Significance tests of differences between two crossing survival curves for small samples

/,+& #,(!,%,0&! #1223#1455# 65478# !"#$%& '()*+,-+.&/3#0-$ 12.+3*$//

!"#$"%"&'$&( )(!)! *% +"%%(,($&(! -().(($

).* &,*!!"$# !/,0"0'1 &/,0(! %*, !2'11

!'231(!

'4567896:#*9:;<;=>#=?=>@A<A#<A#BC?BD:?DE#F<GH#AG9E@<?I#GHD#G<JD#KDGFDD?# D?G:@#GC##

=# AG9E@# =?E# =# A9KADL9D?G# D;D?GM# "<JDNGCND;D?G# <A# BC?A<ED:DE# =A# =# BC?G<?9C9A# ;=:<=K>DM# OHD?# GHD# C9GBCJD# CP# =# AG9E@# <A# GHD# G<JD# KDGFDD?# C?D# D;D?G# =?E# =?CGHD:3# =# ?9JKD:# CP# Q:CK>DJA# B=?# CBB9:3# A9BH# =AR# GHD# E<AG:<K9G<C?# CP# GHD# ;=:<=K>D# GD?EA# GC# KD# 9?S?CF?3# CKAD:;DE#E<AG:<K9G<C?A#=:D#AG:C?I>@#ASDFDE3#JC:D#C;D:#FD#>CAG#GC#PC>>CF#9Q#ACJD#D?G<G<DA# T:<IHG#BD?AC:<?IUM##

"HD# =AADAAJD?G# CP# C;D:=>># HCJCID?D<G@# CP# A9:;<;=># B9:;DA# <A# =# SD@# D>DJD?G# <?# A9:;<;=>#=?=>@A<AM#)DBD?G>@#GHD:D#H=;D#KDD?#ED;D>CQDE#AD;D:=>#GDAGA#GH=G#BCJQ=:D#A9:;<;=># =G#GFC#C:#JC:D#BCHC:GA#DMIM#JCAG#QCQ9>=:#>CIN:=?S#GDAG#=?E#GDAGA#CP#VDH=?3#"=:C?DNO=:D3# WDGCNWDGC3# X=::<?IGC?N/>DJ<?I3# )D?@<NG@QDM# %D;D:GHD>DAA# =# ><GG>D# =GGD?G<C?# <A# E:=F?# GC# BCJQ=:<AC?#CP#=QQ><B=K<><G@#CP#GHDAD#GDAGAM#

"HD# J=<?#IC=>#CP#GH<A#Q=QD:#<A#GC#DY=J<?D#=#AJ=>>NA=JQ>D# BH=:=BGD:<AG<BA#CP#=KC;D# GDAGAM# "HD:D# FD:D# J=ED# =# ;=:<DG@# CP# A<G9=G<C?A# K@# JD=?A# CP# 0C?GD# !=:>C# A<J9>=G<C?AM# O<GH#GHD#=AA9JQG<C?#GH=G#A9:;<;=>#B9:;D#H=A#OD<K9>>#E<AG:<K9G<C?3#GHD:D#FD:D#G=SD?#<?GC# BC?A<ED:=G<C?# E<PPD:D?G# AH=:D# CP# BD?AC:DE# CKAD:;=G<C?A# T:=?ECJ>@# =QQD=:DE# E9D# GC# 9?<PC:J# E<AG:<K9G<C?U# =?E# GHD# =K<><G@# CP# GHDAD# GDAG# GC# EDGDBG# C;D:=>># E<PPD:D?BDA# KDGFDD?# B:CAA<?I#A9:;<;=>#B9:;DAM##

;<= >?7@5A# *9:;<;=># =?=>@A<A3# !D?AC:<?I3# !:CAA<?I# A9:;<;=># B9:;DA3# *G=G<AG<B=>#

QCFD:3#(PPDBG<;D#A=JQ>D#A<ZD#

": "$),*+/&)"*$ #

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

######################################## ###################

[#WH-3#-DQ=:GJD?G#CP#*G=G<AG<BA3#$?<;D:A<G@#CP#VE=\AS3#]9:S<DF<BZ^FZ:M9IMDE9MQ>M# [[#WH-3#-DQ=:GJD?G#CP#*G=G<AG<BA3#$?<;D:A<G@#CP#VE=\AS3#F@B<?S=^FZ:M9IMDE9MQ>M#

"HD#=<J#CP##GH<A#=:G<B>D#<A#=#BCJQ=:<AC?#CP##GHD#QCFD:#CP#ACJD# GFC#A=JQ>D# GDAGA# JCAG# :DBCJJD?EDE# <?# ><GD:=G9:DM# OD# PCB9ADE# C?# PC9:# A<G9=G<C?A# GH=G# ;D:@# CPGD?#CBB9:#<?#:D=>#E=G=#AG9E<DA#=?E#<?#FH<BH#GHD#QCFD:#=?E#CGHD:#BH=:=BGD:<AG<BA# CP#BCJQ=:DE#GDAGA#B=?#E<PPD:R#

