Catalogue no XIE. Survey Methodology

Transcription

1 aalogu o -00-XIE Survy Mhodology 005

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4 SURVEY METHODOLOGY Joural ublshd by Sass aada Survy Mhodology s absrad Th Survy Sasa Sasal Thory ad Mhods bsras ad SRM Daabas of Soal Rsarh Mhodology Erasus Uvrsy ad s rfrd h urr Id o Sass ad Joural os Qualav Mhods MGEMET ORD hara D Roy as har GJ raso R la Mbrs J Gabo J Kovar H Mal EDITORIL ORD Edor M Sgh Sass aada Duy Edor H Mal Sass aada ssoa Edors DR llhous Uvrsy of Wsr Oaro D dr Sass aada JM r Wsa I awll US urau of h sus JL Elg US urau of Labor Sass W Fullr Iowa Sa Uvrsy J Gabo Sass aada M Hdroglou Off for aoal Sass G Kalo Wsa I Ko aoal grulural Sass Srv J Kovar Sass aada Lahr JSM Uvrsy of Marylad G aha Hbrw Uvrsy D fffra Hbrw Uvrsy JK Rao arlo Uvrsy TJ Rao Ida Sasal Isu sssa Edors EDITORIL OLIY E Raour (roduo Maagr D Roy M Sgh J-F auo D ad W Yug Sass aada J Rr Du Uvrsy L- Rvs Uvrsé Laval Shr aoal r for Halh Sass FJ Shur aoal Oo Rsarh r J Sr Uvrsy of Souhao E Sasy Oho Sa Uvrsy D Sl Uvrsy of Wollogog L Sos Souhr Mhods Uvrsy M Thoso Uvrsy of Warloo Y Tllé Uvrsé d uhâl R Valla JSM Uvrsy of Mhga VJ Vra Uvrsà dgl Sud d Sa J Wasbrg Wsa I KM Wolr Iowa Sa Uvrsy Zaslavsy Harvard Uvrsy Survy Mhodology ublshs arls dalg wh varous ass of sasal dvlo rlva o a sasal agy suh as dsg ssus h o of raal osras us of dffr daa sours ad ollo hqus oal survy rror survy valuao rsarh survy hodology srs aalyss sasoal adus dograh suds daa grao sao ad daa aalyss hods ad gral survy syss dvlo Th hass s lad o h dvlo ad valuao of sf hodologs as ald o daa ollo or h daa hslvs ll ars wll b rfrd Howvr h auhors ra full rsosbly for h os of hr ars ad oos rssd ar o ssarly hos of h Edoral oard or of Sass aada Subsso of Mausrs Survy Mhodology s ublshd w a yar uhors ar vd o sub hr arls Eglsh or Frh lro for rfrably Word o h Edor Dr M Sgh sgh@saaa (Houshold Survy Mhods Dvso Sass aada Tuy s asur Oawa Oaro aada K 0T6 For forag sruos las s h gudls rovdd h Joural Subsro Ras Th r of Survy Mhodology (aalogu o -00-X s D $58 r yar Th r luds aada sals as ddoal shg hargs aly for dlvry ousd aada: Ud Sas D $ ($6 ssus; Ohr ours D $30 ($5 ssus Subsro ordr should b s o Sass aada Dssao Dvso rulao Maag 0 ardal vu Oawa Oaro aada K 0T6 or by dallg by fa or by E-al: ordr@saaa rdud r s avalabl o brs of h ra Sasal ssoao h Iraoal ssoao of Survy Sasas h ra ssoao for ubl Oo Rsarh h Sasal Soy of aada ad l ssoao ds sass sass du Québ

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9 Survy Mhodology Ju 005 Vol 3 o - Sass aada aalogu o -00-XIE I Ths Issu Ths ssu of Survy Mhodology s ddad o Gordo J raso who rly rrd fro Sass aada H was sssa hf Sasa for h Iforas ad Mhodology fld ad had b hara of h Survy Mhodology aag board s 987 Hs ouous suor o h oural has b ard by gra sgh ad ovad by a osa dsr o fosr hgh sadards of hodology ras Furhr h also auhord svral arls ha aard h oural W wsh o rss our r graud o Gordo J raso Th urr ssu oas gh rgular ars o a vary of os ad hr shor ouaos s od h rvous ssu of h oural w ar rodug a w Shor ouaos so Survy Mhodology Ths so wll oa shorr ars yally aroud four ags ossbl os of shor ouaos lud rsao of w das whou h full dvlo of a rgular ar brf rors of ral wor ad dsussos or suls rlad o ohr ars ublshd h oural For h as four yars h Ju ssu of Survy Mhodology has ludd a vd ar hoour of Josh Wasbrg Sarg hs yar hs aual vd ar wll b ublshd h Dbr ssu of h oural brgg or l wh h assoad Wasbrg addrss dlvrd a Sass aada s aual hodology syosu h auu Th auhor of hs yar s Wasbrg ar s JK Rao ad hs ar wll b o h Irlay w Sal Survy Thory ad Mhods: a rasal I h og ar of hs ssu Wgl Valla ad Shur rs a w sulao aroah o sao of rror ras for hrshold slo rord lag For ah oal ahd ar hr s a vor of oarso ouos ha drs h lag wgh uloal odl s assud for ah oarso ouo wh dffr uloal dsrbuos for ru ahs ad ru o-ahs Th dsrbuos ar sad fro a sal ad h usd o sula h dsrbuos of h lag wghs for ru ahs ad ru o-ahs Th hod s llusrad a as sudy usg daa fro h US Mdal Edur al Survy (MES Krws Dwa Wag arl Zls ad Mall vsga h ffs of rord lag rrors boh fals osvs ad fals gavs o rs sas ohor suds Thy show aalyally how lag rrors rodu boh bas ad addoal varably o obsrvd ad d ubrs of dahs as wll as o sas of sadardzd oraly raos ad rlav rs rgrsso offs Thy dsuss hr rsuls hr olusos ad o o furhr wor ha ds o b do hs ara Th ar by va d ral ad Rss addrsss h robl of sg hyohss bw dffr survy laos suh as dffr qusoar dsgs wh a ol salg dsg s usd dsg-basd hory s dvlod for ass whr h survy laos ar assgd o subsals hrough olly radozd ral dsgs or radozd blo ral dsgs Th hory also as us of asur rror odls Dsg-basd Wald sass ar usd o oar h dffr survy laos Tsuhya aroahs h log-sadg robl of asg rsods ssv qusos a rsg fasho Isad of usg h radozd rsos aroah ha allows ll orol for h rsarhr h rooss ha h ou hqu b adad for ssv qusos Th ou hqu rss h rsod wh a ls of svral hrass fro whh h rsod sls all ha aly o h Th rsarhr osrus h ls wo ways: h frs ls oas h ssv hras whl h sod ls dos o Tsuhya rss varous saors for hs hqu ad gvs a rsg al rlad o h Jaas aoal harar I h ar by DZo Guarra ad Luz f ur odls ar usd o d rrors ha ar du o a orr u of asur a h ollo sag of h survy I a ulvara o ad assug ha h daa ar ulvara oral h rodur a dfy whh varabls ar rror for a gv sald u Th auhors also rovd dagoss for rorzg ass o b vsgad or dly hrough lral rvw Th roosd hodology s llusrad hrough a al wh sulad daa ad a al wh ral daa Sass aada aalogu o -00-XIE

