_ Materials : ; and | | methods

1,3, Individual , | genotype « data

Blood : | samples | , were | taken - | from | | both | | young -and | ‘old | | people | in | Denmark | (Bladbjerg | et al., /EEE:(cid:30) meeThe | group of. old | people ED J OIAconsists | ofof two | om Pestparts. | ‘brew aeThe first set is r—XV—sseafrom the | “osfirst BM A AA A fo”centenarian : aes =**| study | obcarried | — || out r™on | Sree| Funen | | island. | Alls mM pee mee| individuals | ; born | | before | - December | ,/(cid:27) /FED | who \ ) were § —s> still < | alive « >on | / | May, - /EED | are i » included 1 lint 1 the : study.” . They \ / were i NEE EAE I ED- interviewed aNthe s eee> Same ¢ > day, « and‘ ,E ) out ¢ t of: 7/ DEED eeeparticipants < s agreed 1 ito | y have | > blood : wy ee DD| sample t J ume» taken. * . The s > second set of data yeucomes o_o” *from the a pee eeDanish pee SE aLongitudinal Centenarian eee ee ™Study, which covers all people who | became centenarians | EEE DEIbetween / April, /EE7 and ,/ oeMay, /EE1 throughout rere omeDenmark. Blood samples were | collected ~ * ARfrom /DF aaout | of -.J REET ROMparticipants. II IIEAltogether, blood : | samples \ > WETE ° we pee- collected |   | from at \ total « | of /FJ centenarians, ; _ Peeamong | “ree‘them - DJ coo’males “eed; and /D. OE ET| females. The. younger | group | consists | of blood donors. at aothe | ooblood | bank | of Odense University were NNHospital. OOThey of” “br Neehealthy people aged -.51D years 8J7 females and /-1  males).

haemostasis | > genes « ; and | ““—~ ome’| blood | pressure 1 regulating | ; genes | aM Pee; (Table /:(cid:30) . Polymorphic ) ON OD: variations of 1 ' these | eee Es: genes | shave | » been % oN PE Oe| associated sew ASD| with | *(cid:1)3 Oo oN) either « wee Ee ee‘directly OF Fen Me I Oe‘through t eee) their ; - association with | os ow| blood | | levels « of | *(cid:1)3 ) risk | factors ; as | | previously NEE NEE DOdescribed | LIED EEE EE| (Bladbjerg « et cal., /EEE:(cid:30)

1,1, Demographic «

Age-specific | - cohort | - population | | survival i Lis calculated | from « | cohort | life | tables | for | Danes **Dborn | oy YP| between /FED eee} and /EJD(cid:27) , such t 1 that t t the s > survival { | for « reach ¢ Lage i is t s taken | : from ¢ lac . cohort | t life table | for | ‘people oa eeewho | ee ES) reached | | that ; age | in /EED(cid:30)

1,., Analytical . | strategy

hazard of | death for carriers, Br), to that ~—— sfor the — NE Be”non-carriers- or “Jrthe baseline hazard,  g(x). _ Then | according 1 to 1 ) the | PENNE Pg Re- proportional | | hazard < | assumption, , (ar) :     . The « NED> COITe- . . POMS Se Aasponding : - survival : MEN RS esfunction | wfor | “rethe « carriers | is:

. and | $ “Me MUo(x) J ) is t “yp a; the « > cumulative | - hazard ; | at ¢ Lage. SX. ee eee. Although ; Tr ( 8oONcan t | take « >On < any | ‘value § greater | “sd?‘than . Zero, | UN, a § Xn sae| gene allele > with 7 Lr larger t r than / “ow me se”(frailty « IEallele) i ST NE OE) increases t ; the | eh ON DONS> hazard « 1 of « “omeF death, 1 , while  LINO NDgene : “oeallele ' with | rs ‘smaller | “oe‘than / OO(longevity ‘J oe}allele) 1 wf RAEN EN”) reduces | it. _ Taking | —_—~e? Teeheterogeneity | in: | an Oo Neindividual’s 1 ; unobserved I frailty, \ “yee, Which « ore’.1 can < ry See’1 also ¢ EN FO) contribute > tos NI IIE) survival ( SE RENN SD| (Vaupel « let z Neetal., /EJE:(cid:27) into « . consideration, theUi NE LDL TYaverage § > vane oe GS.: survival | | for : a! | group | of "carriers can | we NOY| be aM”: derived ; | as | meg AE A K(x|r) - an (cid:1)/  GUMS!2ao rinso Taulon, Uea(x) lo" when “oNthe unobserved ‘oer *frailty follows  gamma NE RONENdistribution Vewith . ACmean / eeeand VPP usvariance awa |. Accordingly, “ae” Imean Pe ——survival “ S*for non-carriers is 5(x) .  (cid:1)/  alI“ens WG VallalHe?(x).  .

genotype, one | can introduce  ors”simple two-point distribution for the. “Ss &*allele” or genotype omen(Vaupel “s Meeand Yashin, /EF7:(cid:30) “eeeDefine re *the. ~ Frisk of | " gene—sex interaction, lg (99 as the | orrisk ieof Vexss male rerecarriers | to | ney) that | ooof f ae ie aeF female « carriers. ' Then | “ &*| the ; average |  - survival ; “edat; oo" 8ASage.   for | the 1 / mixed population « | consisting | of | both | Carriers ; ; and 1 PEE ED NE NAE| non-carriers | i —is:

Al3~~ Se ( for ee females woand Sreefemales, obtainable   froma STN A ESpopulation NF OE OEstatistics,  n(X) *  (cid:1)/ ~~_ 51 ml       and {elIn(X)) is 9 UlUNe®mean survival for rPyYreesmales carriers eeeand “|Sy p(X) *  (cid:1)/  Texsl   Sil ET exs?o’rlnsy aT fep(X) ° is | / mean | | survival | | for: female « carriers, |   (2)  (cid:1)/   am 9]7 g'Inso  is So,r(   50m mean | SOP NAS| survival | for: ‘male | - non-carriers | and ;  px) :  (cid:1)/ an ia On)a7 Insy —(Al~ey is | SOI, mean | FP “| survival So,p( So, for : ‘female | - non-carriers. ' The | : proportion | TU,| of « Ops* carriers } at age.  OY 

the | data « | containing |  - both | | male ; and |  | female | aeindividuals | can | ov=Ebe ee ee- constructed ;  

8  Pn  Pm  Pr  Pn   

Din Ne (  Ve are t > the t MN ?9> total 1 Ae YN| number « r of | f participants < s at tage J  Int 1 the ¢ > estimation,  “eo “EM. single ¢ (cid:4)- m1S1 "M\* Fo eae *; restricted t onI to ¢ pee) all the ; > alleles i sin ¢ 1 order t tor ve peey reduce 1 “ren> the ¢ ween Es SE> amount ¢ ow het of t F the | - parameters see >sto | ayebe « REE OS» estimated. | . Parameters t that maximize |  the |  likelihood | | function ; | are eee EO Eee- estimated |   the 1 maximum | | likelihood | | procedure i in Gauss : | software | : (Apotech | | System, /EE1:(cid:30)

 , Results