W:CK>DJ# 5R# BCJQ=:<AC?# CP# AJ=>># A=JQ>D# Q:CQD:G<DA# CP# GFC# A=JQ>D# GDAGA# TA=JQ>D#A<ZDU#

W:CK>DJ# 1R# GHD# DPPDBG# CP# <?B:D=A<?I# ?9JKD:# CP# BD?AC:DE# CKAD:;=G<C?A# C?# Q:CQD:G<DA#CP#GDAGA###

W:CK>DJ# aR# GHD# =K<><G@# CP# GDAGA# GC# EDGDBG# C;D:=>># E<PPD:D?BDA# KDGFDD?# ?C?N B:CAA<?I#A9:;<;=>#B9:;DA####

W:CK>DJ#bR#GHD#=K<><G@#CP#GDAGA#GC#EDGDBG#C;D:=>>#E<PPD:D?BDA#KDGFDD?#B:CAA<?I# A9:;<;=>#B9:;DA#FHD?#GHD#B:CAA<?I#QC<?G#BH=?IDA#######

"C#D;=>9=GD#GHD#QD:PC:J=?BD#CP#GHD#BCJQ=:DE#GDAGA3#0C?GD#!=:>C#A<J9>=G<C?A# FD:D# B=::<DE# C9G# GC# AG9E@# GHD# AG=G<AG<B=># QCFD:# =?E# G@QD# &# D::C:# 9?ED:# =# ;=:<DG@# A<G9=G<C?AM#

"": 1")(,')/,( !)/+"(! #

&G# <A# AG:DAADE# <?# ><GD:=G9:D# GH=G# GHD# >CIN:=?S# GDAG# H=A# CQG<J=># >CB=># QCFD:# GC# EDGDBG# E<PPD:D?BDA# <?# GHD# H=Z=:E# :=GDA3# FHD?# GHD# H=Z=:E# :=GDA# =:D# Q:CQC:G<C?=># 6c>D<?3#0CDABHKD:ID:#5dd73#QM#1445e#*<9#=?E#=>>#144b3#QM#12d8M#OHD?#GH<A#GDAG#<A# =QQ><DE#GC#A=JQ>DA#P:CJ#QCQ9>=G<C?A#FHD:D#GHD#H=Z=:E#:=GD#B:CAA3#GHDAD#GDAGA#H=;D# ><GG>D#QCFD:#KDB=9AD#D=:>@#E<PPD:D?BDA#<?#P=;C:#CP#C?D#I:C9Q#=:D#B=?BD>DE#C9G#K@# >=GD#E<PPD:D?BDA#<?#P=;C:#CP#GHD#CGHD:#G:D=GJD?GM#*BH9J=BHD:#T5d`bU#=?E#/>DJ<?I# T5d`7U# BC?E9BGDE# A<J9>=G<C?A# =?E# BC?B>9EDE# GH=G# PC:# ?C?# Q:CQC:G<C?=># C:# B:CAA<?I# H=Z=:EA# GHD# )D?@<# GDAG# ADDJA# GC# QD:PC:J# J9BH# KDGGD:# GH=?# 9A9=># >CIN :=?S# GDAG#PC:#><IHG#BD?AC:<?I# 6*G=K>D<?3#cC9G:C9;D><A# 5d`28M# !:=JD:# ;C?# 0<AADA# GDAG# =?E# GNGDAG# FD:D# Q:CQCADE# =A# C?DA# F<GH# I:D=GD:# QCFD:# GC# EDGDBG# B:CAA<?I# H=Z=:E#:=GDA#GH=?#O<>BCYC?#G@QD#GDAGA#6c>D<?3#0CDABHKD:ID:#5dd73#QM#15b8M##

""": )(!)! %*, ).* !/,0"0'1 &/,0(! #

OD#BCJQ=:DE#GHD#QCFD:#CP#PC9:#I:C9QA#CP#GDAGA#PC:#GFC#A9:;<;=># B9:;DAM#&?# GHDAD#GDAGA#GHD#?9>>#=?E#=>GD:?=G<;D#H@QCGHDA<A#=:D#PC:J9>=GDE#=AR#

X4R# 5T4U#f# 1T4U#f#MMM#f# 5T4U##PC:#=>>#4#g#!# X5R +T4U#"# 6T4U##PC:#=?@#4#g#!#

/<:AG# I:C9Q# FD:D# O<>BCYC?# G@QD# GDAGA# TO<>BCY# &jkU3# GHD@# =:D# K=ADE# C?# FD<IHGDE# BCJQ=:<AC?A# CP# GHD# H=Z=:E# :=GDA# <?# GFC# I:C9QAR# 1₅

