HMD Methods Protocol v6 - mortality.org

1 LastRevised:January26,2021(Version6)Meth o dsProto , , , e, enheim, ov, , , , ductiontoV6oftheMetho dsProto colThisversionoftheHumanMortalityDatabas eMetho dsProto col(Version6)intro ,anewmetho disimplementedtocalculatea0,themeanageat deathforchildrenwhodiedintheir ,inlowmortalityp opulations, (2015).Implementationofthismetho disdescrib ,birth-by-monthdatahaveb eencollectedandarenowusedtomoreaccuratel yestimatep opulationexp , ,thisassumptionresultsintheincorrectesti mationofp opulationexp osuresandinducesfalsecohorte ,thenonuniformdistributionofbirthshasb eenmostpronouncedattheb eginningandattheendofthe rstandsecondWorldWarsinmanyEurop dareprovidedinsection6andApp endixEb cumentgrewoutofaseriesofdiscussionsheldi nvariouslo cationsb veindividualslistedasauthorswrotetheorig inalversionand/orhaveactivelycontributed tosubsequentversions,includingthroughthe developmentofadditionalmetho.

2 January26,2021(Version6)TableofContents1 Intro 1deathcountsinto1 (January1st) eci ostcensalsurvivalmetho :January26,2021(Version6)App endices43 ALinearmo delforsplitting1 1deathcounts44 BComputationalmetho dsfor erio dforsplittingdeathsinanop ecialmetho dsusedforselectedp d:existingcohorts(example)..163bIntercen salsurvivalmetho d:newcohorts(example)..194aIntercensalsu rvivalmetho d:pre-existingcohorts(ingeneral)..204bIn tercensalsurvivalmetho d:infantcohorts(ingeneral)..224cIntercen salsurvivalmetho d:newcohorts(ingeneral)..235 Pre-andp ost-censalsurvivalmetho dsusedforp (withl= 5andx= 1)..27-3-LastRevised:January26,2021(Vers ion6)8 Survivorratiometho erio ve-yearcohort(assumingnomigration).

3 (2).. ortionofdeathsinlowertrianglebyIMR, ortionofdeathsinlowertriangle, ortionofdeathsinlowertrianglebyIMR, ortionofdeathsinlowertriangle, erencesindeaths,WestGermanfemales, delsoftheprop ortionoflower-triangledeaths, delsoftheprop ortionoflower-triangledeaths, (atagex).. (atagex)..711 Intro ductionTheHumanMortalityDatabase(HMD)isa collab orativepro jectsp onsoredbytheUniversityofCaliforniaatBerk eley(UnitedStates)andtheMaxPlanckInstitu teforDemographicResearch(Rosto ck,Germany).2 Thepurp , ,thepro jectdep endsontheco op erationofnationalstatisticalo ,p opulationsintheHMDarerestrictedtothosewi thdata(b othvitalstatisticsandcensusinformation)t hatcovertheentirep ,theHMDcoversalmostallofEurop e,plusAustralia,Canada,Japan,NewZealand, Chile,Israel,HongKong,RepublicofKorea, ,veryfewcountriesp orttoimproveaccesstomortalityinformation forcountriesthatdonotmeetthestrictdatare quirementsoftheHMD, ,knownastheHumanLifetableDatabase(HLD),- 4-LastRevised.

4 January26,2021(Version6)Therawdatagenera llyconsistofbirthanddeathcountsfromvital statistics,plusp opulationcountsfromp erio diccensusesand/oro cialp cumentationandtheindividualstepsfollowed incomputingmortalityratesandlifetablesar edescrib forexample,sourcesofrawdata,sp eci cadjustmentstorawdata,andcommentsab outdataquality arecoveredseparatelyinthedo cumentationforeachp , (includingtheApp endices) ,ap ersonofagex(oragedx)hasanexactagewithint heinterval[x,x+ 1). ,aneventthato ccursincalendaryeart(ormoresimply,inyear t)o ccursduringthetimeinterval[t,t+ 1).Itshouldalwaysb ep ossibletodistinguishb ,thepopulationagedxattimetreferstoallp ersonsintheagerange[x,x+ 1)atexacttimet, ,theexposure-to-riskatagexinyeartreferst othetotalp erson-yearslivedintheageinterval[x,x+ 1) ckand owofap opulationandtheo oses,itisusefulfordescribingb oththeformatoftherawdataandvariouscomput ationalpro eendividedinto1 1cells( ,oneyearofagebyoneyearoftime).]]]]

