n hosptls ws checked. Zmmermn et l. [13] showed the yer chnge of the ftlty rte n ntensve cre unts n the U.S. Fgure shows the yer chnge of ftlty rte. Fg.. Ftlty rte for 48,601 ntensve cre unts from to from the result of Zmmermn et l. [13] From Fgure, the ftlty rte n ntensve cre unts decreses wth the progressng yer. Ths tendency of yer chnge of ftlty rte s smlr to the result of the yer chnge of the coeffcents. Furthermore, Zmmermn et l. [13] cted tht the decrese n ftlty rte mght be ttrbutble to mprovements n qulty of cre. It cn be presumed tht the ftlty rte n hosptl s relted to the medcl technology nd medcl nfrstructure. Although the chnge of the coeffcents of the regresson model s ffected by vrous fctors, t s possble tht one of the fctors whch chnges the coeffcents of the regresson model s the mprovement of medcl technology nd medcl nfrstructure. Ths suggests tht the coeffcents of the regresson model should be chnged when fctors such s the country or yer chnge to reflect current medcl technology nd medcl nfrstructure. In ths study, snce the ftlty probblty functon ws developed usng the ccdent dt from sngle country, ddtonl prmeters relted to dfferent envronments my need to be tken nto consderton to develop more comprehensve regresson model. Addtonlly, whle ths study focused on the ftl outcome, there re mny non ftl outcomes, such s dsblty nd mprment. A smlr knd of regresson model to predct these non ftl outcomes my be dentfed n the future by consderng such nformton bout dsblty s descrbed, for exmple, n the Functonl Cpcty Index (FCI) [14]. V. CONCLUSIONS In ths study, seven types of regresson models were nvestgted to dentfy the best ft ftlty probblty functon ssocted wth njury severty nd ge reltve to US ccdent sttstcs (NASS CDS). Addtonlly, regresson nlyses for the coeffcents of the regresson model were conducted to develop model ncorportng the effect of the yer chnge. The followngs results were found: The best ft ftlty probblty functon ws the mxmum AIS of ech body regon nd ge. The overestmton of the ftltes clculted from the regresson model to the ctul ftltes ncresed wth ech progressve yer. The ccurcy of the regresson model ws mproved by pplyng the regresson functons of the

9 coeffcents s functon of the yer. VI. REFERENCES [1] Unted Ntons Economc Commsson for Europe, Sttstcl Dtbse, Trnsport Sttstcs, Rod Trffc Accdents, Persons Klled or Injured n Rod Trffc Accdents by Country, Ctegory of User, Accdent Type, Age Group nd Tme, TRTRANS/01 TRACCIDENTS/. [] Pettjen A, Trosselle X, Prxl N, Hynd D, Irwn A. Injury Rsk Curves for the WorldSID 50th Mle Dummy. Stpp Cr Crsh Journl, 01, 56: [3] Bker SP, O Nell B, Hddon W, Long, WB. The Injury Severty Score: A method for descrbng ptents wth multple njures nd evlutng emergency cre. Journl of Trum, 174, 14(8): [4] Letgeb J, et l. Outcome fter severe brn trum due to cute subdurl hemtom. Journl of Neurosurgery, 01, 117: [5] Tkhsh Y, Suzuk S, Iked M, Gunj Y. Investgton on pedestrn pelvs lodng mechnsms usng fnte element smultons. Proceedngs of IRCOBI Conference, 010, Hnnover, Germny. [6] Goertz A, Yek J, Compton C. Accdent Sttstcl Dstrbutons from NASS CDS. SAE Techncl Pper [7] Boyd CR, Tolson MA, Copes WS. Evlutng Trum Cre: The TRISS Method. Journl of Trum, 187, 7: [8] Chmpon HR, Scco WJ, Copes WS, Gnn DS, Gennrell TA, Flngn ME. A revson of the trum score. Journl of Trum, 18, :63 6. [] Dokko Y, Ynok T, Ohsh K. Vldton of the ge specfc humn FE models for lterl mpct, SAE Techncl Pper, [10] NHTSA, Ntonl Automotve Smplng System (NASS), Crshworthness Dt System, [11] NHTSA, Ntonl Accdent Smplng System (NASS), Crshworthness Dt Subsystem Anlytcl User's Mnul 00 Fle, U.S. Deprtment of Trnsportton, Ntonl Hghwy Trffc Sfety Admnstrton, Ntonl Center for Sttstcs nd Anlyss, Wshngton, D.C. [1] Assocton for Advncement of Automotve Medcne, The Abbrevted Injury Scle 10 Revson, Updte 8, Assocton for Advncement of Automotve Medcne, Des Plnes, IL, USA, 18. [13] Zmmermn JE, Krmer AA, Knus WA. Chnges n hosptl mortlty for Unted Sttes ntensve cre unt dmssons from 188 to 01. Crtcl Cre, 013, 17:R81. [14] McKenze E, Dmno A, Mller T, Luchter S. The Development of the Functonl Cpcty Index. Journl of Trum, 16, 41: VII. APPENDIX APPENDIX 1 NUMBERS OF AVAILABLE CASES AND UNKNOWN CASES FOR EACH YEAR Avlble Unknown Totl APPENDIX NUMBERS OF FATAL CASES AND NON FATAL CASES Ftl Non Ftl

10 APPENDIX 3 NUMBERS OF CASES BY EACH AGE GROUP 0s s s s s s s s s s APPENDIX 4 NUMBERS OF CASES BY EACH ISS RANGE APPENDIX APPENDIX

11 APPENDIX APPENDIX APPENDIX APPENDIX APPENDIX

12 APPENDIX APPENDIX APPENDIX