1 1 _l U '=:T U T # # 86 ₇ 8 $ ! ! 3# FHD:D#

%

# & & ' ( ) ) * + , # 9 + + + +6 +6 + 6 : ; : ; 4 1 8 5 1_{T!U T U 3#}

%

# &&' ( )) * + , , && ' ( )) * + , # 9 + + + + + +6 + +6 + : ; : : : : : 4 1 5 1 5 5 U T U '=:T! M## '=>9D#CP#GHD#AG=G<AG<B#=?E#A9KADL9D?G>@#GHD#BH=:=BGD:<AG<BA#CP#GHD#GDAG#EDQD?EA# C?# GHD# S<?E# CP# GHD# BHCAD?# FD<IHG# P9?BG<C?# 6h>CAAFD>E3# VC>ABH3# )CHFD:# 14473# QM#7dj`58M# *D>DBG<C?# CP# E<PPD:D?G# FD<IHGA# >D=EA# GC# TADD# G=K>D# 5UR# >CIN:=?S# GDAG# TO<>BCYC?# 5U3# VDH=?# GDAG# TO<>BCYC?# 1U3# "=:C?DNO=:D# GDAG# TO<>BCYC?# aU3# WDGCN WDGC# GDAG# TO<>BCYC?# bU3# JCE<P<DE# WDGCNWDGC# GDAG# TO<>BCYC?# 2U3# X=::<?IGC?N />DJ<?I#GDAG#F<GH#Qf4#=?E#Lf5#TO<>BCYC?#mU3#X=::<?IGC?N/>DJ<?I#GDAG#F<GH#Qf5# =?E#Lf4#TO<>BCYC?#7U3#X=::<?IGC?N/>DJ<?I#GDAG#F<GH#Qf5#=?E#Lf5#TO<>BCYC?#`U3# X=::<?IGC?N/>DJ<?I# GDAG# F<GH# Qf432# =?E# Lf432# TO<>BCYC?# dU3# X=::<?IGC?N />DJ<?I#GDAG#F<GH#Qf432#=?E#Lf1#TO<>BCYC?#54U#6*9B<9#=?E#=>>#T144bU8M#

*DBC?E#I:C9Q#CP#GDAGA#=:D#)D?@<#G@QD#GDAGA#T)D?@<#55j14U#GH=G#=:D#BD?AC:DEN E=G=#=?=>CIC9A#CP#GHD#cC>JCIC:C;N*J<:?C;#AG=G<AG<BAM# <#f#A9Qno84o3#4#-#!pq.T!U3#

FHD:D#

%

- &&' ( )) * + , # ! * 4 * * *: *: * 4 : ; : ; 4 1 8 T U 3#

%

- , , # ! ! . * 4 * * * * * * * * * ; : ; : : : : : 4 1 5 U T U T 1 5 1 1 _M# "HD#;=>9D#CP#GHD#AG=G<AG<BA#=>AC#EDQD?EA#C?#GHD#BHCAD?#FD<IHG#P9?BG<C?M#"HD# ADG#CP#GHD#FD<IHG#P9?BG<C?A#<A#GHD#A=JD#=A#PC:#GHD#O<>BCYC?#G@QD#GDAGAM## # "=K>D#5M#OD<IHG#P9?BG<C?A#PC:#O<>BCYC?#=?E#)D?@<#G@QD#GDAGA# %C# "DAG# OD<IHG#1T4+U# &###k&# +CIN)=?S# 5# &&###k&&# VDH=?# :+ &&&###k&&&# "=:C?D#j#O=:D# T:+U4M2# &'###k'&# WDGCNWDGC# T U l + 4 = #FHD:D#

/

- 0 & ' ( ) * + , # 4 4 : ; + + + + 4 = 5 5 U T l # '###k'# 0CE<P<DE#WDGC#j#WDGC# =lT4₊U3:₊q

1

:₊05

2

# '&###k'&# X=::<?IGC?N/>DJ<?I#> f#43#? f#5# 5#j#=rT4_+,5U# '&&###k'&&# X=::<?IGC?N/>DJ<?I#> f#53#? f#4# =rT4_+,5U# '&&&###k'&&&# X=::<?IGC?N/>DJ<?I#> f#53#? f#5# =rT4_+,5UT5#j#=rT4_+,5UU# &k###k&k# X=::<?IGC?N/>DJ<?I#> f#4M23#? f#4M2# =rT4_+,5U4M2T5#j=rT4_+,5UU4M2_# k###kk# X=::<?IGC?N/>DJ<?I > f#4M23#? f#1# =rT4_+,5U4M2T5#j=rT4_+,5UU1# *C9:BDR#h>CAAFD>E3#VC>ABH3#)CHFD:#14473#QM#7dj`5M#