10 I Ths Issu hu Yul Zauo ad Zaslavsy rs a hod for ull uao of ssg oual varabls for us rgrsso aalyss For ah rord ssg h varabl ad for a sal of ol rords ahd ass ar sld basd o a s of ahg varabls Th sal of ol rords s h usd o sa a rgrsso adus for ohr varabls o ludd aog h ahg varabls Th oual varabls for h ol rords ar h ully ud Th auhors h show a alao o a oloral ar sudy ad us sulaos o oar hr aroah o hr ohr orsos adus hods adra ad ho a h ora robl of ogorabl orsos sall-ara sao of a halh saus varabl Wh ofrod wh a al whr h usual saors ar basd baus of h ssv ubr of orsods hy a o aou for h dffrs hrough odlg adra ad ho us wo ogorabl orsos hrarhal ays odls a slo odl ad a ar odl o aalyz h halh daa ora osdrao o hr odlg s h ororao of h u fro doors org h orsos ar ad h ouo varabl Th rsuls gv a aura o-rsos adus ad a br asur of rso ar ad Fullr roos a hod o rdu h robably of obag gav sao wghs wh usg a rgrsso saor Thr hod osss of frs aroag luso robabls odoal o Horvz-Thoso sas for a vor of aulary varabls ad h usg hs aroa odoal luso robabls as al wghs a rgrsso saor Thr hod s show o wor wll a sulao sudy Th wghs obad fro hs hod ar also oard o wghs fro quadra rograg h rag rao h log rodur ad au llhood I h frs of hr shor ouaos ludd hs ssu drsso ad Thorbur show ha h oal rgrsso saor a b rssd as a albrao saor wh a aroraly hos dsa fuo Th rsulg oal saor s asyoally or ff ha h usual Gralzd Rgrsso (GREG saor sall sulao sudy llusras svral suaos whr h oal saor f sgfaly or ff ha h GREG saor Ly ad Gablr d h rsuls of Gablr Hadr ad Lahr (volu o Ksh s rsso for h dsg ff du o lusrg Thy gv a raal aroah o sag Ksh s quay a h sal dsg sag wh oly h oal ubrs of obsrvaos ad of lusrs ar dd Mza ad Lahr a h laos of a sadard rgrsso odl slo rro Mallows sas for sd rror rgrsso odls Thy show ha whl a sraghforward alao of Mallows sas ay rsul ff odl slo hods a suabl rasforao of h daa ay b h aswr Fally w would l o for you ha Harold Mal wll ow hold h w oso of Duy Edor Harold has b ar of h Edoral oard for h las 5 yars Hs ddao o h oural has b oabl ad hs ouous volv h doral ross has b srual surg ha Survy Mhodology ras a hgh qualy ublao M Sgh Sass aada aalogu o -00-XIE

11 Survy Mhodology Ju Vol 3 o 3- Sass aada aalogu o -00-XIE as Sudy Rord Lag M Wgl R Valla ad F Shur bsra Rord lag s a ross of arg rords fro wo fls ad ryg o sl h ars ha blog o h sa y Th bas frawor uss a ah wgh o asur h llhood of a orr ah ad a dso rul o assg rord ars as ru or fals ah ars Wgh hrsholds for slg a rord ar as ahd or uahd dd o h dsrd orol ovr lag rrors urr hods o dr h slo hrsholds ad sa lag rrors a rovd dvrg rsuls ddg o h y of lag rror ad h aroah o lag Ths ar rss a as sudy ha uss sg lag hods o l rord ars bu a w sulao aroah (SRa o hl dr slo hrsholds ad sa lag rrors SRa uss h obsrvd dsrbuo of daa ahd ad uahd ars o gra a larg sulad s of rord ars assgs a ah wgh o ah ar basd o sfd ah ruls ad uss h wgh urvs of h sulad ars for rror sao Ky Words: Fl ahg; Lag rror ras; Mah wgh; Slo hrshold; Mdal rords Iroduo Th bas rord lag frawor by wob Kdy ford ad Jas (959 ad Fllg ad Sur (969 uss a ah wgh o asur h llhood of a orr ah ad a dso rul o lassfy rord ars Th oal dso rul uss wo ah wgh hrsholds for slo (a ur hrshold abov whh a l s rad as a ah ad a lowr hrshold blow whh a l s rad as a oah Th ho of hs hrsholds dds o h aabl r-s lag rror ra ad h rqur o z h ubr of ls wh dra saus bw h wo hrsholds owadays raors of ourzd lag syss of us a sgl slo hrshold o avod aual rvo of h dra ls Lag dsos ar yally ad auoaally afr h sys s ud o ahv r-s rror lvls Th hallg s ha urr hods o dr h slo hrshold ad o sa lag rrors a rodu dvrg rsuls ddg o h y of lag rror h ho of oarso sa ad h sao hod Ths ar shars our r wh fllow raors who d a hod o gud lag slo ad rror sao Our as sudy usd dal v fls fro h US Mdal Edur al Survy (MES MES olls dal dur daa fro boh houshold rsods ad hr dal rovdrs Th uros s o ob h daa fro boh sours for suorg aual saos of dal ulzao ad durs (s gy for Halhar Rsarh ad Qualy 00 for or dals o MES Hr w dsuss h lag wh hr ss of aual dal v fls MES 996 MES 997 ad MES 998 Eah s ossd of a houshold fl oag vs rord by houshold rsods for a gv yar ad a dal rovdr fl oag h orrsodg vs rord by dal rovdrs of h houshold rsods O avrag aroaly dal vs wr rord for los o 0000 rsos ad aroud 5000 rso-rovdr us ah yar W usd wo odl-basd alravs for lag rror sao O of hs uss sulao o dvlo a dsrbuo of h wghs for varous lvls of agr Ths hqu alld SRa bgs by grag wgh dsrbuos for ahd ad uahd rord ars Usg hs SRa a h rovd sas of lag rror ras for dffr hrshold lvls Th rror ras a h b usd as a gud o ao ad a way o asur suss SRa s orasd wh a sod odlg aroah rad by l ad Rub (995 s w ho o show hr s a rol for boh aroahs; ah has srghs as llusrad h oarsos Mur Modls ad Sra roahs Th ur odlg hod of lag rror sao as rsd l ad Rub (995 has svral arav faurs I s flbl a ss ha h wgh rao ross dos o hav o b osdrd drly H hs hod a b alabl o ay dffr ways of rag wghs O a odl s sfd rror M Wgl Wsa Sasal Grou 650 Rsarh oulvard Rovll MD US; R Valla Jo rogra for Survy Mhodology Uvrsy of Marylad ad Uvrsy of Mhga; F Shur OR Uvrsy of hago

12 4 Wgl Valla ad Shur: as Sudy Rord Lag ras a b ad for a ouu of oal hrshold valus ad ofd bads a b osrud o oor h rso of rror sas (s so 7 Mur odlg dos hav laos Whl h hod rovds a arular d of rror ra h rooro of ld rords ha ar aually uahd ars ovrall fals osv ad fals gav rror ras ao b sad s old ars ar o osdrd Th rror ra ha s sad s odoal o h s of ld ars of rords Furhror odl arars ay b hard o sa f h wgh dsrbuos for h ahd ad uahd ss ar o sarabl (s Wlr 994 y assuo h l Rub aroah s ha s ossbl o rasfor h dsrbuos of h wghs h ahd ad uahd ss o a h oral ow a ral dffuly ss hr ha h rasford wghs ay b far fro oral wh h wgh dsrbuo for hr h ahd or uahd ss s ulodal ohr ral rqur s o hav a rag daa s whos hararss ar vry slar o hos ha ar o b ahd Whou a good rag daa s h u arar sas for h ur odl ay b oor affg h fal sad rror ras obad asd o our alao usg aual dal v daa rad ovr hr yars h arars wr o sabl ovr Ths sably ssad a rag s for ah yar ag h l Rub aroah raal our alao baus of h os ad rqurd Th sulao aroah SRa l ur odlg has h ably o a dffr hrsholds allowg h usr o oor boh h ssvy ad sfy of h dso rul for slg ld ars s log as h ross usd o ra ah wghs a b ralsally odld usozd hods of wgh assg l h o usd h urr as sudy a b aoodad Th hod dos rqur h grao of ars of rords usg h dsrbuo of hararss for h ahd ad uahd ss So ffor s dd o ralsally gra h oulaos of ars I our wor w hav b sussful wh uloal odls for grag hs oulaos 3 Thrshold Wgh ad Lag Error Esao Svral hods ar avalabl h lraur for slg ru ahs ad for sag lag rrors (g arl Krws Wag ad Zls 993 rsrog ad Mayda 993 l 993 l ad Rub 995 ad Wlr S Fllg (997 for a ovrvw of voluos rord lag Tg (968 ad Lars ad Rub (00 for ohr lg hods ad Shur (983 for a aur-raur hod o sa osso rror oarso of sas fro h dffr aroahs s olad by h fa ha ah aroah ds o fous o dffr rror oos I fa h hods usd h lag lraur o osru lag rror ras ar sowha oss W llusra hs robl blow Tabl shows a ogy abl abulag h ubrs of ru ahd ad uahd ars ad dlard ld ad old ars sld by lag syss Esas of lag rror ras a b osrud rlav o h ru oals show h olus sa of fals osv lag rror ra udr h Fllg ad Sur frawor s μˆ ( U / ad ha of fals gav lag rror ra s λˆ ( 3 M / (s also rsrog ad Mayda 993 Ths ar h ras ha SRa s dsgd o sa Thy aswr h quso Of h s of ru ahd (or uahd ars wha rooro s o orrly dfd? Tabl ogy Tabl for Evaluag Lag Errors Tru s Dlard s Mah (M Uah (U Dlard oal L ( ol ( 3 ru osv fals osv fals gav ru gav Tru oal So lag valuaos hav also osdrd ras rlav o h dlard oals h rows For sa Goaa arr r ad Mhll (00 usd / ad labld h osv rdv owr of h lag sys Ohrs howvr hav labld hs as h fals ah ra (l ad Rub 995 or fals osv dlard ra (arl al 993 Ras osrud hs ar aswr h quso Of h dlard ld (or old ars wha rooros ar wrog? oh qusos ar ora slg ahd ars ad should b addrssd Tha s o of h aals loyg boh SRa ad l Rub f ossbl 4 Sra Wgh Dsrbuo Mhods o Esa Lag Error How o bs sa h lag rrors gv a ld budg ad shdul s a dfful quso ura sao of lag rrors should dd o a las wo faors h owr of h dfyg flds o uabguously dfy vs ha ar ru ahs ad h lag hod usd Ta oghr s h ossbl a gv sg o sfy lag agors sa agr robabls ad dr ah wghs Sass aada aalogu o -00-XIE

