current statistical methods for mortality (failure … · tape of the presentation can be obtained...

51
CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE TIME) DATA TEACHING SESSION JOHN D. KALBFLEISCH University of Waterloo Waterloo, Ontario N2L 3Gl The following pages contain copies of the overhead trans- parencies used in Dr. Kalbfleisch's presentations. An audio tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds .. University of Waterloo. -327-

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Page 1: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

CURRENT STATISTICAL METHODS FOR MORTALITY

(FAILURE TIME) DATA

TEACHING SESSION

JOHN D. KALBFLEISCH

University of Waterloo Waterloo, Ontario

N2L 3Gl

The following pages contain copies of the overhead trans­parencies used in Dr. Kalbfleisch's presentations. An audio tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds .. University of Waterloo.

-327-

Page 2: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

Cu~t~6111T S'-.Ansntl'(. 11~11+c>DS

FO/t Hdii..TIIU1Y (FI+I~fiU TIH~) bATA·

p.,, ~·sc. ~ I. E STI/'1 A T.4 '"~"' 01' DISTAl ~,: T 1;.,,~ !

T AAIIl l-. -Re ~~~e,vc;e~:

I< A&.ISFc.eiStll ., P~•N Tit~ (,•,.> T~ ~+al#h'cJ A,..t.,sls

of hn .. ,, -,-,·"'~ D"ta, Wif•y

J.AW~ ss C "' tl J S +-.1-; J ,.,.<•l 11 «At Is -. 11 e t~ o i. s (o .,.. J,.,•lt HM/1\t ~fa. J w; w '1

C'oll~b.£. lt-.~1.) l(~~.,~~si~ Hodtlra ~ L..iffl T(l.lole ~ c w 1 tt.. ~i r-t,. ss ; P\) ~ ~ ~ s a ~ , , ~ .. , "'o

-328-

Page 3: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

C.tfi~N A

P••A. " . . i:.o ,.,. s ,,., ,, ' ,,, lfO ,,,

.z. 0' a. of .Ill .114. &.1.0 l&~ ~\0 Z.''f &¥-. I.C.S" 3o¥ ~.!\t:

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R t Gr H'T t.fftl SoR lNG- - V E It y ~oltf~tllfl

H47?IOI)S l'tosr lfCUNI¥o•lf.'1"~ TillS.

-329-

Page 4: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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A'e. pr··~ ~ro.py 0• Jto 1~:1'' Ct ttl +., f -t oer.fo,""•,.ce sha.+M.s.

-330-

Page 5: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

A u6c..e.cAn o ~.·"~ l~srs. -lOll IO,Cf+

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re lo. te fQ.; l~re V'"tA tt. +o C.ufft11 t · a~ d..

P·'w ,· O'-l \ v" lw 1 s of i-t tL

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Page 6: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

F AII.IJ~~ "'"''I 4~ ANY (JAI~ Ill" Sllll~ltlff.

'0•~~£/l.IAJT rY~4S.

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How do w~ ~nsfruc.t C.o1ult~tt&ct J-tt~dt.ls ?

How dot..s fv'e«+ wtt"'t (or o~..- ~ ',) o. fftc.:t­

fa; ft.tt.e (fA. fe "t o-f o"• +y pe. ?

-332-

Page 7: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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-we.ay be. lrtffrest~d i)\ fe(att""~ (AtL

of ~H- Qtk s +o {f.,.) po lf~Ah·~ lei« Is.

or fo reee"t his+o-ry d f 4tto.ttcs.

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11 ~ l+ipl.e r~A/Iu.~~ T'f pt s.

H•th'p·l<t. Fa,·lu.~e l/mts.

