A Monte Carlo method to estimate the confidence intervals for the concentration index using aggregated population register data

A Mon e Ca lo me hod o es ima e he con idence in e als o he concen a ion index using agg ega ed popula ion egis e da a Sonja Lumme •Reijo Sund •Alas ai H. Leyland •Ilmo Keskima ¨ki Recei ed: 2 Ap il 2014 / Re ised: 19 Janua y 2015 / Accep ed: 5 Feb ua y 2015 / Published online: 18 Feb ua y 2015 The Au ho (s) 2015. This a icle is published wi h open access a Sp inge link.com Abs ac In his pape , we in oduce se e al s a is ical me hods o e alua e he unce - ain y in he concen a ion index (C) o measu ing socioeconomic equali y in heal h and heal h ca e using agg ega ed o al popula ion egis e da a. The Cis a widely used index when measu ing socioeconomic inequali y, bu p e ious s udies ha e mainly ocused on de eloping s a is ical in e ence o sampled da a om popula ion su eys. While da a om la ge popula ion-based o na ional egis e s p o ide comple e co e age, egis a ion comp ises se e al sou ces o e o . We simula e con idence in e als o he Cwi h di - e en Mon e Ca lo app oaches, which ake in o accoun he na u e o he popula ion da a. As an empi ical example, we ha e an ex ensi e da ase om he Finnish cause-o -dea h egis e on mo ali y amenable o heal h ca e in e en ions be ween 1996 and 2008. Amenable mo ali y has been o en used as a ool o cap u e he e ec i eness o heal h ca e. Thus, inequali y in amenable mo ali y p o ides e idence on weaknesses in heal h ca e pe o mance be ween socioeconomic g oups. Ou s udy shows using se e al ap- p oaches wi h di e en pa ame ic assump ions ha p e iously in oduced me hods o S. Lumme (&)I. Keskima ¨ki The Social and Heal h Sys ems Resea ch Uni , The Depa men o Heal h and Social Ca e Sys ems, The Na ional Ins i u e o Heal h and Wel a e (THL), P.O. Box 30, 00271 Helsinki, Finland e-mail: [email p o ec ed] I. Keskima ¨ki e-mail: [email p o ec ed] R. Sund Depa men o Social Resea ch, Facul y o Social Sciences, Cen e o Quan i a i e Me hods, Uni e si y o Helsinki, P.O. Box 33, 00014 Helsinki, Finland e-mail: [email p o ec ed] A. H. Leyland MRC/CSO Social and Public Heal h Sciences Uni , Uni e si y o Glasgow, 200 Ren ield S ee , Glasgow G2 3QB, Sco land, UK e-mail: [email p o ec ed] I. Keskima ¨ki School o Heal h Sciences, Uni e si y o Tampe e, Tampe e 33014, Finland 123 Heal h Se Ou comes Res Me hod (2015) 15:82–98 DOI 10.1007/s10742-015-0137-1 es ima e he unce ain y o he C o sampled da a a e oo conse a i e o agg ega ed popula ion egis e da a. Consequen ly, we ecommend ha inequali y indices based on he egis e da a should be p esen ed oge he wi h an app oxima ion o he unce ain y and sugges using a simula ion app oach we p opose. The app oach can also be adap ed o o he measu es o equali y in heal h. Keywo ds Mon e Ca lo simula ion Heal h and heal h ca e egis e da a Equali y  Concen a ion index Con idence in e al Amenable mo ali y 1 Backg ound A majo heal h policy goal in many coun ies is o educe dispa i ies in heal h and in access o and he quali y o heal h ca e. Measu ing hese dispa i ies is a challenge. In o de o ob ain ex ensi e and p ecise knowledge o inequali ies, comp ehensi e me hods o s udy equali y a e necessa y. Mos s udies o equali y in heal h and heal h ca e, and mos me hodological pape s, ha e ocused on su ey da a. Regis e -based da a p o ide ano he possible sou ce o da a o equali y s udies. So a , good-quali y indi idual-le el admin- is a i e da a including in o ma ion on socioeconomic s a us ha e been a ailable only in a ew coun ies, such as he No dic coun ies, bu he impo ance o such da a is likely o inc ease as be e in o ma ion sys ems inc easingly become a ailable and changes in da a p i acy egula ions will enable b oade u iliza ion o he indi idual-le el da a in o he coun