13 Survy Mhodology Ju Followg wob ad Kdy (96 ad Jaro (989 w ado a wgh dsrbuo aroah our alao ha a a all hs faors o osdrao Th bas s s o frs ou h ah wgh ad ordr all ossbl ofguraos of agr ad dsagr ouos of h oarso flds by ah wgh Th w lo h uulav dsrbuo fuo of h wghs for ahd ad uahd ars ad us h rsulg wgh har o dr hrsholds o aa dsrd lvls of fals osv ad fals gav rror ras dal hod o dvlo hs urvs gh b o bg wh a s of rord ars for whh h ruh s ow If rsours ar avalabl w ould us a larg s of ru ahd ars ordr h by ah wgh ad obsrv wha rooro s abov or blow a gv hrshold Slarly w ould a a larg s of ars ow o b ru uahd ars ordr h by wghs ad aga abula h rooro o hr sd of h hrshold Th rooro of ru ahd ars wh wghs blow h hrshold ad h rooro of ru uahd ars wh wghs abov h hrshold would h b sas of h rror ras assoad wh h way whh h ahg algorh s ld O hod o aroa hs dal aroah (s also arl al 993 s o sal rord ars ad us aual rvw o dr h ru ah saus O h ru ars ar ow w a aah h ah wghs fro whavr lag sys s bg usd ad h dvlo uulav wgh dsrbuos as dsussd abov Ths hod s of ours sub o h wll-ow ad ohr rsour laos of aual rvw ad s sldo raal wh a larg sal alrav hod s o gra h uulav wgh dsrbuos hrough sulao Tha s h har of h SRa aroah To la so dal do a rord ar by r ad a oarso fld by v ( v K V flds Th oarso ouo suaos our alao ludd aral agrs ad ull ouo agors byod h bas agr ad dsagr agors (s also wob 988 Thrfor w do ha ah fld v has K v ouo agors Th ouo daor s y rv ( yrv K yrv v a vor of daors showg h agory o whh ar r falls O of h valus of y rv wll b ad h ohrs 0 for ah fld Th arular hory suorg h SRa aroah s o assu ha y rv has o uloal dsrbuo f ar r s a ahd ar ad a dffr uloal dsrbuo f s a uahd ar W a h odl h y rv vors as havg a uloal dsrbuo wh arars v ( v K v f h ar s a ahd ar v ad arars u u K u f h ar s a v ( v vv uahd ar Th h robably v (fld v agory agrs ar r r M s h odoal robably of agr for fld v agory I gv ha h rord ar r s h s M of ru ahd ars I oras h robably u v (fld v agory agrs ar r r U s h odoal robably of agr for fld v agory I gv ha h rord ar r s h s U of ru uahd ars ssug dd of h ahg varabls v K V w a sfy h o robably of y y K y f a ar r s a ah as r ( y ( r rv V r r M v v Th orrsodg robably of h sa ofgurao of daa f h ar s rally a uahd ar s ( y r r U V v v SRa uss Mo arlo sulao hods o gra a larg ubr of ralzaos of ahd ars ad uahd ars usg sas of h robabls v ad u v For ah sulad ar a ah wgh w r whh als o a gv ofgurao of daa s alulad For a gv ralzao y r a wgh w r s oud for h ar by sug h wghs for h radoly grad agors ha h ar fll o Th ah wgh w r of a rord ar s yally sad as V v y r v v log v w r V v yr v uv v S so 6 o h ah wghs usd our sulao Th uulav dsrbuo of hs wghs for h sulad ahd ars s h lod as S M Slarly h rvrs uulav dsrbuo for h uahd ars s lod o gra S U (s Fgur so 8 for a al of h sulao urvs usd hs sudy Th sulad rooro of ahd ars whos wghs ar blow h uoff s h sa of h fals gav rror ra Th sulao rooro of uahd ars whos wghs ar abov h uoff s h sa of h fals osv rror ra Ths aroah rqurs ha ral sas b ad of h dsrbuos aog h ahg varabls of boh ru ahd ad ru uahd ars Ev hough h wgh algorh ay volv h assuo of dd aog ahg varabls h aual daa ay show dd s log as arfal ars a b grad ha ralsally follow h obsrvd dsrbuo of h daa (ororag ay dds h hs hod should rovd suabl rror ra sas u y v y v r v rv Sass aada aalogu o -00-XIE

