Sensitivity Determination of cancer screening with the aid of interval cases F W Schwartz

8/7/2019 Sensitivity Determination of cancer screening with the aid of interval cases F W Schwartz

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J Canc er Res C lin Oncol (1981) 101: 331-337d o uma t of~CancerResearchCl in ical O nco logy9 Springer-Verlag 1981

S e n s i t iv i ty D e t e r m i n a t io no f C a n c e r S c r e e n i n g P r o g r a m m e sw i t h t h e A i d o f " I n t e r v a l C a s e s "F . W . S c h w a r t zZen tralinstitut fiir die kassen/irztliche Versorgtmg in der Bund esrepublik Deutschland ,Haedenkam pstr. 5, D -5000 K61n 41, Fede ral Republic of Germ any

Summary.T h e d e t e r m i n a t i o n o f " i n t e r v a l c a se s " b e a r s g r e a t s i g n i fi c an c e i n t h ee s t i m a t i o n o f t h e d i a g n o s t ic s e n s i ti v it y o f a c a n c e r s c r e e n i n g p r o g r a m m e a n dt h e s e t t in g o f a n a p p r o p r i a t e p e r i o d i c i t y o f t h e s c r e e n in g te r m s . T h e c o n c e p t c a no n l y b e a p p l i e d p u r p o s e f u l l y w i t h r e g a r d t o t u m o r k i n e ti c s a n d i t s r e l a ti o n s h i p st o t h e p r o b a b i l i ty o f t u m o r d e t e c ti o n t h r o u g h t h e e x a m i n a t i o n m e t h o d s a p p li ed .T h e m e t h o d i c a l c o n s i d e r a t i o n s p r e s e n t e d a l s o r e s u l t i n a c r i t i c i s m o f th e" l e n g t h - b i a s e d s a m p l i n g " w h i c h h a s c o n s t a n t l y b e e n p o i n t e d o u t i n t h es c r e e n in g t h e o r y i n r e c e n t y e a rs .Key words: C a n c e r s c r e e n i n g - S e n s i t i v it y - E a r l y d e t e c t i o n - I n t e r v a l c a s e s

T h e d i a g n o s t i c e f f e ct iv e n e s s o f s c r e e n in g p r o g r a m m e s is g e n e r a ll y d e s c r ib e d w i t ht h e t e r m s s e n s i t iv i ty , s p e c if i c it y a n d w i t h p r e d i c t i o n v a l u e s . F a m i l i a r i t y w i t h t h e s eb a s i c e p i d e m i o l o g i c a l t e r m s i s a s s u m e d i n t h e f o l l o w i n g p a p e r . P r e d i c t i o n v a l u e s ,u s e d a l s o i n m a n y c l i n i c a l s t u d ie s , a r e i n a p p r o p r i a t e f o r o b j e c t i f y i n g e f f e c t iv e n e s sd e t e r m i n a t i o n s o v e r a lo n g p e r i o d o f ti m e o r i n c o m p a r i s o n w i t h d i f f e re n t p o p u l a -t io n s b e c a u s e t h e y d e p e n d o n t h e p r e v a l e n c e o f t h e t a r g e t d i se a s e in t h e r e s p e c t iv ep e r i o d s o f t i m e o r p o p u l a t i o n s . S e n s i t i v i ty o r s p e c i f ic i t y a r e m e a s u r a b l e v a r i a b l e sw h i c h a r e i n d e p e n d e n t o f t h e p r e v a l e n c e o f t h e d is e as e ; b u t t h e i r d e t e r m i n a t i o nn o r m a l l y p re s u p p o s e s p r e v i o u s a n d f o l lo w - u p e x a m i n a t i o n o f t h e s c re e n e d p o p u -l a t i o n b y m e a n s o f a b e t t e r t e s t t h a n t h e s c r e e n i n g t e s t ( r e f e r e n c e te s t; c r i t e r i o n v a -l id i ty ) . S u c h a p r o c e d u r e c a n n o t b e u t il iz e d w i t h a m a s s s c r e e n i n g p r o g r a m m e b u ti s r e s t r i c t e d t o s m a l l - s c a le s t u d i es . H o w e v e r , t h e r e su l t s o f s u c h s t u d i e s c a n n o ta u t o m a t i c a l l y b e t r a n s f e r r e d t o c o n d i t i o n s w h i c h a r e d e t e r m i n i n g f o r n a t i o n - w i d em a s s s c re e n in g . F o r t h is , t h e c o n c e p t o f " i n t e r v a l c a s e s " c a n b e a p p l i e d , a s v a r i o u sa u t h o r s ( e .g ., K i r c h a n d K l e i n 1 9 78 ) h a v e d o n e f o r b r e a s t c a n c e r s c re e n in g . I t c a nb e u s e d i n t h o s e c a s e s w h e r e , in o n e s p e c i fi c r e g i o n , c a n c e r i n c i d e n c e a n d , a t t h es a m e t im e , p a r t i c i p a n t s a n d s c r e e n in g r e s u lt s a r e r e c o r d e d v e r y re l ia b l y .T h e b a s i c i d e a b e h i n d t hi s m e t h o d is , s o t o s p e a k , t o t a k e " t h e t i m e " a s a r e f -e r e n c e te s t: t h e c a n c e r c a s e s s y m p t o m a t i c a l l y d e v e l o p i n g w i t h in a c e r t a i n i n t e r v a l

