Modeling Heterogeneous Mediation Effects in Survival Analysis via an Interpretable M-Learner Framework

Mediation analysis is a useful tool to evaluate surrogate endpoints in clinical trials. We propose a novel method, the M-survival learner, for estimating heterogeneous indirect treatment effects in the presence of censored outcomes. The proposed appr…

Authors: Xingyu Li, Qing Liu, Xun Jiang

Modeling Heterogeneous Mediation Effects in Survival Analysis via an Interpretable M-Learner Framework
! Biometrics 59,$1 – 25 $ DOI:$10.1111/j .1541 - 0420.2005.00454.x ! December$2006 ! Modeling)Heter ogeneous)Mediation)Effects)in)Survi val)Anal y sis)via)an ! Interpr etable)M - Learner)Fr amew ork ! Xingyu'Li 1 ,'Qing'Liu 2 ,'Xu n'Jiang 2 ,'Hong'Am y'Xia 2 ,'Brian'P .'Hobbs 3 ,'P eng'W ei 1 ∗ ! 1. Department$of$ Biostatisti cs,$The$University$of$T exas$MD$Anderson$Cancer$Ce nter , ! Houston,$TX,$7 7030,$USA. ! 2. Center$for$Design$and$Analysis,$Amgen,$Thousand$Oaks,$CA, $91320,$USA. ! 3. Te l p e r i a n $ I n c , $ T X , $ 7 8 7 3 8 , $ U S A . ! * email:' PW ei2@mdanderson.org ! Summary: Mediati on) ana lysis) is) a ) usefu l) tool ) to) evaluate) s urrogate) endpo ints) in) clini cal) t rials .) W e) propose) a)n ov el) method, ) the)M - surviv al)learner , ) for)estimating) heterogeneous)i ndirect)treatment) effects)i n) the) presence)of) censored) outcomes.)The) proposed) approach) enables) the) identi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`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a$! (.!'3=9!GJEEb!c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d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e%!'22(3()'.(/!'&&)1 5 '3!&'.#8 ' : =! ?&(2$7$2'33: 9! 1,)! 21+.)$*,.$1+%! ')(\! 8(! 01)-'3$O(! %,))16'. (! 5'3$/$.:! '%! '! #(.() 16(+(1,%9! $+/$5$/,'3 < 3( 5 (3! &)1&().:! ) '.#()! .#'+! '! 631*'3! 2#')'2.()$%.$2 =! ] (! /(5(31&! '! 3(')+() < *'%(/! C73(H$*3(! -'2#$+(! 3(')+$+6! -(.#1/9! %,2#! '%! f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g =! @$+'33: 9! ?(2.$1+! h! %,--')$O(%! 1,)! 7$+/$+6%! '+/! /$%2,%%(%! .#($)!$-&3$2'.$1+%!'+/!&1.(+.$'3!(H. (+%$1+%=! 2.)Surrog ate)Biomark er)and)Mediation)Model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b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d1%.! (H$%.$+6! '&&)1'2#(%9! #18 (5 () 9! 012,%!1+! '5 ()'6(! (00 (2.%! '.!.#(! &1&,3'.$1+!1)! 3'.(+.!%.)'.,-!3(5 (39! $-&3$2$.3:!'%%,-$+6!#1-16(+(1,%!%,))16 '.(!5'3$/$. :!'2) 1%%!&'.