ies. Regis e -based da a a e ypically seconda y da a, i.e., hey ha e no been col- lec ed o he pu poses o speci ic s udies (Sund 2003). Ano he , possibly e en mo e impo an , di e ence is ha egis e -based da a o en con ain o al popula ions ins ead o samples. In o he wo ds, i may be in alid o use s a is ical me hods ha assume sampling a ia ion is he sou ce o unce ain y when measu ing he phenomenon o in e es . Fo example, when es ima ing he unce ain y o he measu ed indica o om sample da a, only sampling e o is adi ionally aken in o accoun . O he possible sou ces o unce ain y a e igno ed. When using o al popula ion da a, such sampling e o does no exis . I is, howe e , ob ious ha o he sou ces o e o exis , since many e en s such as dea hs a e assumed o be s ochas ic and consequen ly p oduce a na u al a iabili y in i al s a is ics (B illinge 1986). In addi ion, people in he egis e a one pa icula ime could be seen as a sample o a supe -popula ion, and eco ded e en s on hese people can be conside ed o be one o a se ies o possible esul s ha could ha e occu ed unde he same ci cum- s ances (Cu in and Klein 1995). I is, howe e , a complica ed ask o assess he unce ain y in he indica o o in e es using popula ion-based da a (Sø ensen e al. 1996). The e a e mul iple sou ces o e o s ha can a ec he unce ain y, and he sou ces e iden ly a y be ween si ua ions (Sund 2003). The quali y o he da a is he main in luence on unce ain y. E o s in he da a may ha e o igina ed a he s age o egis a ion due o a ying p ac ices and accu acy in he p ocesses. Me ging di e en da abases, da a handling ( o example h ough agg ega ion o he da a), o p ocessing e o s may o m challenges. De e io a ion o he da a quali y is possible also la e in he analysis phase as a esul o mis akes in a iable coding o p og amming e o s. In addi ion o da a quali y, o he sou ces may in oduce unce ain y in o he indica o such as he de ini ion o he a iables o coding p ac ices. Wha i he a iable is eco ded co ec ly, bu does no desc ibe he phenomenon unde examina ion Heal h Se Ou comes Res Me hod (2015) 15:82–98 83 123 o all indi iduals p ope ly? The unce ain y is commonly quan i ied using a con idence in e al which p o ides a means o assessing and epo ing he unce ain y and is in u- i i ely s aigh o wa d o in e p e . The concen a ion index (C) is a widely used indica o o he quan i ica ion o so- cioeconomic equali y in heal h and in he use o heal h ca e (e.g., an Doo slae e al. 1997; Wags a 2000; Vikum e al. 2012). The Cgi es comp ehensi e summa y in o ma ion abou he whole dis ibu ion o he s udied ou come in a single alue, which is a pa icula ad an age when making compa isons in ime o be ween gende s, a eas, coun ies, o hospi als. In addi ion, i has he bene i ha he le el o he inequali y can be isualized wi h he concen a ion cu e. This pape is abou he me hodology o he concen a ion index when measu ing so- cioeconomic equali y in heal h and heal h ca e using agg ega ed egis e da a. The mea- su ed heal h o heal h ca e a iable can be, o example, dea hs, hospi aliza ions, o ce ain p ocedu es. In his con ex , he e m ‘‘agg ega ed da a’’ is aken o mean da a ha a e o iginally indi idual le el and a e la e g ouped by income. Assessmen o he egis e - based es ima es in ol es he abo e-men ioned unce ain ies. Thus, we in oduce se e al echniques o e alua e unce ain y by calcula ing con idence in e als o he Cusing empi ical da a, as he majo i y o he p e ious s udies using and de eloping he me hod- ology o he Cha e ocused on su ey da a o hypo he ical da a, which equi e di e en me hods ( o example, see Kakwani e al. 1997; Wa e s 2000; Bu s o ¨m e al. 2005; an Ou i 2004; Wags a 2005; an Doo slae e al. 2006; Chen and Roy 2009; Cla ke and an Ou i 2010; Konings e al. 2010; Chen e al. 2012). In many o hese pape s, he unce ain y in