0171-5216/81/0101/0331/$1.40


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a f t e r a s c r e e n i n g t e s t h a s b e e n c a r r i ed o u t a r e e v a l u a t e d a s " f a l se n e g a t i v e s " . T h i sr a i se s th e q u e s t i o n w h e t h e r a s u b s e q u e n t c a s e o f d i se a s e w a s a c t u a l l y p r e s e n t a t t h et i m e o f s c r e e n in g ( a n d w h e t h e r it w o u l d h a v e b e e n d e t e c t a b le b y m e a n s o f t h e b e s tr e f er e n c e m e t h o d ) . O b v i o u s l y , t h e a n s w e r d e p e n d s o n t h e i n te r v al c h o s e n a n d t h et u m o r g r o w t h a s w e l l a s o n t h e r e la t i o n s h ip b e t w e e n t u m o r k i n e t ic s a n d d e t e c t a b il -i ty . T h e r e l a t i o n s h i p s b e c o m e c l e a r i n F i g . 1 .

I n t h e m o d e l i n t r o d u c e d i n F i g . 1 w e a s s u m e t h a t, w i t h in c r e a s in g g r o w t h , e a c ht u m o r p a s s e s t h r o u g h t h r e e p h a s e s o f i d e a l t y p e: ( 1 ) a " n o n - d e t e c t a b l e p r e c l i n i c a lp h a s e " ( S o ) , ( 2 ) a "d e t e c t a b l e p r e c l i n i c a l p h a s e " ( Sp ) a n d ( 3 ) a "c l i n ic a l p h a s e " ( So ).T h e t r a n s i t i o n f r o m S p t o S c is u n d e r s t o o d s u c h t h a t , a t th i s p o i n t i n t im e , S p i sr e g u la r ly e n d e d b y t h e o c c u r r e n c e o f c l in i c a ll y m a n i f e s t s y m p t o m s . T o s i m p l i fym a t t e r s , w e f u r t h e r p r e s u m e t h a t t h i s i s a l w a y s t h e c a s e i f t h e t u m o r i s o f t h e s a m e

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F i g . 1 . S c h e m a t i c r e l a ti o n s h i p b e t w e e n t u m o r k i n e t ic s a n d d e t e c t a b il it y b y s c r e e n i n g