$(+.%!Ca$! (.! '3=9! GJEED=! P)1-$+(+.! (H'-&3(%! $+23,/(! &)$+2$&'3! %.)'.$7$2'.$1+! *'%(/! -(.#1/%9! 8#$2#! /(7$+(! %,))16'.( < )(3' .( / ! 2' , %' 3 ! ( 00( 2 .% ! 8 $ .# $ +! 3 ' .( +. ! % , *6 )1 ,& % ! 2# ' )'2 .( ) $O ( /! *: ! & 1 .( +. $ '3 ! 1,.21-(%b! -(.'< '+'3:.$2! '&&)1'2#(%9! 8#$2#! '66)(6'. (! %,) )16'. (! 1,.21-(! '%%12$'.$1+%! '2)1%%! -,3.$&3(! .)$'3%! .1! (5 '3,'.(! &1&,3'.$1+<3( 5(3! %,))16'2:b! '+/! -(/$'.$1+! '+'3 :%$%! -(.#1/%9! %,2#! '%! .#(! &)1&1).$1+<(H&3'$+(/! 0) '-(81)I! 1)$6$+'33 :! &)1&1%(/! *:! @) ((/-'+! C@) ((/-'+! '+/! ?2#'.OI$+9! EFFGD=! ]#$3(! .#(%(! 0)'-(81)I %! &)1 5$/(! 5'3,'*3(! $+%$6#.%! $+.1! 15()' 33 ! 1 )! 3 ' .( +. ! % ,) )1 6' .( ! (0 0( 2 .% 9! .# (: ! ' )(! + 1 .! / ( %$ 6 +( / ! .1 ! 2# ' )'2 .( ) $O ( ! #1 8! %, ))1 6' .( < -(/$'.(/!.) ('.-(+.!(00(2.%!5 '):!'2)1%%!$+/$ 5$/,'3%!1)!23$+$2'33 :!/(7$+(/!%,*&1&,3'.$1+%=! !" #$%&'&() " )*(%+* % , 7 ! "#(%(!7$+/$+6%!#$6#3$6#.!'!0,+/'-(+.'3!3$-$.'.$1+!10!&1&,3'.$1+< 3( 5(3!%,)) 16'. (!5 '3$/'.$1+=! 45 (+! 8#(+! '! *$1-')I()! %'.$%7$(%! 21--1+3:! ,%(/! 2)$.()$'! 01)! %,))16'. (! 5'3$/$.:! 1+! '5 ()'6(9! $.%! )(3$'*$3$.:! '%! '! %,))16'.(! -':! 5'):! %,*%.'+.$'33:! '2)1%%! $+/$5$/,'3%! 1 )! %, * 6)1,&%9! )(73(2.$+6! #(.() 16(+($.:! $+! .#(! ,+/()3 :$+6! 2',%'3! &'.#8 ': %! 3$+I$+6! .)('.-(+.9! *$1-')I() 9! '+/! 23$+$2'3! 1,.21-(=! U (3$'+2(! 1+! &1&,3'.$1+<3(5(3! 5'3$/'.$1+! '31+(! -':! .#()(01) (! 3('/! .1! ())1+(1,%! /(2$%$1+%! $+! (')3 :! .)$'3! .()-$+'.$1+9! '22(3() '.(/! )(6, 3'.1): ! '&&)15 '39! 1)! $+/$5$/,'3$O(/! 23$+$2'3! /(2$%$1+ <-'I$+6=! "#(%(! 21+2()+%! #'5 (! 21+.)$*,.(/! .1! $+2)('%$+6! 2',.$1+! '-1+6! )(6,3'.1):! '6(+2$(%9! $+23,/$+6! .#(! @A B9! )(6 ')/$+6! .#(! ,%(! 10! %,)) 16'.(! (+/&1$+.%! $+! %(..$+6%! 2#')'2. ()$O(/!*:!*$1316$2'3!'+/!23$+$2'3!# (.() 16(+($.: = ! " 16(.#() 9! .#(%(! 21+%$/()'.$1+%! -1.$5 '.(! .#(! /(5(31&-(+.! 10! -(.#1/1316$2'3! 0)'-(81) I%! .#'.! (H&3$2$.3 :! '221,+.! 01)! #(.()16(+($.:! $+!%,)) 16'.(! 5'3$/$.: =! M+! &').$2,3') 9!.#() (! $%! '! +((/! 01)! '&&)1'2#(%! .#'.! 2#') '2.()$O(! $+/$5$/,'3 +$.! " )('.-(+.! g '3,(! B%%,-&.$1+! C?>"g BD! CU,*$+!(.!'3=9!EFFJD= ! Q=E! D9%5&"E"(.&"#5 ) @ 133 18$+6! M-'$! (.! '3=! CGJEJD9! 8(! -'I(! .#(! 013318$+6! %(;,(+.$'3! $6+1)'*$3$.:! '%%,-&.$1+! .#)1,6 #.9! '33 18$+6!01)!.#(!$/(+.$7$2'.$1+!10!.#(!+'.,)'3!/$) (2.!'+/!$+/$)(2.!.) ('.-(+.!(00(2.%=! !" #$%&'&() " )*(%+* % , 9 ! Assump)on 1 CU'+/1-$O'.$1+D\! M+! '!)'+/1-$O(/!21+.)133(/! .)$'39!.#(! .)