14 6 Wgl Valla ad Shur: as Sudy Rord Lag I our as sudy w odld daa flds as havg dd uloal dsrbuos bu hs ay o b rasoabl ohr alaos Th SRa o a aly o ay algorh whr wghs ad a uoff o ar usd for lassfao Thus hods ohr ha Fllg ad Sur (969 l l ad Rub (995 gh also b valuad hs way If hods ar dd o dal wh dd agoral varabls h ulvara uloal dsrbuos Johso Koz ad alarsha (997 har 6 ay b arora Howvr alaos slar o ours h sls rodur for aoug for dd s o for ross-lassfaos of h varabls ha ar rlad ad o sa robabls for ah ll a ross-abl For al f wo varabls wh ad agors ar assoad h w a sa h o robably for ah ll h * abl ad us hos h sulao Sars daa wll aurally l h ubr of lls for whh hs s fasbl u h rs of sars daa h aly for odl falur us b sall 5 Rord Lag of MES Mdal Evs Rord lag of MES dal vs usd fv dfyg flds: v das (yar oh day ad day-ofw dal odo ods rodur ods global-f ods ad lghs (ubr of days of hosal say Ths flds ar dsrbd or dal Wgl Valla r ad Mahl (000 rag sal fro MES 996 was loyd o drv ah ruls ad ouo agors ad o sa h robabls of agr for ah agory allowg for aral agr ad valu sf ouos Th sa ah ruls wr rad ah yar wh or aduss of h ahg arars For h rag s w usd h lag sys uoah (Mahwar 996 ad h uqu ah algorh o sl ld ars I uqu ahg a Fl rord s oally ld o oly o Fl rord (Jaro 989 I addo w usd h ay-o-ay ah algorh o gra a rado sal of old ars o fala lag rror sao Howvr h hods for sag rror ras dsrbd blow aly o ay sofwar ha ls h lag hods basd o ah wghs Thy ar o sf o uoah Th radoff drg h slo hrshold for MES was bw gg a hgh ah ra ad lg sah lag rrors hgh hrshold wgh would z fals osv (sah rrors a h s of lowrg h ah ra ad losg valuabl daa olld fro dal rovdrs O h ohr had a low hrshold would ras fals osv rror ad ay aff h alloao of dur daa a way ha would rqur sal aaly hqus o ovro ad v h oly wh uray S boh daa sours had rord o ossbly h sa dal vs for h sa rsos ovr h sa rod h sragy was o aa a rasoably hgh ah ra ad o odu a aual rvw of a ld ubr of qusoabl ld ars afr slo o assss h aaly a of falsly ag h asd o hs dso h avrag ah ra for h aual MES dal rords fls was abou 85 r Th 996 MES rag sal M urv labld h Tra M urv was grad by alyg ah wghs o ru ahd ars for a rado sal of 500 rsos MES 996 For hs rsos h aual rvw fls oad 507 vs fro houshold rsods ad 804 vs fro dal rovdrs Kowldgabl daa aagrs rvwd h vs ad sld 50 ars W osdrd hs as h ru ahd ars hs valuao Th aually ahd ars wr assgd h wghs drvd fro our ah sfao o gra a uulav dsrbuo fuo Th 996 rag sal U urv labld h Tra U urv was grad usg a rado sal of uahd ars W usd a sl rado salg wh rla hod o sl 500 vs ah fro h ahg fls ad loyd a ay-o-ay ah algorh o gra all ossbl v ars For hs radoly sld ss of ars h ha of hr bg ay orrly ahd ars s glgbl; hus h r s was a o oss of uahd ars W ald h ah wghs fro our ahg sfao ad lod h Tra U urv qual o us h uulav dsrbuo of h wghs of hs ars Fgur so 8 shows boh h Tra M ad Tra U urvs for h 996 MES Th urvs show hs fgur wr soohd usg a oarar lowss fuo (habr lvlad Klr ad Tuy 983 S LUS 000 (999 6 Sra Ilao MES Th SRa wgh dsrbuo hod usd Mo arlo sulao hods o gra sara ss of 0000 sulad ahd ad uahd ars for rag h wgh urvs To gra h S M wgh dsrbuos w sad h robabls v fro ld ars assgd by a uqu ahg algorh W usd h ud lag sys o sl ahd ars fro h 996 aual ahg fls ad abulad h obsrvd frqus for ah ouo agory for ah of h fv ahg flds Th rooro of ars ha fll o agory of fld v was h usd as h sa ˆ v of h robably v Sass aada aalogu o -00-XIE

15 Survy Mhodology Ju For h uahd ars ad h S U urv h u v robabls for uahd ars wr sad usg h sa sal of uahd ars usd rag h Tra U urv Th dffr s ha w usd hs ars o obsrv h rlav frqus for ah ouo agory for ah of h fv ahg flds aog uahd ars Th rooro of ars ha fll o agory of fld v was h usd as h sa û v of h robably u v For a sulad ahd ar a ralzao of h uloal rado varabl y rv was grad for ah ah fld For al a ofgurao l (agr o v da agr o lgh of hosal say agr o h array of odo ods o agr by y of rodur ad valu sf agr for a global-f daor was grad usg h ah robabls ˆ v for ah ouo agory Slarly for ah uahd ar a ralzao was grad of a agory for ah of h fv flds usg h uahd robabls û v dsussd abov For a gv ralzao y r a wgh w r was oud for h ar by sug h wghs for h radoly grad agors ha h ar fll o Th aual wghs usd our sulao wr adusd os ha w sfd rahr ha os dfd drly by h ahg sofwar (s Wgl al 000 Thus w ar sulag h way whh ahg would aually b ld To do hs w alulad h ah wgh for boh h ahd ad uahd ss of 0000 ars ad lod h sulad ah wgh fuos Tabl shows als of so h aral agr agors usd for ahg v da ad h sas of ˆ v uˆ v ad w r usd SRa sulao W dfd a oal of 9 ouo agors for ahg by v da 9 agors for durao of hosal say 7 agors by dal rodurs ad 3 agors ah for dal odos ad global f For al for h ouo agory a agr o v da h sa of ˆ v was 069 ag ha 69 r of h ld ars had a agr o v da Th sa of û v for hs ouo agory was 0003 showg ha oly 03 r of h uld ar showd agr o hs fld Th ah wgh for a agr o da of v was 85 ad ha for ol dsagr (dffr of or ha wo ws aar ad o dffr day of w was 664 (s Wgl al 000 for h ah wghs by ah flds ad ouo agors W sld h ah flds ha wr aroaly dd hs as sudy For al w foud o fuoal assoao bw h da of dal vs ad ohr ah flds l dal odo ad lgh of hosal say For flds suh as h daors for surgry radology ad laboraory rodurs w usd h-squar ss ad foud so dd bw h ourr of surgry ad radology To hadl hs suao w sad h o robabls ad sfd ah ruls o ra hs rodur flags as a sgl ah fld (s so 4 abov H w ould h aly h dd uloal dsrbuo for sulao Tabl Esas of Muloal robabls for Mahd ars ˆ ad Uahd ars ( u ˆ v ad Mah Wghs ( w v for h Mah Fld Ev Da ( v Mah rul for Ev Da ˆ v û v w v Mssg Ea ah Off / day Off / 3 day Off / 5 day Off / 7 day Mah by day of w oly Dsagr Tabl 3 shows h rsuls of lag rror sas fro SRa ad h rag urvs a h hrshold wgh of w for MES 996 MES 997 ad MES 998 SRa was asy o ra ah yar Rag h aual-basd wgh urvs howvr ddd ar o aual rvw ad w had oly o rlabl rag sal ha for 996 o ha h ld ars usd SRa wll aurally gra so rag of fals osvs ad fals gavs so ahd ad uahd ars ar orr Thus h ˆ v robabls oud hs way for h dfd flds ar sub o rror I would hav b rfrabl o sa h robabls fro a ruh s whr w wr ofd ha all ahs wr orr Howvr h aually ahd rag ss w wr abl o rodu wr oo sall o yld sabl sas all of h dald ah agors ad aual slo s also rf Ths dffr ay la ar h slghly hghr ovrall rror ra sas fro SRa ha fro h rag sal wgh urvs Tabl 3 Wgh urv Mhods o Esa Lag Error Ras a Thrshold Wgh MES Mhod Error Ra SRa sulao urvs Fals gav Fals osv Trag sal urvs Fals gav* Fals osv** * Esas fro h 996 Tra M urv wr usd for all hr yars ** Esas fro h 996 Tra U urv usd sals of 500 rords fro ah ah fl ad a oal of uahd ars Th 997 ad 998 sas usd dffr Tra U urvs loyg sals of 000 rords fro ah ah fl ad a oal of uahd ars Sass aada aalogu o -00-XIE