he Chas no been assessed, bu Kakwani e al. (1997), an Ou i (2004), Chen and Roy (2009), Konings e al. (2010), and Chen e al. (2012) used imp o ed me hods o es ima e he unce ain y. The unce ain y in he indica o is an essen ial ques ion, pa icula ly when making compa isons o equali y. Ou app oaches o es ima e he unce ain y in he Ca e based on se e al Mon e Ca lo simula ions. Simula ion has p e iously been shown o be an e ec i e me hod o he Cas well as o he inequali y indices using su ey da a (Chen e al. 2012; Mills and Zand akili 1997; Se gean and Fi h 2006; Moda es and Gas wi h 2006; an Ou i and Cla ke 2011). We demons a e he esul s o his s udy empi ically using an ex ensi e Finnish agg ega ed egis e da ase on amenable mo ali y. We compa e ou esul s o he commonly used s anda d eg ession me hod and he imp o ed me hod de- eloped by Kakwani e al. (1997). 2 Me hods The concen a ion index (C) can be used o measu e he deg ee o socioeconomic inequali y in heal h and heal h ca e ac oss he dis ibu ion o he whole s udy popula ion (Wags a e al. 1989). The index is based on he Gini coe icien , which is used o assess inequali y in income o weal h. The Cis based on he concen a ion cu e L(s), which is a ool o isualize he deg ee o inequali y. When using agg ega ed da a, L(s) plo s he cumula i e p opo ion o he heal h ou come a iable agains he cumula i e p opo ion o he popula ion (s), anked by socioeconomic g oup (SEG) om he leas o he mos ad an aged. The Cis de ined as wice he a ea be ween he diagonal and L(s). In a case o comple e equali y, he Cge s a alue o 0. Nega i e alues indica e a disp opo iona e concen a ion o he heal h ou come among hose classed as disad an aged and ice e sa. The Cis es ic ed o alues be ween -1 and 1 when he heal h a iable is no bina y (Wags a 2005). 84 Heal h Se Ou comes Res Me hod (2015) 15:82–98 123 Fo agg ega ed da a—in which he g oups comp ise SEGs and he socioeconomic indica o is measu ed on an o dinal scale— he quan i a i e measu e o inequali y can be es ima ed as C¼2 yX G g¼1 yg gRg1ð1Þ whe e y g is he heal h ou come (such as he annual mo ali y a e) o he g h SEG, and yis he mean o he y g ac oss SEGs weigh ed by he popula ion sha e g . The R g is he ela i e ank o he SEG, de ined as R g =P c=1 g-1 c ?0.5 g and indica es he cumula i e p o- po ion o he popula ion up o he midpoin o each g oup in e al. In his s udy, y g deno es he di ec ly age-s anda dized amenable mo ali y a e (pe 100,000 pe son-yea s) o he g h income g oup: yg¼PI i¼1 dig pigwi;whe e iis he age g oup, d ig is he numbe o dea hs and p ig is he popula ion size in he i h age g oup o he g h SEG, w i is he weigh o he age g oup acco ding o he s anda d popula ion. The sum o he s anda d popula ion is 100,000, i.e., P i=1 I w i =100,000. The Chas also been es ima ed using a weigh ed leas squa es me hod (WLS) (Le man and Yi zhaki 1984; Wags a e al. 1991). The use o agg ega ed da a necessi a es he use o weigh s. The slope pa ame e b 1 o he eg ession model has a compu a ional equi a- lence wi h he Cand is ob ained om he WLS model 2 2 R yg yffiffiffiffiffi pg p¼b0ffiffiffiffiffi pg pþb1Rgffiffiffiffiffi pg pþeg;ð2Þ whe e p g is he popula ion size in he g h SEG. The size o he weigh indica es he powe o he in o ma ion con ained in he associa ed obse a ion. Thus, i SEGs a e o equal size, he weigh s do no ha e any e ec since each g oup has equal in luence on he inal es ima e. The a iance R 2 is he weigh ed a iance o he ank R g , de ined as R 2 = P g=1 G g (R g -0.5) 2 . This con enien eg ession me hod gi es he C, i espec i e o whe he he p incipal model assump ions apply, because he eg ession me hod is an a i icial echnique o calcula e he C(Kakwani e al. 1997). Thus, he possible se ial co ela ion esul ing om he anked na u e o he independen a iable ( ank is o de ed and cumula