0C:DC;D:#FD#GCCS#<?GC#BC?A<ED:=G<C?##!:=JD:#;C?#0<AADA#GDAG#T!:=J0<ADAU# =?E# GN*G9ED?G# ID?D:=><ZDE# GDAG#TGN*G9EUM# !:=JD:# ;C?# 0<AADA#GDAG#<A# K=ADE# C?#GHD# <?GDI:=GDE3#AL9=:DE#E<PPD:D?BD#KDGFDD?#GHD#GFC#DJQ<:<B=>#A9:;<;=>#P9?BG<C?AR## # # #

%

4

5

4

5

-, 0 6 , 6 _, # ! + + + + 4 + + 4 3= 4 4 4 @ 4 @ 3 < T U T ₅U 1 U T 5 U T r U T r 1 1 1 5 _3### # FHD:DR

%

-# 6 ! + 4 +6 +6 + 6 : ; 4 U T r ₃

%

7 , # 4 4 +6 +6 +6 + 6 + : : ; 4 = U 5 T U T

1 _3#@T4+U#f#3=1_T4+UqT5#s#3=1_T4+UU3#

=1T4+U#f#=51T4+U#s#=11T4+UM##

"HD#GN*G9ED?G#GDAG#<A#=#BD?AC:DE#E=G=#;D:A<C?#CP#GHD#GDAG#PC:#GHD#E<PPD:D?BD#<?# A=JQ>D#JD=?A#KDGFDD?#GHD#GFC#QCQ9>=G<C?AR## # # # 1 3 5 .5A 1 8 # 3## FHD:DR#

4

5

4

5

%

, # 0 , , # 5 5 1 5 5 1 5 _{T U} r_{T U} r _{T U} 9 + + + + + + 5A 4 4 -4 = 4 = 4 3 3 3 1 3#

4

5

%

, # , , , , , , , 0 # 5 5 1 3 5 5 1 3 5 5 1 5 5 5 1 1 5 5 5 5 1 3 5 1 3 5 1 1 1 3 5 r T U r T U U T r U T r U T r U T r U T r U T r 9 + + + + + + + + + + _{= 4 = 4} 4 B 4 B 3 4 B 3 4 B 3 4 = 4 = @ . 3

4

5

%

, # 0 , # 5 ₅ T Ur₅₃₁T U 9 + * * * * * + 4 4 -4 = 4 @ M# # "H<A#GDAG#<A#K=ADE#C?#c=Q>=?N0D<D:#DAG<J=GC:A#<?#GFC#A=JQ>DA3#GHD#QCQ9>=G<C?# JD=?A# =:D# B=>B9>=GDE# K@# GHD# =:D=# 9?ED:# GHD# c=Q>=?N0D<D:# B9:;DA# 6c>D<?3# 0CDABHKD:ID:#5dd73#QM#5d5j1148M#

"0: 3,*&(+/,( *% )B( 2*$)( &',1* '$'1C!"! #

"HD# QD:PC:J=?BD# CP# GHD# BCJQ=:DE# GDAGA# F=A# D;=>9=GDE# C?# GHD# K=A<A# CP# QAD9EC:=?ECJ# E=G=# TW)%VAU# ID?D:=GDE# K@# <?;D:A<C?# JDGHCE# P:CJ# OD<K9>># E<AG:<K9G<C?# F<GH# E<PPD:D?G# Q=:=JDGD:AM# &?# D=BH# CP# 544M444# A<J9>=G<C?# DYQD:<JD?GA#GFC#:=?ECJ#<?EDQD?ED?G#A=JQ>DA#CP#A<ZD#35#f#31#FD:D#ID?D:=GDEM#,?#

AG=G<AG<BA# F=:D# B=>B9>=GDEM#"HD# DAG<J=GDE# AG=G<AG<B=># QCFD:# F=A# B=>B9>=GDE# =A#GHD# P:=BG<C?#CP#A=JQ>DA#<?#FH<BH#FD#:D]DBG#GHD#?9>>#H@QCGHDA<A#=G#4M453#4M42#=?E#4M54# A<I?<P<B=?BD#>D;D>M##

OD#9AD#PC>>CF<?I#ADGA#CP#Q=:=JDGD:A#<?#A<J9>=G<C?AR#

/C:# Q:CK>DJ# 5R# E<AG:<K9G<C?A# j# 5AG# OD<K9>>T5e5U3# 1?E# OD<K9>>T5e5U# T?9>># H@QCGHDA<A# G:9DUe# A=JQ>DA# A<ZDR# 523# 143# a43# b43# MMM3# 544# BCJQ>DGDE# s# 14t# BD?AC:DEM#