('.-(+.!$+/$2'.1)! ?/ $%!$+/(&(+/(+.!10!*'%(3$+(!215 ')$'.(%! X 9!.#'.!$%9 ! ?/ ⊥⊥ ! X @/ X k!f * ! Assump)on 2 CM6+1)'*$3$.:! 10! .)('.-(+.! '%%$6+-(+.D\! X1+/$.$1+'3! 1+! *'%(3$+(! 21 5 ')$'.(%! X 9! .#(! .)('.-(+.! '%%$6+-(+.! $%! $6+1)'*3(! 8$.#! )(%&(2.! .1! .#(! &1.(+.$'3! -(/$'.1)! '+/! &1.(+.$'3! 1,.21-(%9!.#'.!$%9! l 2 C C ∗ @1 C C DD @1 C C D m! ⊥⊥ ! ?/ p! X @/ C@ C ∗" k!lJ @ Em * ! Assump)on 3 CM6+1) '*$3$.:! 10! .#(! -(/$'.1)D\! X1+/$.$1+'3! 1+! .#(! 1*%()5 (/! .)('.-(+.! '%%$6+-(+.! '+/! *'%(3$+(! 215 ')$'.(%9! .#(! -(/$'.1)! $%! $6+1) '*3(! 8$.#! )(%&(2.! . 1! .#(! &1.(+.$'3! 1,.21-(%9!.#'.!$%9! 2 C C ∗ @1 C C DD! ⊥⊥ ! 1/ p! ?/ o! C@ X @/ C@ C ∗" k!lJ @ Em * ! Assump)on 4 CP1%$.$ 5$.:D\ ! ] (!'%%,-(!&1%$.$5$.:!10!.#(!-(/$'. 1) 9!%,2#!.#'.! < M l 1 C C D!o! $/ p! ?/ o! C@ X m! F/ J @/ 01) !' 33 ! $/ k!d @/C/ k!lJ @ Em @/ X k!f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d'+:! (H$%.$+6! -(/$'.$1+! '+'3:%$ %! -(.#1/%! 01)! .$-(< .1 <(5(+.! 1,.21-(%! ,+/()! .#(! X1H! &)1&1).$1+'3! #'O')/%! -1/(3! /(7$+(! .#(! -(/$'.$1+! (00(2.! 1+! .#(! 316< #'O')/! %2'3(! Cg '+/()] ((3(9! GJEED9! 8(! /(7$+(! .#(! 21+/$.$1+'3! /$)(2.!'+/! $+/$) (2.! .)('.-(+.! (00(2.%! 1+! .#(! 316 <#'O')/! %2'3(! ,+/()! ' ! X1H! &)1&1).$1+'3! #'O')/%! 0)'-(81) I=! "#(! 1,.21-(! -1/(3! $%! %&(2$7$(/!'% ! G C & p X @? @1 D!o! G 0 C & D %47 C - C X @? @1 DD @/ CED ! 8#()( ! - C X @? @1 D!o! H 1 C X D!q! H 2 C X D! r! ?/ q! H 3 C X D! r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d1)(!6(+()'33 : 9!.#(%(! 0,+2.$1+%!')(! '3318(/! .1! *(! 6(+() '3! 0,+2.$1+%! 8$.#! 7$+$.(! (H&(2.'.$1+%9! '221--1/'.$+6! 73(H$*3(! '+/! &1.(+.$'33 :! +1+3$+(')! )(3'.$1+%#$&%9!8(! 2'33! $.! 21-&3(H!'%%,-&.$1+b! -1)(! / $%%2,%%$1+! 2'+! *(! 01,+/!$+!B&&(+/$H!B=! "#(!-(/$'.1)!$%!-1/(3(/!'%! 1/ o! H 4 C X D!q! H 5 C X D! r! ?/ q! I@/ CQD ! !" #$%&'&() " )*(%+* % , 11 ! 8#()( ! H 4 C X D! )(&)(%(+.%! .#(! *'%(3$+(! 215')$'. (! (00(2.%! 1+! .#(! -(/$'.1) 9! H 5 C X D! /(+1.(%! .#(! .)('.-(+.! (00(2.! 1+! .#(! -(/$'.1) 9! '+/! I/ $%! '! -('++/()! .#(%(! +1.'.$1+%9! .#(! .1.'3! .)('.-(+.! (00(2.%! C""4D! '+/! +'.,)'3! /$)(2.! '+/! $+/$)(2.! .)('.-(+.! (00 (2.%!CA "49!M"4D! 1+! 316!#'O') /! %2'3(!21+/$.$1+'3! 1+! 215 ')$'.(%! ')(!6$ 5 (+!*: 9 ! w" w ∗ ! @ 1)! %$-&3$2$.:! 10! +1.'.$1+9! 2 w, M w" $%! /(+1.(/! '%! 2 C C@ 1 C C DD9! 21,+.()0'2.,'3! 316! #'O')/! 21+/$.1+'3! 1+!215 ')$'.(%! X =) x $%!/(+1. (/!'%!316 l G T w,Mw" C & p X =) x Dm=! ?$+2(!8(! 012,%!1+! .