5 Each45 linerepresentsanindividuallifetime,which mayendindeath,denotedbyx(linescande),oro ut-migration,denotedbyasolidcircle(lineb ).Anindividualmayalsomigrateintothep opulation,denotedbyanop encircle(linesdandg).Otherlife-linesmaym erelypassthroughthesectionoftheLexisdiag ramunderconsideration(linesaandf ).Supp osewewanttoestimatethedeathrateforthe1 1cellthatishighlightedinFigure1( ,foragextox+ 1andtimettot+ 1).Iftheexactco ordinatesofalllife-linesareknown,thenthe exp osure-to-riskinp erson-yearscanb ecalculatedpreciselybyaddingupthelengtho feachlinesegmentwithinthecell(ofcourse,t heactuallengthofeachsegmentmustb edividedby 2,sincelife-linesare45 fromtheageortimeaxes).Followingthispro cedure,theobserveddeathrateforthiscellwo uldb ,whichisthenumb erofdeaths(inthiscase,one)dividedbythep erson-yearsofexp osure(ab ).

6 Thisistheb estestimatep ossiblefortheunderlyingdeathrateinthatce ll( ,thedeathratethatwouldb eobservedatthatageinaverylargep opulationsub jecttothesamehistoricalconditions). :January26,2021(Version6)Figure1:Example ofaLexisDiagramAgex + 2x -1t -1tt + 1t + 2 Time oxox + 1x xabdegcfHowever,exactlife-linesarerarely knowninstudiesoflargenationalp ,weoftenhavecountsofdeathsoverintervalso fageandtime,andcountsorestimatesofthenum b erofindividualsofagivenagewhoarealiveats p eci ,thep opulationcountatagexis2attimet(linesband c)and1attimet+ 1(linee).Givenonlythisinformation,ourb estestimateoftheexp osure-to-riskwithinthecellismerelytheave rageofthesetwonumb ers(thus, erson-years).Usingthismetho d,theobserveddeathratewouldb e1 = ,whichislowerthanthemoreprecisecalculati ongivenab oveb ecausetheactualexp osure-to-riskhasb outindividuallife-lines,althoughestimate sbasedonaggregatedatausingsuchapro cedurearegenerallyquitereliableforlargep ,yearofdeath( ,p erio d),andyearofbirth( ,cohort).

7 Suchcountscanb erepresentedbyaLexistriangle,or, :January26,2021(Version6)Figure2:Illustr ationofLexistrianglesAgex + 2x + 1x -1t -1tt + 1t + 2 Timecohort t-xcohort gurationsofageandtimeForalldatainthiscol lection,ageandtimearearrangedin1-,5-, gurationofamatrixofdeathrates(orsomeothe rquantity)isdenotedby1 1,5 1,5 10, ,the rstnumb eralwaysreferstotheageinterval,andthesec ondnumb ,1 10denotesacon ,deathratesandlifetablesaregenerallypres entedinsixstandardcon gurations:1 1,1 5,1 10,5 1,5 5,and5 ,thedatabaseincludesestimatesofdeathcoun tsbyLexistriangleandofp opulationsize(onJanuary1st)bysingleyears ofage,makingitp ossibleforthesophisticatedusertocomputed eathratesandlifetablesinanycon ,theagegroup10 14extendsfromexactage10upto(butnotinclud ing)exactage15,andthetimep erio ddesignatedby1980 84b eginsatthe rstmomentofJanuary1,1980,andendsatthelas tmomentofDecemb er31, ,thefollowingconventionsareusedthroughou tthedatabasefororganizinginformationbyag eandtime: 5-yeartimeintervalsb eginwithyearsendingin0or5and nishwithyearsendingin4or9;-7-LastRevised :January26,2021(Version6) 10-yeartimeintervalsb eginwithyearsendingin0and nishwithyearsendingin9.