/C:#Q:CK>DJ#1R#E<AG:<K9G<C?A#j#5AG#OD<K9>>T5e5U3#1?E#OD<K9>>T1e#nMm3#53#5MbpU# T?9>># H@QCGHDA<A# P=>ADUe# A=JQ>DA# A<ZD# a4# BCJQ>DGDE# s# 14t3# b4t3# m4t3# `4t3# 544t3#524t3#144t#BD?AC:DEM#

/C:# Q:CK>DJ# aR# E<AG:<K9G<C?A# j# 5AG# OD<K9>>T5e5U3# 1?E# OD<K9>>Tn53# 5M53# MMM3# 1M2pe#5U#T?9>>#H@QCGHDA<A#P:CJ#G:9D#GC#P=>ADUe#A=JQ>DA#A<ZD#a4# BCJQ>DGDE#s#14t# BD?AC:DEM#

/C:# Q:CK>DJ# bR# E<AG:<K9G<C?A# j# 5AG# OD<K9>>T5e5U3# 1?E# OD<K9>>T1e# nMa3# M23# MMM3# aM5pU#T?9>>#H@QCGHDA<A#P=>ADUe#A=JQ>DA#A<ZD#a4#BCJQ>DGDE#s#14t#BD?AC:DEM#

0: (23","&'1 !)/+C ,(!/1)! #

/<:AG>@#FD#ID?D:=GDE#CKAD:;=G<C?A#PC:#GFC#A=JQ>DA#F<GH#GHD#A=JD#E<AG:<K9G<C?# TOD<K9>>T535UU#=?E#CKAD:;DE#GHD#BH=?IDA#<?#GHD#E<PPD:D?BD#KDGFDD?#CKAD:;DE#=?E# DYQDBGDE# QN;=>9D# <?# =# A<G9=G<C?# GH=G# A=JQ>D# A<ZD# I:CFA# F<GH# GHD# P<YDE# AH=:D# CP# BD?AC:DE# E=G=M# "HD# KDAG# BH=:=BGD:<AG<BA# PC:# AJ=>># A=JQ>DA# # H=E# O<>BCYC?# GDAGA# TF<GH# FD<IHGA# 5j2U3# O<>BCYC?# GDAG# F<GH# FD<IHGA# mj54# FD:D# L9<BS>@# <JQ:C;<?I# GHD<:#BH=:=BGD:<AG<BA#F<GH#GHD#I:CFGH#CP#A=JQ>D#A<ZDM#,GHD:#GDAGA#:D;D=>DE#GC#H=;D# J9BH#FC:AD#BH=:=BGD:<AG<BAM#&?#GH<A#J=GGD:#C9:#CKAD:;=G<C?A#FD:D#BC?A<AGD?G#F<GH# CGHD:# DJQ<:<B=># AG9E<DAM# *9KADL9D?G>@# FD# DY=J<?DE# GHD# QCFD:# CP# GDAGA# <?# =#A<G9=G<C?#GH=G#FD#E:CF?#A=JQ>DA#P:CJ#GFC#E<PPD:D?G#QCQ9>=G<C?A##TOD<K9>>#T535U# =?E# OD<K9>># T134MmU# FHD:D# :D=># A9:;<;=># B9:;DA# B:CAA# <?# GHD<:# KDI<??<?IAM# "HD# I:D=GDAG# QCFD:# PC:# AJ=>># A=JQ>DA# H=E# KCGH# O<>BCYC?# =?E# )D?@<# GDAGA# F<GH# FD<IHGA# ?9JKD:# m# =?E# 543# AC# FD# B=?# BC?B>9ED# GH=G# <?# GH<A# A<G9=G<C?# JCAG# <JQC:G=?G# P=BGC:# <?# GHD# GDAG# AG=G<AG<B# <A# S<?E# CP# FD<IHG# P9?BG<C?M# O<>BCYC?# GDAGA## &&j'# EC# ?CG# <JQ:C;D# GHD<:# QCFD:# D;D?# <P# GHD# ?9JKD:# CP# <GDJA# <?# GHD# A=JQ>D# <?B:D=ADAM#)DAG#CP#GHD#DY=J<?DE#GDAGA#FD:D#<JQ:C;<?I#GHD<:#BH=:=BGD:<AG<BA#=A#GHD# A=JQ>D#A<ZD#FD:D#I:CF<?I#C?>@#K@#=EE<G<C?#CP#BD?AC:DE#CKAD:;=G<C?A#T/<I9:D#5UM#

&?# GHD# A<G9=G<C?# GH=G# GFC# B9:;DA# B:CAA# B>CAD# GC# GHD# JDE<=?# ;=>9D# =>># CP# GHD# GDAGA#TDYBDQG#!:=JD:#;C?#0<AADA#GDAGU#H=E#GHD#BCJQ=:=K>D#QCFD:#=?E#:D=BG#F<GH# GHD#A=JD#:=GD#PC:#<?B:D=AD#<?#?9JKD:#CP#BD?AC:DE#CKAD:;=G<C?A#TP<I9:D#1UM#