#(! +'.,)'3!$+/$)(2.!.)('.-(+.! (00(2.%!21+/$.$1+'3! 1+! ?/ o! E9! 8(!7$H! C/ o! E! $+!.#(!1,. 21-(!-1/(3! '+/!%(.! C ∗" o!J!$+! .#(!-(/$'. 1)!/$%.)$*,.$1+=!?,*%.$.,.$+6! C/ o!E! '+/! C ∗" o! J! $+.1! .#(! ( H&)(%%$1+! CKD! .#()(0 1)(! :$(3/%! .#(! $+/$)(2.! .)('.-(+.! (00(2.! 21+%$/()(/! .#)1,6#1,.! .#$%!&'&() = ! Theorem 1 CM/(+.$7$2'.$1+D : A59%'/6)),$7&"#5/JKL/C"&8/' .'%/%M%5&/.)),$7&"#5@/&8%/"59"'%(&/ &'%.&$%5&/%<<%(&/(#,;9/N%/"9%5&"E"%9/.) ) D23 C & p X o! x D!o! H 3 C x D H 5 C x D!o! - C x p ?/ o!E @1/ o! E i 1 p C/ o!E @ X o! x jD s! - C x p ?/ o!E @1/ o! E i 1 p C/ o!J @ X o! x jD */ CRD ! Remark 1: >+/()! B%%,-&.$1+%!ESK! '+/!.#(! ) ')(!(5(+.!'%%,-&.$1+9! D23 C & p X D9!8#$2#! 8(! )(0()! .1! '%! .#(! +'.,)'3! $+/$)(2.! (00(2.! 21+/$.$1+'3! 1+! 215')$'. (%! CtM4XXD9! '/-$.%! '! &').$2,3')3:! %$-&3(!0 1)-=! ?&(2$7$2'33: 9! '3. #1,6#!.#(! tM4XX! $%! /(7$+(/!'.! .$-(! & 9! $.%!7$+'3! ( H&)(%%$1+! /1(%! +1.! /(&(+/! 1+! & =! "#(! tM4XX! $%! 6$ 5(+! *:! .#(! &)1/,2.! H 3 C x D H 5 C x D9! 8#$2#! 2'&.,)(%! .#(! (00(2.! 10! .#(! -(/$'.1)! 1+! .#(! 1,.21-(! '+/! .#(! (00(2.! 10! .#(! .)('.-(+.! 1+! .#(! -(/$'.1) 9! )(%&(2.$ 5(3 : =! 223 C & p X o! x D! \o ! 316 l G T w,Mw" C & p X =) x D m!s! 316 l G T w ∗ ,M w ∗ C & p X =) x Dm @ ! ! D23 C & p X o! x D! \o ! 316 l G T w,Mw" C & p X =) x D m!s! 316 l G T w,M w ∗ C & p X =) x Dm @ ! ! O2 3 C & p X o! x D! \o ! 316 l G T w,M" ∗ C & p X =) x D m!s! 316 l G T w ∗ ,M " C & p X =) x Dm * ! CKD ! 12 ) -'./*0%'1#2, 3*1*/4*%, 2006 ! 4;,$ 5'3(+.3 : 9! .#(!%'-(! ;,'+.$.:!2'+! *(!( H&)(%%(/! '%! .#(!/$00 ()(+2(! $+!.#(! 1,.21-(! )(6) (%%$1+! 0,+2.$1+! - CrD!(5 '3,'.(/!'.!.#(!(H&(2. (/!-(/$'.1)!5 '3,(%!,+/()! ?/ o!E!'+/! ?/ o!J9!21+/$.$1+'3 ! 1+! X =) x =! Remark 2: " 1! $33,%.)'. (!#(.()16(+(1,%!-(/$'.$1+! (00(2.%9!8(!&)1 5$/(!'+! (H'-&3(!$+!@$6,)(!E! C2D! '+/! C/D=! M+! .#$%! %(..$+69! &'. $(+. %! $+! Z)1,&! E! Cg ')E! F/ J @ g' ) G ! F/ JD! #'5 (! *1.#! M"4! '+/! A"49! 8#()( '%! &' .$ (+. %! $+! Z)1, &% !G !'+ /! Q! (H#$ *$. !1 +3:! A"4= ! "#(! tM4XX!'/-$.%! '! &').$2,3')3 :!%$-&3(! )(&)(%(+.'.$1+=!P)110!10! "#(1) (-! E! $%! &)1 5$/(/! $+! B&&(+/$H! A! '+/! '//$.$1+'3! /$%2,%%$1+! '+/! /(.'$3%! 10! .#(! (%.$-'.$1+! &)12(/,)(!')(! &)15$/(/! $+!B&&(+/$H!B=! 4.)Clustering)and)Identify)P atient)Pr oJiles) K=E! :;,)&%'"5-/N.)%9/#5/)"$";.'"&>/ ] (! ;,'+.$0:! .#(! .)('.-(+.! (00(2.! .) '+%-$..(/! .#)1,6#! .#(! %,))16 '.(! ,%$+6! '! #(.() 16(+(1,%! -(/$'.$1+! '+'3:%$%! 0)'-(81)I! .