16 8 Wgl Valla ad Shur: as Sudy Rord Lag 7 Mur Modl Ilao MES ur odlg aroah by l ad Rub (995 vws h dsrbuo of obsrvd ah wghs fro a ourzd lag sys as a ur of wghs for ru ahs ad fals ahs I rl h ur odl hod has wo arav faurs suabl for MES Frs a hadl rad alaos ffly Wh global arar sas of h rasford arars ad h rao of h varas of h wo dsrbuos ar avalabl hs sas a b ald o slar daa for sao S h MES rord lag s do aually global sas drvd fro arly rag sals ould ovably b ald for lag rror sao lar yars wh aual rvw sals wr o avalabl Th sod advaag s ha h ur odl a draw fro ull ss of arar sas fro dffr rag sals ad a rfl varaos Ths faur s sally aalg for MES baus aual rvw s a ol ross ad o ssarly always aura H a alrav s o vw h our sys slo as h ruh ad us h o rovd a alrav s of arar sas Ths ross a also b rad usg rag sals fro or ha o yar Our alao of h l Rub aroah usd h sa rag sals fro MES 996 ad a sod rag sal of h sa sz fro 997 Followg l Rub s als w ald h ur odlg hod usg aually dfd ru ad fals ah ars fro a o-o-o ahg sys (o ha suh syss rovd rlavly fw fals ah ars for sao W oud odl sas for MES 996 ad MES 997 assug h aual slo o b h ruh ad for sg h bhavor of h odl w oud a sod s of sas assug our sys sld ah ars o b h ru ars Ilao volvd wo rodurs h o ad o (964 rodur for global arar sao ad h albra rodur (l ad Rub 995 o f a ur odl for rror ra sao for alyg o o h wghs wr rsald bw ad 000 Th o o rasforao dsussd by l ad Rub (995 was Ψ γ wr ( wr γ γ w whr w r s h ah wgh for ar r w s h gor a of h w r wgh ad γ s a arar ha s dd o whhr h ar s h ahd or uahd s For h ur odl rodur o b ffv h rasford wghs should b aroaly orally dsrbud Th urasford wgh dsrbuo wh our daa showd bodaly ad alos o ovrla ah wgh bw ahd ad uahd ars (bodaly was also obsrvd l Rub 995 For al alao of hr rasforao rodur o h 996 MES sys ars rsuld arar sas of w 5857 ad γ 5 for h ru ahd ars ad w 3 ad γ 0 48 for h fals ahd ars Th rasford wghs howvr showd rlavly ll rov owards oraly S h ah wghs ar h log of a rodu or h su of logs w gh ho ha h wghs would b orally dsrbud f hr wr ay oos h su Howvr w had oly fv flds o us for ahg Th sall ubr of flds ay hav aoud ar for h la of oraly wh our rasford daa Tabl 4 shows h rsuls of alyg h l Rub ur odl o MES 996 Ths abl shows h odl sad fals ah ras h 95 r ofd rval of h sad ra ad h aual obsrvd fals ah ra a h hrshold wgh of Usg h aual rvw ars as h ru ahd ars h odl sa of h d fals ah ra a h hrshold of w was 9 r wh a 95 r ofd rval ragg bw 60 ad Th aual obsrvd fals ah rror ra howvr was 45 r whh s hghr ha h ur 95 r ofd boud o ha hs ar ras of h for / Tabl Ths ar o h sa ras sad by SRa ad h wgh urv aroah MES 996 Tabl 4 Mur Modl Lag Error Esas rag fals ah rror Ed Lowr Ur Obsrvd ra ra oud* oud* Maual ah Sys ah * Th lowr ad ur bouds ar h 95 r ofd rval of h d rror ra S aual rvw ay o always b aura a oo for h uros of valuao s o ra h our sys ld ars as h ruh ahd ars ad us h for odlg Udr hs assuo h odl sa of h d rror ra s 09 ad a 95 r ofd rval bw 06 ad Th aual obsrvd ra hs as 0 r was a hyohal ouo rag h our-ld ars as orr Of ours raly hr wll b so ozro lvl of rror so ha h ur odl ofd rval s o ssarly wrog W grad global arar sas usg boh h rag sal aual slos ad sys slos for Sass aada aalogu o -00-XIE

17 Survy Mhodology Ju MES 996 ad MES 997 ad usd h as four ss of us o rovd global sas for odlg lag rror for MES 998 Ths should b ossbl baus h daa rad slar ad rord ars wr sld usg h sa ah ruls for all 3 yars dffr was ha aual rvw was o odud for MES 998 ad w ould o us h o o rodur for global arar sao for 998 (baus hr was o sara aual daor for ru ad fals ars For hs alao w us a boosra hod h l ad Rub albra rodur o draw fro ull arar ss o rfl uras sao Ths alao howvr dd o ovrg afr 50 raos of h sao rodur W ould oly olud ha h global arar sas fro arlr rag sals fald o gralz ad rovd rror ra sas for rad lag alaos 8 oludg os ad aly Ilaos Th ross of hrshold slo ad lag rror sao s a rav ross volvg rad yls of obsrvao sao ad odlg Our as sudy loyd odlg aroahs for sag lag rrors ad for oorg h rdv owr of h lag sys oh hods rovdd valuabl forao for drg h lag slo ad for valuag h qualy of h dlard ahd ars as w foud MES Th wgh urvs aroah of sao has h aal ha o a hoos a slo hrshold o aa h aabl lag rror lvl For al Fgur shows h rag sal ad h SRa sulao wgh urvs basd o h 996 MES ahg fls vral l s draw a h slo hrshold wgh of w ; h rror lvls for 996 MES (show Tabl 3 wr h sad by h uulav rag a hrshold lvl y sldg hs hrshold o a a o z h oal lag rror by slg a hrshold a h rossg o of h M ad U urvs I hs as sudy h oal hrshold suggsd by boh ss of wgh urvs s farly oss W ludd a llhood rao sal hs fgur o rovd a rough llhood rrao of h ah wgh For al a h ah wgh of w h llhood rao sor s Ths as ha for rords wh a ah wgh of w or abov h rlav llhood of bg ru ars s a las o uulav rag ssgd Mah Wgh / 0 / Llhood Rao Fgur Wgh urvs for MES 996 usg h SRa ad Trag Sal Mhods; h dashd vral rfr l shows h hrshold valu of Sass aada aalogu o -00-XIE

18 0 Wgl Valla ad Shur: as Sudy Rord Lag Sys ars 996 ad 997 Maual ars 996 Maual ars Lowr boud (95% I Ed ra Ur boud (95% I Obsrvd ra Wgh Fgur Mur Modl Esas of Fals Mah Ras by Wgh 996 ad 997 MES Trag Sals (a vral l s draw a wgh whh s hrshold For ld ar qualy Fgur shows h dsrbuos of fals ah ra sas fro ur odlg Ths fgur shows h odl sad fals ah ra h ur ad lowr 95 r ofd bouds of h rror ra sas ad h aual obsrvd ras al shows h sas rag h our sys ld ars as h ru ahd ars als ad 3 show h sas fro h 996 MES ad 997 MES rag sals Th dffr bw als ad 3 shows h ossy of aual slo by dffr rvwrs our alao I all hr als h 95 r ofd rval of h odl sas fald o ovr h ru obsrvd valus Idally o would us boh Fgur ad Fgur oghr o gud h ho of slo hrsholds W hav foud SRa o b a forav ad flbl ool for drg slo hrsholds ad sag rror ras our alao Gv uloal or ohr odls for h ahg varabls h SRa hod rovds rror ra sas ha would b obad fro rad alao of h ahg algorh o a larg ubr of adda rord ars I s also flbl aoodag h hos of oarso ss of ars for oug ras Whl our alao ahvd h ahg ad rror ra sao goals for MES or wor gh b do ror o or durg h aalyss sag Sa dos o r us o dvlo hs h o of h urr as sudy bu wo gral aroahs gh b od Frs s ossbl o rwgh h fal rsuls ad adus for fals oahs rag h a ar aalogous o u orsos (g as Oh ad Shur 980 To hadl sahs h das Shur ad Wlr (993 ad 997 ad Lahr ad Lars (00 gh b worh osulg Whhr hs addd ss ar dd of ours dds o h fal uss o whh h ld daa wll b u owldgs Th bas lag rsarh rord o hr was odud udr oras ad sosord by h gy for Halhar Rsarh ad Sass aada aalogu o -00-XIE