i e) does no a ec he es ima ed eg ession coe icien . In addi ion, i is impo an o no e ha a linea ela ionship be ween he dependen a iable and he ank is no necessa y due o he a i icial na u e o his es ima ion. Bo h models (1) and (2) can be applied o popula ion o sample da a o calcula e he C. The s anda d e o o he eg ession slope in he WLS model (2) desc ibes he a i- abili y o he es ima e a ound he unknown slope pa ame e b 1 . Howe e , in o de o cons uc a con idence in e al o he b 1 using o mula (2), he key WLS eg ession assump ions should no be iola ed. The independence o e o s may be iola ed due o he abo e-men ioned se ial co ela ion causing ei he unde - o o e es ima ed s anda d e o s. The e o e ms, e.g., in he eg ession, ei he ha e o be no mally dis ibu ed and inde- penden , o he numbe o obse a ions in he eg ession has o be su icien ly la ge. Usually, when s udying equali y, he numbe o SEGs is ela i ely low (5–20); hus, he la e assump ion is unlikely o be me . Due o i s simplici y, using his eg ession me hod in s a is ical packages appea s o be a con en ional means o ob aining con idence in e als also o he C(deno ed as REG in his s udy). Kakwani e al. (1997) de eloped es ima o s o he s anda d e o o he C, which ake in o accoun he se ial co ela ion in he da a applicable o da a d awn om a sample. We deno e his echnique as KWV in his s udy. Heal h Se Ou comes Res Me hod (2015) 15:82–98 85 123 In his s udy, we in oduce i e di e en Mon e Ca lo simula ion echniques o es ima e he con idence in e al o he Cusing income as a socioeconomic indica o . These simula ion echniques di e om each o he in dis ibu ional assump ions and in he phase o he simula ion p ocess; one echnique simula es he ou come a iable o he eg ession me hod (2), h ee o hem simula e obse ed e en s (d ig ), and one simula es obse ed age- adjus ed a es (y g ). As one o he echniques applies he eg ession me hod (2), he es o he simula ion echniques apply ei he he eg ession o he o mula me hod (1). Ou echniques can be applied o he da ase s whe e socioeconomic a iable is g ouped by p opo ions, o example income quin iles. The SEGs mus be de ined by he p opo - ions o he pe son yea s (o de ed by income). The numbe o pe son yea s in each income g oup can be assumed o be a he s able when using egis e da a due o la ge da ase s. Due o ixed p opo ions, he anking is ixed in all ou simula ion echniques when es ima ing he unce ain y ( he possible miscoding o he income eco d and heal h a i- able) and his allows modeling a ia ion only in he heal h ou come a iable. Conse- quen ly, e en hough he p opo ions in each income g oup a e ixed, he unce ain y in ol ed in eco ding income in o ma ion is inco po a ed in ou me hod. The biasing e ec o co ela ion be ween he ank and he ou come a iable is a oided in all ou app oaches because he s anda d e o is no es ima ed om he eg ession model; we simula e he o iginal da a o es ima e he unce ain y o he C. In addi ion, he ad- an age o ou app oaches is ha hey aim o model he assumed e o o he da a and he concen a ion cu e and no he e o o he slope pa ame e o he i ed eg ession line. One o hese simula ion echniques was de eloped in ou ecen s udy (Lumme e al. 2012) in which we made a simple assump ion o unce ain y a ound he dependen a iable 2 R 2 (y g /y g y) in Eq. (2). We deno e his echnique as MC in his s udy, and i can be applied only o he eg ession me hod (2) o es ima e he C. We accoun ed o ha unce ain y by assuming 2 2 R yg yNðlg; 2 gÞ, whe e he mean l g is he obse ed alue o 2 2 R yg y om he da ase and he a iance g 2 is he obse ed alue o 2 2 R yg yffiffiffiffi ng p  2 ;wi h n g being he numbe o e en s (such as amenable dea hs) in he g h income g oup. We hen e-es ima ed he Cby eplica ing he eg ession es ima ion 10,000 imes o accoun o he unce ain y. The lowe and uppe