#'.! '3318%! .#(! t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d1.$5 '.(/! *:!.#$%! 1*T(2.$5(9!8(!&)1&1%(!'!+15(3!%$-$3')$.:< *'%(/!23,%.()$+6!'&&)1'2#!*,$3.! ,&1+! '! -1/$7$(/! ./P.&"%5&/P'#E";%)/ M+.()&) (.'*$3$.:! $%! 2),2$'3! 01)! .)'+% 3'.$+6! %.'.$%.$2'3! &'..()+%! $+.1! 23$+$2'3! &)'2.$2(=! d'2#$+(! 3(')+$+6!-1/(3%9! 8#(+!'&&3$(/!$+! 23$+$2'3!)(%(')2#9!%#1,3/!$/('33:!:$(3/!$+.()&)(.'*3(!)(%,3.%! .#'.!') (!*1.#! ,+/()%.'+/'*3(! '+/!316$2'33 :!%1 ,+/!01 )!&) '2.$2$+6! 23$+$2$'+%=! B3.#1,6#!'22,) '.(! 1,.21-(! &)(/$2.$1+! $%! +(2(%%'): 9! $.! $%! +1.! %,07$2$(+.! 01)! /(5(31&$+6!(00(2.$5 (! -1/(3%! . 1! 6,$/(! .)('.-(+.! %(3(2.$1+=! N8$+6! .1! .#(! &) 1&().$(%! 10! .< ?t49! %$-$3')! 1*%()5'.$1+%! .(+/! . 1! 21+2(+.)'. (! +(')! .#(! 2(+.()%! 10! 23,%.()%! $+! .#( ! (-*(//(/! %&'2(=! X1+%(;,(+.3 : 9! 8(! '&&3 :! [ < -('+%! 23,%.( )$+6! .1! $/(+.$0:! 21+2) (.(! %,*6)1,&%=! A(2$%$1+! .)((%! 100()! '! #$6#3:! $+.()&)(.'*3(! 0)'-(8 1)I! 01)! 23$+$2'3! /(2$%$1+! -'I$+6! .#'.! $%! ('%:! .1! /$%%(-$+'.(! .#)1,6#! %.),2.,)(/! /$'6)'-%! /(&$2.$+6! '! %.(&< *: < %.(&! % (;,(+2(! 10! 5')$'*3(! '%%(%%-(+.%=! B%%(%%$+6! '! .)((e%! '3$6+-(+.! 8$.#! 23$+$2'3! )('%1+$+6! $%! %.) '$6#.0 1)8') /! 0 1)! 23$+$2$'+%9! '%! $.! /1(%! +1.! )(;,$) (! '+! ,+/()%.'+/$+6!10!.#(!&1.(+.$'33 :!21-&3(H!-1/(3$+6!&) 12(%%(%!,%(/!.1!6(+() '.(!$.=! L1.#! . < ?t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rrr! @ X k =! ?.(&! E\! ] (! ,%(! '! /(2$%$1+! .) ((! .1! 7$.! 0/ 23,%.()%! 0) 1-! .#(! [ <-('+%! 23,%.()$+69! /(+1.$+6! ('2#! .()-$+'3!+1/(!10!.#(!/(2$%$1+!.) ((!3('0=! ?.(&!G\!" 8 1!X1H!-1/(3%!') (!7$..(/9! 14 ) -'./*0%'1#2, 3*1*/4*%, 2006 ! G C & D! o! G 0 C & D(H& l Q 1 ? m @ ! CVD ! G C & D! o! G 0 C & D(H& l Q 2 ?/ q! Q 3 3('0!q! Q 4 3('0! u! ? m * ! ChD ! a(.! ; 1" '+/! ; 2" /(+1.(!.#(!-'H$-$O(/! &').$'3!316<3$I(3$#11/%!10! -1/(3%!CVD! '+/!ChD9! )(%&(2.$ 5 (3: =! "#(!3$I(3$#11/!) '.$1!.(%.!%.'.$%.$29 ! s GC ; 2" s! ; 1 D! v! R 2 C 9< D @ ! CwD ! 8#()( ! 9+/()! .#(! 21-&3(H! '%%,-&.$1+9! @$6,) (! G! $33,%.)'.(/! .#(! %(3(2.(/! .#)(%#13/! ,%(/! 01)! %,*6)1,&! $/(+.$7$2'.$1+=! "#(! 7$6,)(! %#18 (/! .#'.! .#(! &)1&1%(/! -(.#1/! %,22(%%0,33:! $/(+.$7$(/! )(6$1+ %! 8$.#! #(.() 16(+(1,%! -(/$'.$1+! (00(2.%9! (00(2.$5 (3:! /$%.$+6,$%#$+6! %,*6)1,&%! 8$.#! /$%.$+2.! -(/$'.$1+! &'..()+%=! @$6,)(! Q! %#18(/! .#(! (-&$)$2'3! 2,-,3'.$ 5(! /$%.)$*,.$1+! 0,+2.$1+! 10! 7 leaf 9! .#(! )(%,3.%! %#18(/! .#(! '*$3$.:! 10! .#(! &)1&1%(/! -(.)$2! .1! /$%.