19 Survy Mhodology Ju 005 Qualy ad h aoal r for Halh Sass Th auhors would l o ha Sv oh Sv Mahl ad Jol oh of h gy for Halhar Rsarh ad Qualy for hr os o varous sags of hs rsarh ad Thoas l for hs suggsos o a arlr draf Rfrs gy for Halhar Rsarh ad Qualy (00 ME Mdal Edur al Survy <h://wwwahrqgov/daa/s h> rsrog J ad Mayda JE (993 Modl-basd sao of rord lag rror ras Survy Mhodology arl S Krws D Wag Y ad Zls JM (993 Evaluao of rror ras larg sal ourzd rord lag suds Survy Mhodology 9 3- o GE ad o DR (964 aalyss of rasforaos (wh dsussos Joural of h Royal Sasal Soy Srs l TR (993 Evaluao of sours of varao rord lag hrough a faoral r Survy Mhodology l TR ad Rub D (995 hod for albrag falsah ras rord lag Joural of h ra Sasal ssoao habrs JM lvlad WS Klr ad Tuy (983 Grah Mhods for Daa alyss Dubury rss oso Fllg I ad Sur (969 hory for rord lag Joural of h ra Sasal ssoao Fllg I (997 Rord lag ad ubl oly Dya Evoluao rodgs of h Iraoal Worsho ad Eoso Fdral o o Sasal Mhodology Off of Maag ad udg Washgo D Goaa S arr R r ad Mhll G (00 ral oao of rord lag rodurs Sass Md Jaro M (989 dvas rord lag hodology as ald o ahg h 985 sus of Taa Florda Joural of h ra Sasal ssoao Johso L Koz S ad alarsha (997 Dsr Mulvara Dsrbuos w Yor: Joh Wly & Sos I Lahr ad Lars MD (00 Rgrsso aalyss wh ld daa (Draf ausr Lars MD ad Rub D (00 Irav auoad rord lag usg ur odls Joural of h ra Sasal ssoao Mahwar Thologs I (996 uomah: Gralzd Rord Lag Sys Usr s Maual Slvr Srg MD: Mahwar Thologs I wob H (988 Hadboo of rord lag: Mhods for halh ad sasal suds adsrao ad busss Oford Uvrsy rss w Yor wob H Kdy JM ford SJ ad Jas (959 uoa lag of val rords S wob H ad Kdy JM (96 Rord lag: Mag au us of h dsrag owr of dfyg forao ouaos of h ssoao for oug Mahry Oh HL ad Shur F(980 Fddlg aroud wh oahs ad sahs Suds fro Iragy Daa Lags Srs Soal Sury dsrao Ror o Shur F (983 Dsg ad sao for larg fdral survys usg adsrav rords rodg of h So o Survy Rsarh Mhods ra Sasal ssoao Shur F ad Wlr WE (993 Rgrsso aalyss of daa fls ha ar our ahd Survy Mhodology Shur F ad Wlr WE (997 Rgrsso aalyss of daa fls ha ar our ahd II Survy Mhodology S-lus 000 (999 MahSof I Daa alyss rodus Dvso Sal Washgo Tg J (968 odl for ou lag of rords Joural of h ra Sasal ssoao Wgl M Valla R r JM ad Mahl S (000 robably ahg of dal vs Joural of Eoo ad Soal Masur Wlr WE (99 oarav aalyss of rord lag dso ruls rodgs of h So o Survy Rsarh Mhods ra Sasal ssoao Wlr WE (994 dvad Mhods for Rord Lag urau of h sus Sasal Rsarh Dvso Sasal Rsarh Ror Srs RR 94/05 Wlr WE (995 Mahg ad rord lag I usss Survy Mhods (Eds G o D dr haa hrsaso MJ ollg ad S Ko w Yor: Joh Wly & Sos I Sass aada aalogu o -00-XIE

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21 Survy Mhodology Ju Vol 3 o 3- Sass aada aalogu o -00-XIE Th Eff of Rord Lag Errors o Rs Esas ohor Moraly Suds D Krws Dwa Y Wag S arl JM Zls ad R Mall bsra Th adv of ourzd rord lag hodology has falad h odu of ohor oraly suds whh osur daa o daabas ar lroally ld wh oraly daa fro aohr daabas Ths howvr rodus lag rrors du o sahg a dvdual fro o daabas wh a dffr dvdual fro h ohr daabas I hs arl h a of lag rrors o sas of dologal daors of rs suh as sadardzd oraly raos ad rlav rs rgrsso odl arars s lord I s show ha h obsrvd ad d ubr of dahs ar affd oos dro ad as a rsul hs daors a b sub o bas ad addoal varably h rs of lag rrors Ky Words: ohor sudy; ourzd rord lag; Lag rrors; Lag hrshold wgh; osso rgrsso; Rlav rs rgrsso; Sadardzd oraly rao Iroduo I r yars a ubr of hsoral ohor suds hav b arrd ou vroal dology usg sg adsrav daabass as forao sours (How ad Sasoff 986; arr ad Far 990 I gral rs hs volvs lg rords of hua osur o vroal hazards wh rords o halh saus of usg ourzd hods for ahg dvdual rords fro dffr daabass I a ohor oraly sudy h val saus of ah ohor br s drd by lag wh oraly rords aad by govr ags Ess oraly wh h ohor rlav o h gral oulao ay b du o osurs rd by h ohor brs I sf rs rord lag s h ross of brgg oghr wo or or saraly rordd s of forao rag o h sa y (arl Krws Wag ad Zls 993 rodurs for ourzd rord lag (RL hav bo hghly rfd usg sohsad algorhs o valua h llhood of a orr ah bw wo rords (Hll 988; wob 988 Sass aada has dvlod a RL sys alld LIK whh s aabl of hadlg boh sgl fl lags ad lags bw wo sara fls (How ad Ldsay 98; Sh ad Sls 98 I hs sys wghs rflg h llhood of a ah ar aahd o ars of rords Two hrsholds ar s: oal ahs wh lag wghs abov h ur hrshold ar osdrd o b ls whras oal ahs wh wghs blow h lowr hrshold ar osdrd o b ols oal ahs wh wghs bw h ur ad lowr hrsholds ar rsolvd usg addoal forao wh avalabl Ohrws a sgl hrshold s sld o dsra bw ls ad ols Th ofdaly of rords rod udr h Sass s srly aad ay sudy whh rord lag s loyd ll suds rqurg lag wh rod daa bass us sasfy a rgorous rvw ad aroval ross ror o lao followg wllsablshd rodurs for daa ofdaly (Sgh Fdr Dua ad Yu 00 ll ld fls wh dfyg forao ra h usody of Sass aada (Labossèr 986 ourzd rord lag hods hav b usd o l vroal osur daa o h aada Moraly Daa as (MD For al a sudy of aada far oraors was ad o vsga ossbl rlaoshs bw auss of dah ovr far oraors aada ad varous soo-dograh ad farg varabls arularly sd us (Jorda-Sso Far ad olqu 990 I hs sudy h MD was ld wh h 97 sus of oulao ad h 97 sus of grulur ohr ogog larg-sal sudy s basd o h aoal Dos Rgsry (DR of aada (shor ad Groga 985 shor ad Davs 989 Th DR D Krws MLaughl r for oulao Halh Rs ssss Uvrsy of Oawa Oawa Oaro aada K 65 Shool of Mahas & Sass arlo Uvrsy Oawa Oaro aada KS 56 To who orrsod should b addrssd; Dwa ld Sass U Ida Sasal Isu Kolaa Ida; Y Wag Halhy Evros ad osur Safy rah Halh aada Oawa Oaro aada K 0L; S arl Halhy Evros ad osur Safy rah Halh aada Oawa Oaro aada K 0L; JM Zls Halhy Evros ad osur Safy rah Halh aada Oawa Oaro aada K 0L; R Mall MLaughl r for oulao Halh Rs ssss Uvrsy of Oawa Oawa Oaro aada K 65 Shool of Mahas & Sass arlo Uvrsy Oawa Oaro aada KS 56