limi s o he 95 % con idence in e al o he Cwe e ob ained as he 2.5 and 97.5 pe cen iles o he dis ibu ion o he simula ed slopes. The median o he dis- ibu ion o he slopes is equal o he Ccalcula ed om he obse ed da ase , de e mined by se ing he obse ed alues o he dependen a iable in Eq. (2) as he expec ed alues in he simula ions. The p ope y ha he median o he dis ibu ion o he slopes is equal o he C esul s s aigh om he no mal dis ibu ion assump ion, since he median and he mean a e equal by de ini ion. This p oduces symme ical con idence in e als a ound he obse ed C. I he e is a eason o assume la ge e o s ( o example due o consis en miscoding o some a iable), he a iance g 2 can be enla ged by educing he ac o o he denomina o n g . This would indica e ewe e en s in an income g oup and hus assume mo e a ia ion. Changing he size o he dis u bance, howe e , would no change he median o he dis ibu ions (i.e., he C), bu na u ally i would enla ge he con idence in e als o he C. The second model (deno ed as MC a e) assumes ha he age-adjus ed a es ollow no mal dis ibu ions ygNðyg; y2 g ngÞ;, and bo h me hods (1) and (2) can be used o es ima e he con idence in e als. In he nex app oach, we made mo e assump ions and de eloped he MC echnique u he o model he unce ain y in mo e de ail. A equi emen o he independence o he 86 Heal h Se Ou comes Res Me hod (2015) 15:82–98 123 e o e ms is no needed because his me hod does no use e o s es ima ed om a eg ession. I epea s he es ima ion o he Cby allowing some a iabili y in he heal h ou come (e en s) by income g oups and also in he o al numbe o e en s. Bo h me hods (1) and (2) can be used o assess he C. We deno e his echnique as BIN. The a iabili y is app oxima ed om he obse ed da a wi h he ollowing assump ions and s eps such as: 1. The obse ed p ig ( he popula ion size), he denomina o o he a e, is held ixed in he simula ion. This is based on he assump ion ha he in o ma ion on age and pe son- yea s in he egis e s is pe ec . 2. The second assump ion conce ns he e en s ha a e ea ed as being andom. The numbe o e en s is allowed o a y due o ac ha he e is some e o in he coding o he e en s (such as causes o dea hs). The obse ed o al numbe o e en s in age g oup iis he sum o e income g oups P g=1 G d ig =D i . 3. The numbe o e en s is allowed o a y be ween income g oups wi hin he age g oup. This is pe mi ed because he income in o ma ion p esumably does no exac ly measu e he pe son’s eal weal h. I migh no desc ibe he eal weal h le el o a pe son since all asse s a e no eco ded in he adminis a i e egis e s. Income is ob ained om mul iple adminis a i e sou ces and, in addi ion, may a y conside ably e en o e a sho pe iod. Now, he numbe o e en s in g oup ig is simula ed assuming o ollow a binomial dis ibu ion d ig *B(D i ,q ig ). The denomina o D i is he same o all income g oups wi hin he same age g oup. P obabili ies q ig (wi h he cons ain s ha P g=1 G q ig =1 and 0 Bq ig B1) a e es ima ed om he obse ed da a qig ¼dig Di: 4. Simula ion s ep (3) is epea ed N imes; hus, Nis he numbe o simula ed da ase s. 5. Nex , Nse s o age-adjus ed a es a e calcula ed using he simula ed numbe o e en s, he obse ed pe son-yea s a isk om he o iginal da ase , and he weigh s om he o iginal s anda d popula ion. 6. Now, N alues o he Ca e calcula ed using me hods (1)o (2) om he simula ed da a yielding a dis ibu ion o he C. The 2.5 and 97.5 pe cen iles o his dis ibu ion comp ise he 95 % con idence in e als o he C. Binomial dis ibu ion may no be symme ic, bu wi h la ge nand no oo ex eme q ig , i is in p ac ice qui e o en e y symme ic. Thus, he median o he dis ibu ion o he slopes is likely e y close o he Ccalcula ed om he obse ed da a. To es he obus ness o he abo e-men ioned simula ion echniques o es ima e he con idence in e al o he C, we pe o med mo e analyses