$+6,$%#! .#(! #(.()16(+(1,%! %2(+')$1%! '+/! #1-16(+(1,%! %2(+')$1%=! "#(! (%.$-'.$1+! '22,)'2:! 10! tM4XX! 8'%! (5 '3,'.(/! $+! B&&(+/$H! Y9! ] (*! " '*3 (! E=! d1)(! /$%2,%%$1+! '+/! '//$.$1+'3! /(.'$3%! )(6 ')/$+6! 215 ')$'.(! %(3(2.$1+! '+/! .#(! (H 23,%$1+! 10! 2'%(%! 013318$+6! 2'3$*)'.$1+! 8() (! &)(%(+ .(/! $+! B&&(+/$H! M=! "#(%(! )(%,3.%! %,66(%.(/! .#'.! .#(! &)1&1%(/! -(.#1/! 8'%! '*3(! .1! $/(+.$0:! )(6$1+%! (H#$*$.$+6! #(.() 16(+($.:!$+!-(/$'.$1+!.)('.-(+.!(00 (2.%=! i@$6,)(!G!'*1,.!#() (=j ! !" #$%&'&() " )*(%+* % , 17 ! i@$6,)(!Q!'*1,.!#() (=j ! 6.)Real)D ata)Application:)The)A CT G175)T rial ) ] (! '+'3:O(/! /'.'! 0) 1-! '! &#'%(! MMM! )'+/1-$O(/! YMg! 23$+$2'3! .)$'3! 1)$6$+'33 :! )(&1).(/! *:! CY'--()! (.! '3=9! EFFVD=! 43$6$*3(! &').$2$&'+.%! 8() (! '6(/! EG! :(')%! 1)! 13/() 9! #'/! 3'*1)'. 1):21+7$)-(/! YMg < E! $+0(2.$1+9! '! *'%(3$+(! XAK! 2(33! 21,+.! *(.8((+! GJJ! '+/! RJJ! 2(33%_-- 3" -('%,)(/! 8$.#$+! QJ! /': %! &)$1)! .1! )'+/1-$O'.$1+9! +1! #$%.1):! 10! BMA?< /(7$+$+6! $33+(%%! 1.#()!.#'+! -$+$-'3! -,212,.'+(1,%! ['&1%$e%! %')21-'9! '! [')+10%I:! &()01)-'+2(! %21)(! 10! '.! 3('%.! hJ9! '+/! '22(&.'*3(! *'%(3$+(! 3'*1)'.1):! 5 '3,(%=! "#(! .)$'3! 8'%! %.) '.$7$(/! *:! &)$1)! '+.$)(.) 15$) '3! .#()'& :! (H&1%,) (=! @ 1)! $33,%.)'.$1+9! 8(! 012,%(/! 1+! .81! .)('.-(+.! ')-%\! .#(! 21+.)13! ')-! 8$.#! c$/15,/$+(! CcAgD! -1+1.#()'&: 9! '+/! .#(! .)('.-(+.! ')-! 8$.#! c$/15,/$+(! &3,%!A$/'+1%$+(! CcAgq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hR! .)('.-( +.! C&)('+.$D9! )'2(9! 6(+/() 9! %:-&.1-'.$2! %.'.,%9! '+/! *'%(3$+(! XAK! 2(33! 21,+.! CXAKJD=! XAK! 2(33! 21,+.! -('%,)(/! '.! GJ! 8((I%! '0.()! )'+/1-$O'.$1+! Cy R! 8((I%D! 8'%! %(3(2.(/! '%! .#(! %,))16'.(! *$1-')I () 9! )(&) (%(+.$+6! '+! (')3 :! $--,+1316$2! )(%&1+%(! )(3'.$ 5 (! .1! .#(! -(/$' +! 013318 < ,&! /,)'.$1+! 10!EKQ! 8((I%=! "#$%!%,)) 16'.(! &)(2(/(%! .#(!23$+$2'3! (+/&1$+.!'+/!2'&.,) (%!%#1). <.()-! .)('.-(+.! (00(2.%=! "#(! &)$-'):! (+/&1$+.! 8 '%! /(7$+(/! '%! '! 6) ('.()! .#'+! RJW! /(23$+(! $+!XAK! 2(33! 21,+.! 0)1-! *'%(3$+(9! &) 16)(%%$1+! .1! '2;,$)(/! $--,+1/(7$2$(+2:! %:+/)1-(! CBMA?D9! 1)! /('.#=! @ 1)!%$-&3$2$.: 9!.#$%!21-&1%$.(!(+/&1$+.!$%!#()('0.()!) (0()) (/!.1!'%!N?=! N,)! '+'3 :%$%! 21+%$%.(/! 10! .81! &').%=! ] (! 7$)%.! 21+/,2.(/! .#(! '+'3 :%$%! ,+/()! 3$+(')! -1/(3! '%%,-&.$1+%! '+/! .#(+! (H.(+/(/! .#(! '+'3:%$%! .1! '! -1)(! 21-&3(H! -1/(3$+6! 0)'-(81) I=! ] (! 18 ) -'./*0%'1#2, 3*1*/4*%, 2006 ! &)(%(+. (/! 