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SensitivityDetermination of Can cer Screening Programmes with the Aid of "Interval Cases" 333s iz e. C o r r e s p o n d i n g c o n s i d e r a t i o n s a r e a s s u m e d f o r t h e t r a n s i t i o n o f S o to S p . O nt h e o n e h a n d , t h i s p o i n t i n ti m e is d e f i n e d b y t h e siz e o f t h e t u m o r a n d , o n t h e o t h e rh a n d , b y t h e a b i l i ty o f th e a p p l i e d d e t ec t i o n m e t h o d t o r e c o g n i z e t h e t u m o r w i t ht h e s i ze it h a s a t t h i s p o i n t i n t i m e . A c c o r d i n g l y , t h e d e t e c t a b i l i t y o f a ll t u m o r s l ie sb e t w e e n t h e b e g i n n i n g o f S p a n d t h e b e g i n n i n g o f So , i n o t h e r w o r d s d u r i n g S p. I fw e c o n s i d e r a l o n g i n t e r e x a m i n a t i o n i n t e rv a l , i.e . a s c r e e n i n g w h i c h i s c a r r i e d o u ta t C 1 , a n d t h e n a t Cz, i t b e c o m e s o b v i o u s t h a t i t i s m a i n l y t h e s l o w l y d e v e l o p i n gt u m o r s ( a ", a" ; b " ) w h i c h a r e d e t e c t e d a t t h e s e tw o p o i n t s i n t i m e , w h e r e a s t h e i n -t e r v a l c a se s , v iz . t h o s e w h i c h w e r e o v e r l o o k e d a t t h e f i r st e x a m i n a t i o n a l t h o u g h t h et u m o r s w e r e i n p h a s e S v, c o n s i s t o f t h e r a p i d d e v e l o p m e n t s (b , b') . O f c o u r s e , i tm u s t b e s t a t e d h e r e t h a t , w i t h t h e s e c o n s i d e r a t i o n s , t h e d e t e c t i o n m e t h o d s a r e a s -s u m e d t o e x h i b i t a s e n s i t iv i t y o f o n e i n p h a s e S p f o r t h e t i m e b e i n g .

I f I r e d u c e t h e i n t e r e x a m i n a t i o n in t e r v a l, I c a n e x p e c t to h a v e n o i n t e r v a lc a s es a t a c e r t a i n p o s i t i o n ( C 3) . H o w e v e r , i f a f te r a f i r st s c r e e n in g a t u m o r w h i c hw a s o v e r l o o k e d i n i t i a l ly a n d w h i c h i s n o w c l i n ic a l ly m a n i f e s t s h o u l d o c c u r w i t h i nt h i s s h o r t o b s e r v a t i o n p e r i o d ( C 1 t o C 3 ) , t h i s w o u l d m o s t p r o b a b l y i n d i c a t e i n a d -e q u a t e s e n s i t i v it y o f m y f i r st e x a m i n a t i o n a t d a t e C 1 . A c c o r d i n g l y , t h i s w o u l d b ea m e a n s o f e s t i m a t i n g th e s e n si ti v it y o f m y e x a m i n a t i o n m e t h o d .

T h e o b v i o u s d i f f i c u l t y w i t h t h i s m e t h o d i s t h e c h o i c e o f th e c o r r e c t i n t e r v a l, f o rw h i c h t h e m e a n s o j o u r n t i m e i n S p i s d e c is iv e . T h i s t im e i s n o t d e f i n e d i n c h r o n o -l o gi c al a n d u n i f o r m t e rm s , b u t i t is d e p e n d e n t o n t h e t u m o r g r o w t h a n d t h e t y p eo f d e te c t io n . I n t h e c a se o f a s h o r t t u m o r d o u b l i n g t im e ( w i t h c o n s t a n t d e t e c ti o nm o d a l i t ie s ) , i t i s s h o r t e r (A C ) t h a n i n t h e c a s e o f s lo w e r d e v e l o p m e n t s ( A " C " ).

W i t h i n c re a s in g s o j o u r n t i m e , i t b e c o m e s m o r e p r o b a b l e t h a t t h e t u m o r w i l l b ed e t e c t e d b y a g i v e n s c r e e n in g m e t h o d . C o n s e q u e n t l y , t h e s c r e e n i n g d o e s n o t d e t e c tc a r r i e rs o f a d i s e a s e b y a c c i d e n t , b u t p r e f e r s t h o s e w i t h t h e e x t e n d e d p r e c l in i c a l so -j o u r n t i m e ( l e n g t h - b i a s e d s a m p l i n g ) ( Z e le n a n d F e i n l e i b 1 9 69 ).