using di e en assump ions. The ou h model (deno ed POIS) is a simula ion app oach equi alen o BIN excep he numbe o e en s in he s ep (3) ollows a Poisson dis ibu ion d ig *Pois(k ig ) whe e he pa ame e k ig is he obse ed numbe o e en s in a g oup ig. Poisson dis ibu ion is asymme ical when he mean is small. Howe e , as he mean becomes la ge, he dis i- bu ion becomes mo e and mo e symme ic and app oaches no mal dis ibu ion. In he i h simula ion me hod (deno ed MN), he o al numbe o e en s wi hin age g oup D i is held ixed. The numbe o dea hs is, howe e , allowed o a y be ween income g oups wi hin each age g oup. The numbe o e en s is simula ed om a mul inomial dis ibu ion wi h pa ame e s D i and q, and mean E{X ig }=D i q ig wi h he cons ain ha P g=1 G X ig =D i . The p obabili ies q i ={q i1 ,…,q iG } (wi h cons ain s P g=1 G q ig =1 and 0 q ig B1) a e es ima ed om he obse ed da a qig ¼dig Di: Table 1p esen s all i e me hods and ela ed modelling assump ions. Heal h Se Ou comes Res Me hod (2015) 15:82–98 87 123 3 Empi ical example As an empi ical example, we used Finnish egis e da a on dea hs amenable o heal h ca e in e en ions. Moni o ing socioeconomic inequali ies in mo ali y amenable o heal h ca e in e en ions—which is used o measu e heal h sys em pe o mance based on ce ain p ema u e dea hs ha should no occu i heal h ca e wo ks e ec i ely and is imely— p o ides use ul in o ma ion on changes in di e en ials in heal h se ice u iliza ion and e ec i eness (Schwa z and Pamuk 2008). These amenable dea hs a e an indica ion o po en ial weaknesses in heal h ca e ha can hen unde go mo e in-dep h in es iga ion (Nol e and McKee 2004). Table 1 Assump ions o he simula ion me hods Me hod Va iable simula ed Modelling assump ions Popula ion assump ions Es ima ion o he C MC 2 2 R yg y2 2 R yg yNlg; 2 g  l g is he obse ed alue o 2 2 R yg y The eg ession me hod (2) g 2 is he obse ed alue o 2 2 g yg yffiffiffiffi ng p  n g is he numbe o e en s in he income g oup MC a e y g ygNy g; y2 g ng  y g is he obse ed a e o he e en The a i hme ic me hod (1)o he eg ession me hod (2) BIN d ig d ig *B(D i ,q ig )D is he obse ed numbe o e en s in age g oup i:P g=1 G d ig =D i Me hod (1)o (2) The popula ion size in g oup ig is held ixed q ig =d ig /D i The numbe o e en s is allowed o a y be ween income g oups wi hin he age g oup POIS d ig d ig *Pois(k ig )k ig is he obse ed numbe o e en s in g oup ig Me hod (1)o (2) MN d ig d ig ollows a mul inomial dis ibu ion wi h pa ame e s D, and qand mean E{X ig }=D i q ig wi h he cons ain ha P g=1 G X ig =D i The p obabili ies qi¼ qi1;...;qig  (wi h cons ain s P g=1 G q ig =1 and 0 q ig B1) a e es ima ed om he obse ed da a: q ig =d ig /D i Me hod (1)o (2) The numbe o e en s wi hin age g oup D i is held ixed The numbe o dea hs is allowed o a y be ween income g oups wi hin each age g oup 88 Heal h Se Ou comes Res Me hod (2015) 15:82–98 123 Table 2 Lis o causes o dea h conside ed amenable o heal h ca e and co esponding ICD-10 codes Place o in e en ion Cause o dea h Age ICD-10 P ima y heal h ca e Timing o in e en ion P ima y p e en ion In es inal in ec ions 1–14 A00–09 Diph he ia, Te anus, Poliomyeli is, and Va icella 1–74 A35–36, A80, B01 Whooping cough 1–14 A37 Measles 1–14 B05 Rubella 1–74 B06 Sca la ina 1–74 A38 Meningococcus 1–74 A39 E ysipelas 1–74 A46 Legionellosis 1–74 A48.1 Mala ia 1–74 B50–54 S ep ococcal pha yngi is 1–74 J02.0 Celluli is 1–74 L03 Ea ly de ec ion and ea men Tube culosis 1–74 A15–19, B90 Malignan neoplasm o colon and ec um 1–74 C18–21 Melanoma o skin 1–74 C43 Malignan neoplasm o skin 1–74 C44 Malignan neoplasm o b eas 1–74 C50 Malignan neoplasm o ce ix u e i 1–74 C53 Malignan neoplasm o ce ix u e i and body o u e us 1–44 C54–55 Malignan neoplasm o bladde 1–74 C67 Benign umo s 1–74 D10–36 Hype ensi e disease 