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Page 8: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Suf"Vivor Func:.+\cf")\. ( Re.l&a.bi li~y F~)\ch'<M)

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Page 9: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

T (A~so~uTeLV) CoNTINuoos.

fl-f> = - ;t Slt>

: /,'W\ prtTE- [t-,t-tAt)} /4t ~t-'>o+

HA!AitD FuNCTION (i"St4Mttuuovs fcdLuft red~, force. o t: ~art c..t1+1)

Att): /t'IK pr ~T'f[t-,t--t•t)IT~t}/4t' ~t-')o+

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T 1\~~t\ ~ lf) ChAt"tAc+e,i!tS t'ke

~i~tt>e'bk+io~ of T.

[f'tt) = ..\ lt) $1-t) .1

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Page 10: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

(J) ~~~tr6s 5EIJtJ~Ifl'1114-t- IJVr~APtt.erAnoAI

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Page 11: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

J. IFf_ IS A SEQVeWCE.

OF BE.f<.I/OUI.Ll -rtriALS

/ ,

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Page 12: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 13: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 14: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

!He KAPLAN ltcJCI( ( PRotJtJt:r L1111r) E s ,,HAT~

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Page 15: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 16: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 17: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 18: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 19: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Dis ~rt fe ( ~ro"'ptd) fC4.&lwf( fiw.e do. ta.. Ce"s•"'"~ Ot~ • ._ct .,f iMftrvals.

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Page 20: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 21: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

- llU•w !•a.,tf·l{t'cafi~ o-f .. ,,.,~.:• ASSeCA'wf•4 ""''H.. v-uiu~r s"•fJ"tA/JS itt.dt'ctaff~ ., IL~ds of f·

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Page 22: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

E /he,. tJ f tl..e co.,•~··a. ft i~ +o oc.t­)tutll-ipl,·catl ~t 1'1 D"' +N lttAJ_.,d.

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II ,·~ A tl ; ! ) : e- • t:.. ~1-f;gJ

tl ss• ciot~d _ '-'fl. h. l = ~ * --343-

Page 23: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 24: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 25: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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Page 26: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

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E11fH~t6: ~14AtllfiOGIAI~$1S DAT'/4

A

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~': l<fA~IIofslcy 7to'C.

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~e~r~l ap_p~••ci.J ,.. T tJ. Jc e ~.'= {!_ a,., d.. se.,. ~Q ( ,.,~

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L.tf [40 =0~ II,) 1 [h,,h.) , · ·· · • [~ .. ,Ia~~) h~ ,_ p•h'lr'fhl tJ f r"'e it\+•"'"' (o,a..l.

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£xr6111SION$:

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f~olt.IRI (tOMT10~

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Page 46: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

1?. £ (,11-eSSitMI ff •1>4 t ~ :

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tU~D,f,?ell /-lALII NIC.I-

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Page 48: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

Cf~t-,siUA.( Ap/*'••'-'· /:1.14 I fl1l.c. l>e '-' fl•'tl ~

A.. A. -T •• T, , .•. , T...., c:o'"' p'fkrA.C ( lAt'l"t) ""'ilc..rc

l +i~• s. 01-Stn c. "" ~

T' ~ ,.,.,;" ( T., .•.. , T....,)

7 = t j I T; ~ TJ6 • 1c • ,j ... ,,.. 1 T"• '"&.L ,,...,,. lllu4 ,. eJ -fu Mc.h·~ is

,., t!... ., ,,· • ~ ~.,.~,·~ •,. ,; "' "'o,. • f -r; ~

&jt:tj;J)= G.lo~···,o,t:; .. o, .. 1 o)

. = ft' i TJ ~t-,.l:, t} TA• eo,rt~p174.d.t'"1 "'-~ ~rd is cr;.ll~d "f~

"c.t ka~ A~d

.......