B y m e a n s o f F i g . 1 a f u r t h e r t e r m c a n b e d i s c u s se d . T h e e x t e n t b y w h i c h t h ep o i n t i n ti m e o f d e t e c ti o n o f a t u m o r c a n b e b r o u g h t f o r w a r d b y s c re e n in g b e f o rep h a s e S o i s r e a c h e d i s ca l l ed " l e a d t i m e " . I n F i g . 1 , f o r t h e t u m o r d e v e l o p m e n t a " ,i t i s r e p r e s e n t e d b y t h e l i n e B " C " . T h u s , i t i s d e p e n d e n t o n t h e s c r e e n in g d a t e d u r -i n g t h e s o j o u r n t i m e i n Sp . I f th e s c r e e n i n g d a t e s i n a p o p u l a t i o n a r e c h o s e n r a n d -o m l y , o n l y t ti e d u r a t i o n o f t h e s o j o u r n t im e i s de c is iv e . T w o i m p o r t a n t c o n c l u s i o n sc a n b e d r a w n f r o m t h es e co n s i d e r a ti o n s .

1. A s c re e n i ng p r e d o m i n a n t l y d e t ec t s t u m o r f o r m s w h i c h h a v e a s l o w d e v e lo p -m e n t ( l o n g s o j o u r n t im e ) .2 . T h e s l o w e r t h e d e v e l o p m e n t ( in c r e a s in g s o j o u r n t im e ) , th e g r e a t e r t h e p o s -s ib l e a d v a n c e o f t h e d a t e o f d i a g n o s i s ( i n c r e as i n g l e a d t im e ) .I f , a m o n g o t h e r t h i n g s , w e w a n t t o u s e th e s e c o n s i d e r a t i o n s t o e s t i m a t e t h e s e n -s it iv i ty o f o u r e x a m i n a t i o n m e t h o d , i t f o ll o w s t h a t3 . t h e s h o r t e r t h e s o j o u r n t i m e , t h e s h o r t e r m y o b s e r v a t i o n i n t e r v a l m u s t b e .F o r c o m p l e t e a s s e s s m e n t , h o w e v e r , i t i s n e c e s s a r y t o c o n s i d e r a n o t h e r f a c t o r .T h e s e n si ti v it y o f th e c u r r e n t l y a p p l ie d , m o r p h o l o g i c a l l y o r i e n t a t e d o b s e r v a t i o n

m e t h o d s g e n e r a l l y i m p r o v e s a s t h e t u m o r i n c r ea s e s in s i ze , i .e . t h e c l o se r t i m e S ca p p r o a c h e s , t h e m o r e p r o b a b l e t h e d e t e c t io n b y a g i ve n s c re e n in g . B y a n a l o g y w i t ht h e i n t r o d u c e d t e r m " l e n g t h - b ia s e d s a m p l i n g " , t h i s c o u l d b e c a ll e d " l o n g i t u d i n a ld e t e c t i o n b i a s " . F r o m t h e s e c o n s i d e r a t i o n s , i t f o l l o w s t h a t


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334

T a b l e 1 a , b .a E xtent of the carcinom a in the testing materialCases %

I Le ss than 10% 42 29.8II Mo re than 10% 68 48.2II I In the total ma terial 22 15.6N ot sufficientlyassessab le 9 6.4To tal 141 100.0

F. W. Schwartz

b Histological classification of the prostate carcinom asof Groups I and II IGroup I Group I I I

High ly differentiated 29 0Slightly differentiated 2 2Cribriform 1 2Solid and anaplastic 0 1Highly and slightly 5 5differentiatedCribriform, and solid 0 0and anaplasticCribriform in others 4 7Other combinations 1 5Total 42 22(Doh m et al. 1979)

4 . t u m o r s w h i c h g r o w r a p i d l y a n d h a v e a s h o r t so j o u r n t i m e a re , d u r i n g s c r e en -i n g , d e t e c t a b l e w i t h a h i g h e r s e n s i ti v i ty t h a n t h o s e w i t h s l o w e r g r o w t h ( i f t h e i n -t e r e x a m i n a t i o n i n te r v a ls a r e s h o r t e r t h a n t h e a v e r a g e s o j o u r n t im e , o r i f w e c o n -s i d e r o n l y o n e s c r e e n i n g d a t e ) .