1–74 I10–13.I15 Ce eb o ascula disease 1–74 I60–69 Imp o ed ea men and medical ca e Diseases o he hy oid 1–74 E00–07 Diabe es melli us 1–49 E10–14 Epilepsy 1–74 G40–41 All espi a o y diseases (excl. pneumonia/ in luenza) 1–14 J00–09, J20–99 As hma 15–49 J45–46 COPD 15–49 J40–44 Specialized heal h ca e Sep icemia 1–74 A40–41 Malignan neoplasm o es is 1–74 C62 Hodgkin’s disease 1–74 C81 Leukemia 1–44 C91–95 Rheuma ic and o he al ula hea disease 1–74 I01–09 In luenza 1–74 J09–11 Pneumonia 1–74 J12–18 Pep ic ulce 1–74 K25–28 Heal h Se Ou comes Res Me hod (2015) 15:82–98 89 123 Ou da ase comp ised all esiden Finnish ci izens aged 1–74 in 1996–2008. Fo his popula ion, we ecei ed yea ly in o ma ion on dea hs om an amenable cause including indi idual demog aphic and socioeconomic a iables such as income, age, and gende . Due o da a p o ec ion egula ions, all a iables we e ca ego ized. By means o unique iden i ica ion codes, he in o ma ion on mo ali y came om he cause-o -dea h egis e and he demog aphic a iables came om he annual indi idual-le el employmen s a is ics da abase. Bo h egis e s a e compiled and main ained by S a is ics Finland. As an indica o o socioeconomic s a us o s udy equali y, we had disposable amily ne income, adjus ed o amily size on he OECD equi alence scale (OECD 1982) and ca ego ized in o 20 income g oups acco ding o he Finnish income dis ibu ion, sepa a ely o each yea . The income eco d applied was o he yea be o e dea h. Age was g ouped om 1 o 4 yea s and hen in 5 yea age bands. The selec ion o causes o dea h conside ed amenable o heal h ca e ocuses on con- di ions o which e ec i e clinical in e en ions exis in people 75 yea s old and in his s udy was an adap a ion o classi ica ions by Page e al. (2006), Nol e and McKee (2008), and McCallum e al. (2013) (Table 2). Causes o dea h (as a main cause) we e coded acco ding o he 10 h Re ision o he In e na ional Classi ica ion o he Diseases (ICD). When age-s anda dized alues we e equi ed, we calcula ed annual amenable mo ali y a es (pe 100,000 pe son-yea s) o 20 income g oups in 1996–2008. The age- and in- come-speci ic a es, i.e., he numbe o amenable dea hs as a p opo ion o pe son-yea s in he ollow-up o he co esponding popula ion, we e di ec ly age-s anda dized o he Eu opean s anda d popula ion (Wa e house e al. 1976). We epea ed he simula ion app oaches 10,000 imes in ou analyses; hus, Nwas 10,000, which we ound o be a su icien numbe o uns, since adding mo e uns did no change he leng hs o he con idence in e als. The compu e ime wi h 10,000 epe i ions o one simula ion was negligible using a s anda d compu e sys em o all me hods. We used SAS (SAS Ins i u e Inc., Ca y, NC, USA) e sion 9.2 o analyze he da a. 4 Resul s 4.1 O e iew o da a In Finland in 1996, acco ding o ou de ini ion, he o al numbe o dea hs conside ed amenable o heal h ca e in e en ions was 4087, o which 52 % occu ed among men. The numbe o amenable dea hs dec eased e enly du ing he ollow-up (p alue o linea Table 2 con inued Place o in e en ion Cause o dea h Age ICD-10 Appendici is 1–74 K35–38 Abdominal he nia 1–74 K40–46 Choleli hiasis and cholecys i is 1–74 K80–81 Neph i is, neph osis, and neph opa hy 1–74 N00–09,N17–19, N25–27 Obs uc i e u opa hy and p os a ic hype plasia 1–74 N13,N20–21, N35, N40 Ma e nal dea h All O00–99 Congeni al ca dio ascula anomalies 1–74 Q20–28 90 Heal h Se Ou comes Res Me hod (2015) 15:82–98 123 Konings, P., Ha pe , S., Lynch, J., Hosseinpoo , A.R., Be k ens, D., Lo an , V., Gecko a, A., Speyb oeck, N.: Analysis o socioeconomic heal h inequali ies using he concen a ion index. In . J. Public Heal h 55, 71–74 (2010). doi:10.1007/s00038-009-0078-y Kuns AE: C oss-na ional compa isons o socio-economic di e ences in mo ali y. PhD hesis. 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