22 4 Krws Dwa Wag arl Zls ad Mall: Th Eff of Rord Lag Errors o Rs Esas oas forao o ouaoal osurs o ozg radao rd by ovr aadas dag ba o 950 Th DR has rly b ld o h MD o vsga assoaos bw ss oraly du o ar ad ouaoal osur o low lvls of ozg radao (shor Krws ad Zls 997; shor Krws Zls Jag Sw ad Léourau 998 Mor rly h DR has b ld o h aada ar Id Daabas (So Zls shor Jag Krws Far ad ad Léourau 00 orhsv ls of ohr halh suds basd o lg osur daa wh h MD has b old by Far (989 Th suss of rord lag suds dds o h qualy of daabass bg ld (Roos Sood ad Jbaa 00 Usg oulao basd logudal adsrav daa Roos al ad daa qualy ssus suds of halh ad halh ar rdal ad Es (00 osdrd sysa rrors adsrav daabass volvd sodary aalyss of halh forao lhough rord lag suds wll bf fro h us hgh qualy daa laos daa qualy ay b offs o a ra by h larg sal szs foud ay adsrav daa bass Rord lag suds hav svral advaags ovr radoal dologal suds y usg sg adsrav daabass h d o oll w daa for halh suds s ruvd ad larg sal szs a of b ahvd wh rlavly ll ffor Ddg o h aur of h daabass ulzd rord lag rovds a sv way of lorg ay ossbl assoaos dologal suds Rord lag also has ra dsadvaags Thr s grally ll orol ovr h forao olld ad hr a b arabl loss o follow-u ohr dsadvaag of rord lag s h ourr of lag rrors whh s h fous of hs ar Ivably so rords ha ah wll fal o b ld ad ohr oahg rords wll b orrly ld Rlavly ll wor has b do o dr h a of hs lag rrors o sasal frs r Mays ad Raaaha (965 usd a sl lar rgrsso odl o aalyz h a of rrors rodud durg h ahg ross Thr rsuls da ha lag rrors fla h rsdual vara ad rodu bas o h sad slo arar Wlr ad Shur (99 drvd a rsso for h bas sas of lar rgrsso offs du o lag rrors dvas h sao of lag rror ras by l ad Rub (99 abld Shur ad Wlr (993 o l a rovd bas adus rodur Lar rgrsso hods for h aalyss of our ahd daa fls ar furhr dsussd by Shur ad Wlr (997 Th uros of hs ar s o lor h a of lag rrors o sasal frs ohor oraly suds Rlav rs rgrsso odls loyd h aalyss of daa fro suh suds ar dsrbd so ad rssos for h obsrvd ad d ubrs of dahs basd o hs odls dvlod Th a of lag rrors o h obsrvd ad d ubr of dahs ad rso-yars a rs s dsussd so 3 aalyss of h a of lag rrors o sas of sadardzd oraly raos (SMRs ad rlav rs rgrsso arars s gv so 4 oh ys of rrors a aus bas ad addoal varably sas of hs arars Our olusos ar rsd so 5 Rlav Rs Rgrsso Modls Sasal hods for h aalyss of ohor oraly suds ar wll sablshd (rslow ad Day 987 Th rary obv of suh aalyss s o dr f h osur o h ag of rs rass h oraly ra aog ohor brs Moraly s hararzd by h hazard fuo whh sfs h dah ra as a fuo of Lg T do h of dah h hazard fuo a u s forally dfd as r{ u T < u Δu T u} λ ( u l Δ u 0 Δu L λ (u do h hazard fuo for a sf aus of dah a u for dvdual a ohor of sz ad l z (u rrs a orrsodg vor of ovaras sf o ha dvdual W assu ha h ff of hs ovaras s o odfy h basl hazard λ *( u aorda wh h rlav rs rgrsso odl ( λ ( u λ* ( u γ{ β z ( u} ( whr γ s a osv fuo of h ovaras ad β s a vor of rgrsso arars Two sal ass of h gral rlav rs rgrsso odl of arular rs ar h ullav ad addv rs rgrsso odls Df h fuo γ ( by ( z ρ log γ ( z (3 ρ Wh ρ h gral rlav rs rgrsso odl rdus o b h ullav rs rgrsso odl λ ( u λ* ( u{ β z ( u} (4 Sass aada aalogu o -00-XIE

23 Survy Mhodology Ju Ths rooroal hazards odl was rodud by o (97 ad s wdly usd h aalyss of oraly daa (Kalbflsh ad r 980 Th addv rs rgrsso odl λ ( * u λ ( u β z ( u (5 ours as a lg as as ρ 0 L 0 ad b h ag a h of ry o h sudy ad h ag a h of loss o follow-u (du o whdrawal fro h sudy rao of h sudy or dah for h h sub of h ohor rsvly L δ or 0 aordg o whhr h h dvdual has or has o dd a h of loss o follow-u Th logllhood fuo basd o h rlav rs odl ( ay b wr as δ log( γ{ β z ( } log L (6 * γ{ β ( } λ ( 0 z u u du Wh hr s a sgl ovara z ( u h au llhood sa of θ {β} rdus o h sadardzd oraly rao SMR OS/EX whr OS δ ad EX ar h obsrvd ad d ubrs of dahs rsvly wh * 0 λ ( u du Mazao of h llhood fuo (6 a b ouaoally burdso wh larg sal szs rslow Lub ad Lagholz (983 slfy h llhood by assug ha h ovaras a o osa valus wh sas hrough whh a sub asss durg h ours of h sudy Th sas ar dfd by rosslassfao of h ovaras of rs Sfally suos ha hr ar J suh sas { S ; J } suh ha z ( u z whvr h h sub s S a u Ths sas ar uually lusv ad hausv so ha a ay gv u ah br of h ohor wll fall o o ad oly o sa Th log-llhood fuo (6 ay h b wr as whr log L { d J log( γ{ β z } γ{ β z * λ ( u du [ z ( u S ] } } s h orbuo o h d ubr of dahs fro all rso-yars of obsrvao h sa S ad d dos h oal ubr of dahs ha sa Lg Λ ( β log( γ{ β z } h au llhood sa βˆ of β s obad as h soluo o h sor quao log L J Λ ( ˆ β { d { Λ ( βˆ } } 0 (9 β β (7 (8 3 Th Eff of Lag Errors o h Obsrvd ad Ed ubrs of Dahs Two ral ys of rrors a our wh lg daa fls RL (Fllg ad Sur 969 fals osv ours wh a br of h ohor who s alv s orrly dfd as dad ad a fals gav ours wh a dasd br s osdrd o b alv Mor sfally for h ahaal dvlo o follow a fals osv ours a arular sa wh a dvdual who ras alv hroughou hs sa s orrly lablld as dad hs sa Slarly a fals gav ours a arular sa wh a br who dd bfor or durg h soour hs sa s osdrd o b alv hroughou hs sa Wh a arular sa fals osvs ad fals gavs hus rrs sal ass of slassfao rror dsussd by drso (974 har 6 I hs so w wll dsuss h ff of hs wo ys of lag rrors o h obsrvd ad d ubrs of dahs rsvly To do hs w frs df ss of ds wh sas whh wll b usd o rrs ss of orrly ahd ad orrly ahd rords 3 Lag Errors L ad D do h s of labls for hos dvduals h ohor who ra alv hroughou sa S ad hos who ar dad S rsvly Wr D as h subs of D orrsodg o hos dvduals who hav dd S L L D L ad D L do h orrsodg ss h rs of lag rrors W furhr df D as h s of labls of hos alv S (ha s bu labld as dad S orrsodg o h fals osvs S Slarly s h s of hos dad S (ha s D bu labld as alv S orrsodg o h fals gavs S L us also wr D as h subs of D orrsodg o hos who ar labld o hav dd S ad slary as h subs of who hav dd S (ha s D Ths ss sasfy h rlaos L L ( D D ( D D ad D L ( D D Th ff of lag rrors o h llhood fuo (7 ay b dsrbd as follows L 0 do h a whh h h dvdual rs aually or by lag rror h h sa S Slarly dos h of dah (f ours aually or by lag rror for h h dvdual S ad h of lavg S aually or by lag rror o ha f ss s lss ha or qual o L us for h sa of sly assu ha f ss s 0 qual o ; ha s all h dahs a sa our a h orrsodg ry s ha sa lhough hs wll udrsa h d ubr of dahs for h Sass aada aalogu o -00-XIE