1+3:! .#(! )(%,3.%! 1*.'$+(/! ,+/()! .#(! 21-&3(H! '%%,-&.$1+%9! 8#$3(! .#(! )(%,3.%! '+/! /$%2,%%$1+!*'%(/!1+!.#(!3$+(')!'+'3: %$%!8() (!&)1 5$/(/!$+!B&&(+/$H!M=! ?,*6)1,&! E!21+%$%. (/! 10! &'.$(+.%! 8$.#! 318!*'%(3$+(! XAK!3( 5 (3%! '+/! (H#$*$. (/! '! %,*%.'+.$'33 :! %.)1+6()! -('+! t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t(5 ().#(3(%%9! -('+$+60,3! /$00() (+2(%! )(-'$+! *(.8((+! .#(! .81! %,*6)1,&%=! ?,*6)1,&! Q! $+23,/(/! &'.$(+.%! 8#1! #'/! )(2($ 5 (/! '+.$)(.)1 5$)'3! .)('.-(+.! &)$1)! .1! (+)133-(+.! C&)('+.$! ⩾ w! /' :%D9! 8#() ('%! ?,*6) 1,&! G! 21+%$%.(/! &)$-')$3:! 10! .)('.-(+.< +'z{5 (! &'.$(+.%=! @ 1)! &'.$(+.%! $+ ! ?,*6)1,&!Q9! .#(! .) ('.-(+.! (00(2.! -(/$'.(/!.#)1,6#! XAK! '&&(')(/!.1! #'5 (! '! /(3': (/! $-&'2. =! B%! %#18+! $+! .#(! 21,+.()0 '2.,'3! %,)5$5 '3! 2,)5(%! $+! @$6,) (! R! C2D9! .#(! .#)((! %,)5$5 '3! 2,)5(%! *(6'+! .1! %(&')'. (! '.! 3'.()! .$-(! &1$+.%9! $+/$2'.$+6! .#'.! .#(! .)('.-(+.! (00(2.! -(/$'.(/! *:! XAK! $-&)1 5 (-(+.!*(2'-(!-1)(!'&&') (+.!15 ()!31+6()!013318 < ,&!&()$1/%= ! M+! 21+.)'%.9! 01)! ?,*6)1,&! G9! .#(! 2,)5 (%! 01)! + CE @1 CEDD! '+/! + CE @1 CJDD! '3-1%.! 21-&3(.(3 :! 15 ()3'&! C@$6,)(! R! C*DD9!%,66(%.$+6! .#'.!X AK!/$/! +1.!-('+$+60,33 :! 2'&.,)(! .#(! .)('.-(+.! (00(2.! $+! .#$%! %,*6)1,&=! "#$%! 1*%()5'.$1+! $%! 21+%$%.(+.! 8 $. #! .#(! /$%.)$*,.$1+! 10! $+/$5$/,'3! tM4XX! %#18+! $+! @$6,) (! R! C'D=! X1-&')(/! 8$.#! ?,*6)1,&! G9! ?,*6)1,&! Q! (H#$*$.(/! 6)('.()! #(.() 16(+($.:! $+! $+/$5$/,'3! tM4XX! 5 '3,(%9! 8#()('%! ?,*6)1,&! G! %#18(/! '! )(3'.$ 5 (3:! 21+2(+.)'. (/! /$%.)$*,.$1+! ')1,+/! O()19! $+/$2'.$+6! '! -1)(! %.'*3(! *,.! +(63$6$*3(! -(/ $'.$1+! (00(2.= ! N5( )'339! @$6,)(%! K! '+/! R! .16(.#()! )(5 ('3(/! 23$+$2'33 :! $+.()&)(.'*3(! #(.()16(+($.:! $+! %,))16 '.(!-(/$'.$1+!(00(2.%!'+/!%,&&1). (/!.#(!5'3$/$.:!10!.#(!$/(+.$7$( /!%,*6)1,&%=! !" #$%&'&() " )*(%+* % , 19 ! i@$6,)(!K!'*1,.!#() (=j ! i@$6,)(!R!'*1,.!#() (=j ! 7.)Discussion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c'*1)!(.!'3=9!GJGJD= ! Y18( 5() 9! .#(! .#()'&(,.$2! 3'+/%2'&(! #'%! %#$0.(/! -')I(/3 :! .18') /! .')6(.(/! '+/! $--,+1-1/,3'.1):! '6(+.%!8$.#!%,*%.'+.$'33 :! -1)(! 21-&3(H! -(2#'+$%-%!10! '2.$1+=!@ 1)!%,2#! .#()'&$ (%9! .#(! )(3'.$1+%#$&! *(.8((+! (')3:! %,))16'. (! %$6+'3%! '+/! 31+6 <.()-! 23$+$2'3! *(+(7$.! $%! 10.(+!$+/$)(2.9! 21+.(H. / 7,) QJF S QEh= ! X3'5 (39!@ =!'+/!Y'+2(9!B=!|=!CGJJKD=!Y$5!/),6!) (%$%.'