8 Incomplete5-or10-yeartimeintervalsareinc ludedinpresentationsofdeathratesorlifeta blesifdataareavailableforatleast2years(a teithertheb eginningortheendoftheseries); forrawdata,datainone-yearagegroupsarealw aysprovideduptothehighestageavailable(fo llowedbyanop enageintervalonlyifmoredetaileddataareno tavailable); foralldataoncountrypages,one-yearagegrou psstopatage109,witha nalcategoryforages110andab ove; for5-yearagegroups,the rstyearoflife(age0)isalwaysseparatedfrom therestofitsagegroup(ages1 4),andthelastagecategoryisforages110anda b ,a5 1con gurationcontainsdataforsingleyearsoftime with(typically)thefollowingageintervals: 0,1 4,5 9,10 14,.. ,105 109,110+.Itisimp ortanttonotethatdatashownoncountrypagesb ysingleyearsofageupto110+havesometimesb eenapproximatedfromaggregatedata( , ve-yearagegroups,op enageintervals)usingthemetho dsdescrib ,itisimp ,theusermusttakeresp , ,asingle lecontainscolumnslab eledFemale,MaleandTotal(notethatthisisal phab eticalorder).

9 However,inthecaseoflifetables,whichalrea dycontainseveralcolumnsofdataforeachgrou p,dataforthesethreegroupsarestoredinsepa rate o , ,allTotalvaluesarea dsandcohortsRawdataareusuallyobtainedina p erio dformat( ,bytheyearofo ccurrenceratherthanbyyearofbirth).Deaths aresometimesrep ortedbyageandyearofbirth,butthestatistic saretypicallycollected,published,andtabu latedbyyearofo erio dformatonly,deathratesandlifetablesarepr ovidedinb othformatsiftheobservationp erio dissu ( ,byyearofbirth) :January26,2021(Version6) , eforeb eingusedasinputstothecalculationsdescrib ersonsofunknownage(ineitherdeathorcensus counts)acrosstheagerangeinprop ortiontothenumb neragecategories inthecaseofdeathcounts,from5 1to1 1data,andfrom1 lesRawdataforthisdatabasehaveb ,allrawdatahaveb eenassembledinto erentformatsforbirths,deaths,censuscount s,andp suchasexp osureestimates,deathrates,andlifetables cument,includingtheapp opulationoverthelongestp ossibletimep erio ,acompleteseriesofannualbirthcountsisnee dedforthetimep erio doverwhichmortalityratesandp erio (onJanuary1stofeachyear)ofindividualcoho rtsfrombirthuntilthetimeoftheir rstcensus, ,birthcountsbymontharerecordedaswell.

10 Theseareusedtoaccountfornon-uniformityin thetemp oraldistributionofeventswhenestimatingex p osure-to-risk(seesection6andApp endixE). nestlevelofdetailavailable ideally,cross-classi edbyage,p erio dandcohort(Lexistriangles).Sometimes,how ever,deathcounts5 Anextinctcohortisonewhosememb ersareassumedtohavealldiedbytheendoftheo bservationp erio ,deathratesforagesnotyetobservedarebased ontheaverageexp ceduresaredescrib ceduresaredescrib ,resp :January26,2021(Version6)areavailableonl yfor1 1 Lexissquaresor5 ,deathsofunknownagearedistributedprop ortionatelyacrosstheagerange,andaggregat eddeathsaresplitinto enecessary,dep endingonthecharacteristicsoftherawdatafo raparticularp edinthep opulation-sp eci cdo cumentation,andaresummarizedinApp ,estimatesofp opulationsizeonJanuary1stofeachyearareei therobtainedfromanothersource(mostcommon ly,o cialestimates)orderivedusingintercensals urvivalmetho ,allavailablecensuscountsarecollectedfor thetimep erio ,p ersonsofunknownagearedistributedprop ortionatelyintootheragegroupsb oveage80,p opulationestimatesarederivedbythemetho dofextinctgenerationsforallcohortsthatar eextinct( )