24 6 Krws Dwa Wag arl Zls ad Mall: Th Eff of Rord Lag Errors o Rs Esas uros of sudyg bas ay o b ha oboabl ssug all h dahs o our a h s of lavg h orrsodg sas also offrs slar slfao Usg (8 ad h dooso of L h d ubr of dahs L S h rs of lag rrors a b wr as whr wh L L 0 0 Δ * λ ( u du * λ ( u du * λ 0 * λ 0 D ( u du ( u du (0 * λ ( u du ad Δ 0 ( * * λ ( u du ad λ ( u du ( 0 0 D For oaoal ov l us wr T λ ( for * 0 λ ( u du wha follows Th r Δ rrss h bas h d ubr of dahs h h sa du o lag rrors I follows fro (0 ad ( ha h fals osvs d o rdu h d ubr of dahs ad h fals gavs d o ras h d ubr of dahs Usg h dooso for D L h obsrvd ubr of dahs d L h rs of lag rrors ay b wr as d L d Δ d (3 whr Δ d d a (4 wh d d ad a dog h ubr of dvduals h ss D D ad rsvly Th r Δ d rrss h dffr bw h obsrvd ubr of dahs h h sa du o lag rrors I follows fro (3 ad (4 ha h fals osvs wll ras h obsrvd ubr of dahs ad h fals gavs wll rdu h obsrvd ubr of dahs Val saus s of drd by lag wh h MD whh s grally uh largr ha h ohor of rs Wh h osur rords of a lv dvdual ar orrly assoad wh hos of a dad rso h dasd dvdual usually dos o blog o h ohor Thus h rso-yars a rs orbud by h rso rag alv wll d raurly h yar of rsud dah; h los rso-yars a rs orrsod o h rod fro h yar of rsud dah ul h d of h follow-u O h ohr had wh h osur rords of a dad dvdual ar orrly assoad wh hos of a lv rso h rso-yars a rs orbud by hs dvdual wll lud a ra rod fro h aual dah-yar o h d of h follow-u Thus fals osvs wll dfla h ubr of rso-yars a rs ad fals gavs wll fla h ubr of rso-yars a rs h ohor 3 Eaos ad Varas of Dffrs w h Obsrvd ad Ed ubrs of Dahs Th ff of lag rrors o h obsrvd ad d ubrs of dahs dds o h fals osv ad fals gav ras L ad do h fals osv ad fals gav ras rsvly S for J whh ar assud o b osa wh S ad sa for all h dvduals ad D rsvly Ths assuo s rasoabl whvr dvduals h sa sa ar hghly hoogous arularly wh rs o arbus suh as h qualy of rsoal dfrs ha flu lag rror ras lhough hs dalzd assuo s ully o b fully sasfd ra affords osdrabl slfao h subsqu valuao of h ffs of lag rrors Forally ( s h odoal robably ha a dvdual ( D s labld dad (alv S Tha s [ D ] ad [ D ] L us wr a d a ad d as h ubr of dvduals D ad D rsvly Th o ha d follows a oal ( a dsrbuo ad a follows a oal ( d dsrbuo lso d follows a oal ( a dsrbuo whr s h odoal robably ha a dvdual s labld o hav dd S Tha s [ D ] larly Slarly a follows a oal ( d dsrbuo whr s h odoal robably ha a dvdual D s labld as alv S Tha s [ D ] lhough hr s o rval rlaosh bw ad gral s rasoabl o assu hs o of lag rrors ssug ha lag rrors rlad o dffr dvduals ar dd h ao ad vara of h dffr h obsrvd ubr of dahs S gv by Δ d (4 ar E[ Δ d ] E[ d ] E[ a ] a d (5 ad V [ Δ d ] V [ d a ] V [ a ] ( d ( (6 Sass aada aalogu o -00-XIE

25 Survy Mhodology Ju S ad D oss of dffr ss of dvduals d ad a ar dd Slarly h ao ad vara of h dffr h d ubr of dahs S gv by Δ ( a b alulad as follows For hs uros s ov o wr ad rs of h followg daor varabls For df ξ { I D } ad { ξ I D } lso for D df ψ I{ } Th fro ( ad h dfos of D ad w hav ad ξ T ( (7 λ ψ T ( (8 D I arular o a wr d ξ ad a D ψ whh ar usful o drv (5 ad (6 Fro (7 ad (8 w hav ad E[ Δ V [ Δ ] E[ ] E[ ] V [ λ ] λ T ( D ] V [ ( ( ] T D λ T ( λ ( T λ ( (9 (0 s ad D oss of dffr ss of dvduals Th rsuls (5 (6 ad (9 (0 da ha rord lag rrors wll lad o bas ad addoal varao h obsrvd ad d ubr of dahs Mzg h vara rs (6 ad (0 s dfful s h wo rror ras ad ar o fuoally dd Grally drasg wll rsul a ras ad v vrsa (s so 5 for furhr dsusso of hs o lhough hs rror ras ar dd of h udrlyg rlav rs rgrsso odl γ ( h a squar rror obad by obg h ao ad vara rs ao b zd whou sfao of h basl hazard λ *( u whh aars T λ 4 Th Eff of Lag Errors o Esas of SMRs ad Rgrsso offs 4 Sadardzd Moraly Raos To dr h ff of lag rrors o h SMR w rla h aual obsrvd ad d ubrs of dahs d ad by h obsrvd ad d ubr of dahs d L ad L h rs of lag rrors h rsso SMR d / Lg SMR L do h sadardzd oraly raos h rs of lag rrors w hav Δ d Δ SMR L SMR ( d I follows fro (0 (4 ha h fals osvs wll ras h SMR whras h fals gavs wll dras h SMR y usg a frs ordr Taylor srs aroao of SMR L abou SMR h dffr ΔSMR SMR L SMR a b rssd as ΔSMR SMR Δ d d Δ ( Th h a ad vara of h rlav dffr h SMR a b aroad by ad E Δ d Δ SMR [ ] [ ] E SMR ΔSMR ~ V SMR d ~ V d V Δ d Δ d ov Δ d E Δ Δ (3 (4 rsvly Th rgh had sd of (3 a b asly alulad by usg (5 ad (9 I ordr o alula h rgh had sd of (4 o ha V Δ d V [ Δ d < ] ov[ Δ d Δd ] (5 Δ V [ Δ ] ov[ Δ Δ ] (6 < V ad ov Δ d ov[ Δ d Δ Δ ] ov[ Δ d Δ ] (7 Sass aada aalogu o -00-XIE

26 8 Krws Dwa Wag arl Zls ad Mall: Th Eff of Rord Lag Errors o Rs Esas Whou loss of graly l us assu for < ha 0 0 for h sa dvdual (alv or dad S ad S ; ha s h ry S s h sa or arlr ha ha S W h hav for < ov[ Δ d Δ d ] (8 D ov[ Δ ov[ Δ d Δ D D D ov[ Δd Δ ] D ( T ( Δ ] D ] D D ov[ Δd λ T ( T ( λ T λ ( ( Δ ( T λ ] ( T λ λ ( ( T T T T ( λ λ λ ( D λ T ( λ ( ( (9 ( ( ad T T λ λ ( ( (30 (3 (3 Usg (5 (3 h vara of h rlav dffr Δ SMR/SMR a b aroad by h rgh had sd of (4 Two olusos a b draw fro (3 ad (4 Frs lag rrors a lad o bas h sa of h SMR Sod boh ys of lag rrors rodu addoal varao o sas of h SMR o ha h frs r (3 s doad by h frs r (9 for < 05 ad h gav ovara r (8 s doad h alulao of h vara (5 Thrfor h addoal vara (4 s srly osv s boh h fals osv ad fals gav ras ar osv 4 Rlav Rs Rgrsso arars To dr h ff of lag rrors o rgrsso arar sas osdr frs h gral rlav rs rgrsso odl ( Rlag h obsrvd ad d ubrs of dahs d ad h log-llhood fuo (7 wh h obsrvd ad d ubrs of dahs h rs of lag rrors d ad w hav log L J L L { d L log( γ{ β z } γ{ β z } } (33 L βˆ ad β ~ do h au llhood sas of β basd o { d } ad { d L L } rsvly Th sor quao ~ (9 a b wr as J Λ ( β β [ d Δ { Λ ( β ~ d }( Δ ] 0 (34 ~ ssug ha Δβ β βˆ s sall a frs ordr aso ~ of { Λ ( β} aroud βˆ gvs ˆ ( ~ Λ { } ~ { ˆ } { ˆ Λ β Λ Λ } Δβ (35 β whr Λˆ Λ ( βˆ ad Λˆ / β s Λ / β valuad a β ˆβ Subsug (35 o (34 lads o J Λˆ [ d { Λˆ } ] β J Λˆ β Δ d γ{ β ˆ z } Δ ˆ { ˆ Λ γ β z } ~ Δβ 0 (36 β ˆ { ˆ Λ γ β z } Δ Δβ β Usg (9 h frs suao (36 s zro osquly s Δ Δβ s sall Δ β ay b aroad by Λˆ ˆ Λ ~ { ˆ Δβ } γ β z β β Λˆ { Δd { ˆ γ β z } Δ } (37 β I follows fro (37 ha ~ Λ [ ] { ˆ Λ Λ E Δβ } γ β z α (38 β β β whr α E[ Δd ] γ{ˆ β z } E[ Δ ] whh a b alulad fro (5 ad (9 Furhr ~ Λ Λ [ ] { ˆ V Δβ γ β z } β β Λ Λ Θ β β Λ Λ { ˆ γ β z } (39 β β wh L Sass aada aalogu o -00-XIE