+2(=! X%C/35-;.59/Y#,'5.;/#/ 136,) EEKw S EERF= ! Y'--() 9! ?=! d=9!['.O(+%. ($+9!A =!B=9!Y,6 #(%9!d=! A =9! Z,+/'2I() 9!Y=9! ?2#113(: 9! U=!" =9! Y',*)$2#9!U=! Y=9! Y(+): 9! ] =! [=9! a(/()-'+9! d=! d=9! P#'$) 9! |=! P =9! t$,9! d=9 ! (.! '3=! CEFFVD=! B! .)$'3! 21-&')$+6! +,23(1%$/(! -1+1.#()'& :! 8$.#! 21-*$+'.$1+! .#()'&:! $+! #$5 < $+0(2. (/! '/,3.% ! 8$.#! 2/K! 2(33! 21,+.%! 0)1-! GJJ! .1! RJJ! &()! 2,*$2! -$33$-(.() =! X%C/ 35-;.59/ Y#,'5.;/ #(8#;#-"(.;/$%&8#9)/ 15,) QJF= ! [',0-'++9! Z=! U=9! P())$+9! a=9! P'+.'3(19! Z=9! N&) '5$39! d=9! @,)) () 9! Y=9! " (3(+.$9! B=9! Y$)%2#(39! L=9! a(/()6()*() 9! L=9! g ()+'OO' 9 ! P =9! L()+'%21+$9! 4=9! (.! ' 3=! CGJJQD=! X/K! . <3:- :.(! )(21 5():! $+! $+/$5$/,'3%! 8$.#! '/5 '+2(/! #$ 5 < E! $+0(2.$1+! )(2($ 5$+6! &1.(+.! '+.$)(.)1 5$ )' 3! . # ()' &: ! 01 )! K ! :(' ) % \ ! . #( ! % 8 $% % ! # $5 ! 21 # 1 ) . ! %. , /: = ! 6'(8" M%)/#/ 22, ! RwG S RwR= ! f,(9!@ =9!" '+69! f=9! [$-9! Z=9! [1(+(+9![=! X=9!d').$+9! X=! a=9! Z'3('9! ?=9! ]$3/-'+9! A=9!>//$+9! d=9! '+/! •,9! B=!CGJGGD=! Y(.() 16(+(1,%! -(/$'.$1+!'+'3 :% $%!1+! (&$6(+1-$2! &.%/!'+/! .) ',-'.$2!%.) (%%!$+! '! &)(/1-$+'+.3 :! '0)$2'+! '-()$2'+! 21#1). =! Y#,'5.;/#/ GJJR= ! 6(( %7&%9/1.'(8/ GJJR= ! !" #$%&'&() " )*(%+* % , 25 ! ! Figure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g ') E! F/ J€g ')G! F/ JD! '+/! Cg ')E! F/ J€g ' )G! ]/ JD! '+/! $+5 '3$/! (3%(8#() (=! "#(! &)1&1%(/! -(.#1/! 21+%.),2.%! '+! tM4XX<*'%(/! /$%%$-$3')$.:! -'.)$H9! &)1T(2.%! 1*%()5 '.$1+%! $+.1! '!.8 1 = ! ! , ! 298 ! ! prea nt i ! ! < ! ! 8 ! ! sample s ! ! = ! ! 310 ! , ! ! mean ! ! NIECC ! ! = ! ! - 0.0 3 ! Ye s ! Subg roup ! ! 3 ! ! CD4 ! ! ( ! ) ! basel ine ! ! >= ! ! , ! 298 ! ! prea nt i ! ! >= ! ! 8 ! ! sample s ! ! = ! ! 368 ! , ! ! mean ! ! NIECC ! ! = ! ! - 0.0 6 ! No ! 28 ) -'./*0%'1#2, 3*1*/4*%, 2006 ! ! Figure) 5 \! C'D! A$%.)$*,.$1+! 10! $+/$ 5$/,'3! $+/$)(2.! .) ('.-(+.! (00(2.%! 21+/$.$1+'3! 1+! 215 ')$'.(%! '2)1%%! .#)((! %,*.:&(%=! 4'2#! &1$+.! )(&)(%(+.% ! '+! $+/$5$/,'3 <3(5 (3! $+/$)(2.! .)('.-(+.! (00(2.! 21+/$.$1+'3! 1+! 215')$'. (%=! L1H (%! $+/$2'.(! .#(! $+.() ;,').$3(! )'+6(! 8$.#! -(/$'+%! %#18+! '%! #1)$O1+.'3! 3$+(%9! '+/! )(/! /$'-1+/%! /(+1.(! %,*6)1,&! -('+%=! "#(! -('+! $+/$)(2.! (00(2.%! ')(! sJ * RQ! 01)! ?,*6)1,&! E9! sJ * JQ! 0 1)! ?,*6)1,&! G9! ' +/! s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

Original Paper

Loading high-quality paper...

Comments & Academic Discussion

Loading comments...

Leave a Comment