OHD?# GFC# A9:;<;=># B9:;DA# B:CAA# B>CAD# GC# GHD# D?E# CP# GHD# B9:;D# GHD# KDAG# Q:DE<BG<;D#QCFD:#H=;D#O<>BCYC?#GDAGA#=?E#)D?@<#GDAG#F<GH#FD<IHGA#5j2#=?E#73#GHD# FD=SDAG#=K<><G<DA#H=E#GDAGA#F<GH#FD<IHG#m#=?E#54#T/<I9:D#aUM###

434 435 431 43a 43b 432 43m 437 43` 43d 534 a4sm a4s51 a4s5` a4s1b a4sa4 a4sb2 a4sm4 # /<I9:D#5M#WCFD:#CP#GHD#GDAGA#PC:#BCJQ=:<AC?#CP#GHD#GFC#A=JQ>DA#E:DF#P:CJ#OD<K9>>T535U## =?E#OD<K9>>T13#4MmU#T8f4345U# # *C9:BDR#CF?#D>=KC:=G<C?M# # 434 435 431 43a 43b 432 43m 437 43` 43d 534 a4sm a4s51 a4s5` a4s1b a4sa4 a4sb2 a4sm4 # /<I9:D#1M#WCFD:#CP#GHD#GDAGA#PC:#BCJQ=:<AC?#CP#GHD#GFC#A=JQ>DA#E:DF#P:CJ#OD<K9>>T535U## =?E#OD<K9>>T13#5U#T8f4345U# # *C9:BDR#CF?#D>=KC:=G<C?M# # 434 435 431 43a 43b 432 43m 437 43` 43d 534 a4sm a4s51 a4s5` a4s1b a4sa4 a4sb2 a4sm4 # /<I9:D#aM#WCFD:#CP#GHD#GDAGA#PC:#BCJQ=:<AC?#CP#GHD#GFC#A=JQ>DA#E:DF#P:CJ#OD<K9>>T535U## =?E#OD<K9>>T13#5MbU#T8f4345U# # *C9:BDR#CF?#D>=KC:=G<C?M#

/<?=>>@#FD#BCJQ=:DE#GDAGA#PC:#GHD#=K<><G@#CP#EDGDBG<C?#CP#E<PPD:D?BDA#KDGFDD?# ?C?#B:CAA<?I#A9:;<;=>#P9?BG<C?AM#"C#CKG=<?#GH<A#:DA9>G#FD#E:DF#A=JQ>DA#P:CJ#GFC# OD<K9>># E<AG:<K9G<C?A# F<GH# GHD# A=JD# AH=QD# Q=:=JDGD:# =?E# E<PPD:D?G# AB=>D# Q=:=JDGD:M#&?#GH<A#A<G9=G<C?#GHD#I:D=GDAG#QCFD:#H=E#O<>BCYC?#GDAG#F<GH#FD<IHG#5# =?E#GHD#QCC:DAG#C?D#!:=JD:#;C?#0<AADA#GDAG#TP<I9:D#bUM#### # 434 435 431 43a 43b 432 43m 437 43` 43d 534 534 535 531 53a 53b 532 53m 537 53` 53d 134 135 131 13a 13b 132 !:=J0<ADA GuAG9E F<>BCYu5 F<>BCYu1 F<>BCYua F<>BCYub F<>BCYu2 434 435 431 43a 43b 432 43m 437 43` 43d 534 534 535 531 53a 53b 532 53m 537 53` 53d 134 135 131 13a 13b 132 !:=J0<ADA GuAG9E F<>BCYum F<>BCYu7 F<>BCYu` F<>BCYud F<>BCYu54 # 434 435 431 43a 43b 432 43m 437 43` 43d 534 534 535 531 53a 53b 532 53m 537 53` 53d 134 135 131 13a 13b 132 !:=J0<ADA GuAG9E :D?@<u5 :D?@<u1 :D?@<ua :D?@<ub :D?@<u2 434 435 431 43a 43b 432 43m 437 43` 43d 534 534 535 531 53a 53b 532 53m 537 53` 53d 134 135 131 13a 13b 132 !:=J0<ADA GuAG9E :D?@<um :D?@<u7 :D?@<u` :D?@<ud :D?@<u54 # /<I9:D#bM#WCFD:#CP#GHD#GDAGA#PC:#BCJQ=:<AC?#CP#GHD#GFC#A=JQ>DA#E:DF#P:CJ#OD<K9>>T535U## =?E#OD<K9>>TY3#5U#T8f4345U# # *C9:BDR#CF?#D>=KC:=G<C?M# 0": &*$&1/!"*$! #