. ·~ .,, hj t+r= - 1~ t, ~lt) = titw\pt~~•lt,t.,.t)l~~tJt

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Page 49: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

f$0 .,. 7"1/~lf.~ It; A 1'-...~,~~ ! J -~.':.~"'"'"•l~·~.;r'·· ··~--·

TA• IllAtA loti, ~·, 1.i , t: ) aroL s" ff.t·c./IJ"

+o ltJl~t1/fy ~MI'f ~.. ~1! .. " s~~Jffc. "-. '-4N~I

F.C'"·· -~-

)j tt;!) = LJ.,., P" 1 Tl [t,'f.,4t),7aj J!, T~t }/4f.~ 4~~0

GLt;, ... ~t~) ~~ 8..jlt;) ·i:.,J ... ,...,.. Qf"C.

t\Ot i 4~+e"fiCAit'f - fkr~tr ASSfA1t4fJ~~S ttftd~t/ •

•• ~,_.,..,:JI:t.. ' '": . -·- -~ .:.•.·.t"!: ..... - ___ __.... ... ·.:..~ ... - ..... ~ ... --~ ... -- ·.-•. ..., .... - ----.1>·1'-•'-·· 'I<' -~".P.

\ r,. ""~'T"~11$

, llo: 6 (f,, •.. ,t'-') s 1r Q_; (t-;) is "'ftofl-,

I CAtt.+f i +o.i.\.c. wi~~+ fkrt~ r AUfUMJO.fiOl\. ----

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Page 50: CURRENT STATISTICAL METHODS FOR MORTALITY (FAILURE … · tape of the presentation can be obtained at nominal cost from the conference organizers, Harry H. Panjer and Frank G. Reynolds

it\; ~N 51"147'/SrtCAt. G.v~STION t ~ilfAT IS TH~ H6l!HI4A11l~ ot: lt~nt~ti,AL ?

C !ttss/c-. I Arero,..~

1Hulfiple eltt't"' ~If t Q l t,.J ... ~ ~~)

Afltr ,t,..ol/a/ of all bat il--k Ca11Jt

Q. .i l f-; ) : G.l 0) .. "0, t-j .. 0~ .. "0} -: pt{ ~- ~ t J A~s t.f .,,. h ·,..! of i "'de pl tt.ti.t "l<-'- o.,. of

PfA ('(A )II\ ~ ty,·(. }4lf ddt. IS ~ •

~., ,.ot- loL t~swU.

@ !Xt,.,fJ .,4 f ~="> Ha,fi ~tall ltJ.fi~ ? No f''·o, v• h'r/ /"'J Ht:t ~ll.."' M ( t f?-'1)

@) .,/. SU41/y o"swe~ f-o ~ ete~h'~Jt S flf Ce.c.cA s~

~t-~1 (fjUt'f~ splei•li l~d 'l9f otlt Is .,~..~

Q((.(J UMt l.r -fltf ~ec.Aa..tcs "" t~e. .fK,' (", (

~'!P'-' a,..d tN. 'W1t.'fkorJ. df 'ftntova.l.

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TAt sfa fisk't~l ~etltl)(/s ou.tli~ttd o..ho tit.

eo"~ e .,. ; t 1l t I y ~ e ttl,.,/ l t fo txo bIt ,., s ;,. voJvi.._, -wr u.l fi pfe fo.ilu.rl fi-.1. s.

n i•~i~·· tltAals t:Ut fo llowetJ. ;.,. fu fc'tt~tf.S of aft Aclc ~·r~ f'l.u,~f.d.. WJt,t- +o ~tlat~ r~tf~ of qtfac.~ ~ +o (,.,.) rl)tlwn·,.., ltft/s. Let ~lf) be. a .,.tQSul'e

of ;~I) 1/uh'oM a f +;,.e. -t

).It: llt>) - ra+e at Cll)f4..c'"- eflf.ltf" OUIAr Af -h'IM t ~it"" CIAII~I!Vt /tltt-f flf

~ lfj ~If)): Ao (f) e ~/t) "

ftott. 9~eT•ffy, 1'1110fiCfS C4fK (A/low /or d.EpiNtdt«U

of ffAf-f. o" ft•?JtAt~tcy trl pN.tli•tAS a71icJs., (ft.

T-t'w..e Si~~tu /o.';f41ttAc.li,.c.fc.

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