A# FD# BC9>E# DYQDBG# PC:# Q:CQC:G<C?=># H=Z=:E# QCQ9>=G<C?A# KDAG# QD:PC:J=?BD# H=E# O<>BCYC?# G@QD# GDAGA3# DAQDB<=>>@# GHCAD# F<GH# FD<IHGA# 5j2M# "HDAD# GDAGA# >CCAD# GHD<:#QCFD:#<?#GHD#A<G9=G<C?#CP#B:CAA<?I#A9:;<;=>#B9:;DAM#!:CAA<?I#QC<?G#H=A#I:D=G# <?P>9D?BD# C?# GHD# QCFD:# CP# Q=:G<B9>=:# GDAGAM# # O<>BCYC?# =?E# )D?@<# GDAG# Tb3m354U# H=;D#GHD#I:D=GDAG#QCFD:#GC#EDGDBG#D=:>@#G<JD#B:CAA<?IA#=?E#!:=JD:3#)D?@<#Ta37U# H=;D# GHD# I:D=GDAG# QCFD:# GC# EDGDBG# >=GD# B:CAA<?IAM# >># CP# GHD# =?=>@ZDE# GDAGA# H=E# BCJQ=:=K>D# QCFD:# <?# =# A<G9=G<C?# CP# B:CAA<?I# QC<?G# =:C9?E# GHD# JDE<=?# ;=>9DM# /:CJ# #:DA9>GA#CP##A<J9>=G<C?A#<G#B=?#KD#E:=F?#GHD#BC?B>9A<C?#GH=G#GHD#BHC<BD#CP#

FD<IHG#P9?BG<C?#H=A#GHD#I:D=G#<?P>9D?BD#C?#GHD#GDAG#QCFD:#<?#Q=:G<B9>=:#A<G9=G<C?M# QQ:CQ:<=GD# 9AD# CP# GDAGA# PC:# GFC# A9:;<;=># B9:;DA# :DL9<:D# Q:<C:# :DBCI?<G<C?# CP## =# G@QD# CP# E<PPD:D?BDA3# <MDM# K@# Q>CGG<?I# c=Q>=?N0D<D:# A9:;<;=># B9:;DA# 6BCJQ=:DR# *9B<9#=?E#=>>3#144bM3#QM#1m44j1m58M##

,(%%(,($&(!

#

h=><BS<# M#T144mU#=()7+7$: $3$:2%+% $3; :+C, 4$D:,%3#WO(3#O=:AZ=F=#T<?#WC><AHU#

hD?DEDGG<#_M#=?E#=>>#T5d`1U#0CC,.4+7, %$#>:, %+&, C") 4,%4% "C .,3%"),; %()7+7$: ;$4$3#h<CJDG:<BA#;C>M#md# h>CAAFD>E#X3#VC>ABH#cM3#)CHFD:#VM#T1447U#07,34 E+%4")2 $3$:2%+%3#+=F:D?BD#(:>K=9J# AACB<=GDA#

W9K><AHD:A3#+C?EC?#

c>D<?#<#0CDABHKD:ID:#0M#T5dd7U#=()7+7$: @3$:2%+%3#*Q:<?ID:N'D:>=I3#%DF#vC:S#

+<?# k3# O=?I# XM# T144bU# @ F,- !,%4+3G @>>)"$.E C") H"#>$)+3G 4E, I7,)$:: J"#"G,3,+42 "C

=()7+7$: H()7,%3#h<CJDG:<B=>#_C9:?=>#bm#

+CI=?#hM3#c>D<?#_M3#.H=?I#0M#T144`U#H"#>$)+3G !),$4#,34% +3 4E, K),%,3., "C H)"%%+3G =()7+7$:

H()7,%L @3 @>>:+.$4+"3 4" M"3, A$))"- !)$3%>:$34$4+"33#h<CJDG:<BA#mb#

*G=K>D<?# -M3# cC9G:C9;D><A# &M# T5d`2U# @ !-"N=$#>:, 4,%4 =,3%+4+7, 4" H)"%%+3G J$&$);% +3

O3.,3%"),; $3; =+3G:2 H,3%"),; 9$4$3#h<CJDG:<BA#b5#

*9B<9# VM3# +DJDAHCF# *3# 0CDABHKD:ID:# 0# T144bU# =4$4+%4+.$: !,%4% "C 4E, 0?($:+42 "C =()7+7$:

H()7,%L P,."3%+;,)+3G $3; I>4+"3%3# =GR# hD>=S:<AH?=?# %M3# )=C# !M)M# @;7$3.,% +3 =()7+7$: @3$:2%+%3#(>AD;<D:#

#

!"#$%& '()*+,-+.&3#0-$ 12.+3*$

)(!)C "!)*)$*D&" ,EF$"& +.E&B ;,GCF/HI&C&B !"J ;,GC.C&B 3,G(FC&"' . 2'KC&B 3,E-'&B

#

# ?=><Z=#Q:ZDw@B<=#GC#ZDAQxy#JDGCE#Ay9wzB@BH#EC#JCED>CF=?<=#BZ=A9#G:F=?<=#SCHC:G@3# SGx:D]# ]DE?CAGS<# Az# CKAD:FCF=?D# CE# ZEDP<?<CF=?DIC# JCJD?G9# QCBZzGSCFDIC# EC# ZEDP<?<CF=?DIC# ZE=:ZD?<=#SC\BCFDICM#!Z=A#G:F=?<=#]DAG#G:=SGCF=?@#]=SC#ZJ<D??=#>CACF=#B<zIy=M#*QDB@P<S=#JDGCE# =?=><Z@#Q:ZDw@B<=#ZF<zZ=?=#]DAG#Z#F@AG{QCF=?<DJ#CKAD:F=B]<#BD?Z9:CF=?@BH#T9B<{G@BHU#C:=Z#G@J3# <w#P9?SB]D#I{AGC|B<#CKAD:FCF=?D]#ZJ<D??D]#Az#BZ{AGC#?<DZ?=?D3#=#:CZSy=E@#A<>?<D#=A@JDG:@BZ?D3#BC# 9?<DJCw><F<=#AGCACF=?<D#JDGCE#S>=A@BZ?D]#AG=G@AG@S<M#

# WCEAG=FCFz# P9?SB]z# AGCACF=?z# F# =?=><Z<D# Q:ZDw@B<=# ]DAG# P9?SB]=# E=>AZDIC# G:F=?<=# F@:=w=]zB=# Q:=FECQCECK<D\AGFC3# wD# ]DE?CAGS=# ?<D# EC|F<=EBZ@# ZE=:ZD?<=# SC\BCFDIC# Q:ZDE# BZ=ADJ# 4M# 0DGCEz# CBD?@3# BZ@# QDF?D# ZJ<D??D# J=]z# FQy@F# ?=# Z:xw?<BCF=?<D# BZ=A9# G:F=?<=# ]DE?CAGDS3# ]DAG# Q:ZDQ:CF=EZ=?<D# GDAGxF# QC:xF?9]zB@BH# S:Z@FD# Q:ZDw@B<=# # ?=# QCEAG=F<D# EFxBH# T>9K# F<{BD]# Q:xKUM# .?=BZ?=# ><BZK=# G@BH# GDAGxF# ZCAG=y=# Z=Q:CQC?CF=?=# F# CAG=G?<BH# >=G=BH3# F# G@J# GDAG@R# +CIN:=?S3# K{EzB@# ]DE?@J# Z# >9K#?=]QCQ9>=:?<D]AZ@J3# GDAG# VDH=?=3# "=:C?DNO=:D3# WDGCNWDGC3# X=::<?IGC?=N/>DJ<?I=3# GDAG@# G@Q9# )D?@<M# O# ><GD:=G9:ZD# J=yC# 9F=I<# QC|F<{B=# A<{# ]DE?=SwD# QC:xF?=?<9#Fy=A?C|B<#G@BH#GDAGxFM#

# O# QC?<wAZ@J# CQ:=BCF=?<9# Q:ZDQ:CF=EZC?C3# Q:Z@# F@SC:Z@AG=?<9# JDGCE@# 0C?GD# !=:>C3# =?=><Z{# QC:xF?=FBZz# JCB@# Q:DE@SB@]?D]# GDAGxF# E>=# EFxBH# S:Z@F@BH# Q:ZDw@B<=# F# J=y@BH# Q:xK=BH#Z#:xw?@J#9EZ<=yDJ#]DE?CAGDS#BD?Z9:CF=?@BHM#+CACF=?C#Q:xK@#Z#QCQ9>=B]<#C#Z=yCwC?@J# :CZSy=EZ<D#OD<K9>>=#Q:Z@#:xw?@BH#Q:CQC:B]=BH#]DE?CAGDS#SCJQ>DG?@BH#<#BD?Z9:CF=?@BH#TC#>CACFD]# SC>D]?C|B<#QC]=F<=?<=#A<{#9AG=>=?D]#F#CQ=:B<9#C#:CZSy=E#]DE?CAG=]?@U#F#BD>9#CS:D|>D?<=#DPDSG@F?D]# F<D>SC|B<# Q:xK# E>=# QCAZBZDIx>?@BH# GDAGxFM# *ZBZDIx>?z# F=I{# QC|F<{BC?C# Q:CK>DJCF<# S:Z@wCF=?<=#A<{#S:Z@F@BH#Q:ZDw@B<=#<#ZEC>?C|B<#GDAGxF#EC#F@S:@F=?<=#:xw?<B#J<{EZ@#S:Z@F@J<# Q:ZDw@B<=#F#G=S<D]#A@G9=B]<M##