T h i s f a c t is c l e a r l y i l l u s tr a t e d b y d e v e l o p m e n t s b a n d a", r e s p e c t i v e l y , i n F i g . 1 .A t t h e s c re e n i n g d a t e C s , b is m o r e e a s i ly d e te c t a b l e t h a n a " . C o n s e q u e n t l y , t h el e n g t h - b i a s e d s a m p l i n g , w h i c h is o f te n e m p h a s i z e d , i s c o u n t e r a c t e d b y t h i s l o n g i -t u d i n a l d e t e c t i o n b i a s e f f ec t . T h i s e f f e c t w i ll b e t h e m o r e p r o n o u n c e d , t h e m o r e t h es e n si ti v it y o f t h e d e t e c ti o n m e t h o d d e p e n d s o n t u m o r g r o w t h .

I n p r a c t i c e , t h i s b e c o m e s p a r t i c u l a r l y n o t i c e a b l e w i t h p r o s t a t e c a r c i n o m a s .W h e r e a s t h e re c o r d e d p r o s t a t e c a r c i n o m a s i n S a a r l a n d e s p e c i a ll y d e t e c te d b yp a l p a t i o n o n l y s h o w a p r o p o r t i o n o f 1 1 . 8 % o f d i f fe r e n ti a te d , s l o w l y d e v e l o p i n gc a r c i n o m a s , t h e s e c a r c i n o m a s d e t e c t e d b y a c c i d e n t (i n c id e n t a l c a r c i n o m a s ) s h o w ap r o p o r t i o n o f 4 1 . 8% ( D o h m a n d H a u t n m m 19 79 ). A fu r th e r b r e a k d o w n o f t hel a t t e r m a t e r i a l c l a ri f ie s t h e re l a t i o n s h i p : W i t h i n t h e g r o u p o f t h o s e c a r c i n o m a sw h i c h c o n s t i t u t e l e s s t h a n 1 0 % o f t h e t e s ti n g m a t e r i a l , t h e p r o p o r t i o n o f th e h i g h l yd i f fe r e n t ia t e d f o r m s w a s 6 9 % . I n t h e g r o u p o f t h o s e h i s to l o g i ca l s a m p l e s w h i c hw e r e c o m p l e t e l y o v e r r u n b y t h e t u m o r , t h is p r o p o r t i o n w a s 0 % ( T a b l e s 1 a , b ).T h e s e f i n d in g s c a n , o f c o u r s e , b e i n t e r p r e t e d o n l y w i t h g r e a t c a u t i o n s in c e t h e yd o n o t o r i g i n a t e f r o m a c le a r ly d e fi n e d p o p u l a t i o n . T h e t e r m " i n c i d e n t a l c a r-


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Sensitivity Determination of Cancer ScreeningProgrammes with the Aid of "Interval Cases" 335c ino ma " p resupposes tha t , in the cases p resen ted , ind ica t ive pa lpa t io n resu l t s wereno t o r have no t ye t been ob ta ined . 1This exam ple is me nt io ned s imply to show tha t - assum ing th is is not a h ighly se-lec ted pop u la t io n o f cases - the s l ight ly d i f fe ren t ia ted tum or deve lopmen ts , i .e . themo re rap id ones, because o f the ir expans ion which i s g rea te r on the average , wou ldhave s tood a be t te r chance than the o thers o f be ing de tec ted by the sc reen ingm e t h o d o f p a l p a ti o n .I f we re tu rn to the beg inn ing o f ou r cons idera t ions , v iz . the in f luence o f the in-te rexam ina t ion in te rva l s , the fo l lowing can be s ta ted: W hen we use the meth od o fes t imat ing the sensi t iv i ty of a screening prog ram by in terva l cases (I) , I is not jus ta fun c t ion o f the sens it ivi ty o f the g iven screen ing method , bu t a l so o f the averageso journ t ime o f the observed tumo rs (tsp ) and o f the observa t ion in te rva l chosen(ti ), i.e. I (q , t sp . I f t~ app roa che s tsp , the pr op or t io n of mo re s lowly develo ping tu-mo rs w ith I wi ll be h igh, and tha t o f rapid ly dev eloping tumo rs will be smal l. Thist rend is reversed i f t~ tends to zero , or i f t i i s far larger than tsv.Befo re d iscuss ing some pract ical ap pl icat ions o f these consid erat ions , i t shouldbe po in ted ou t th a t the so journ t ime in the g iven def in i t ion can be inappr opr ia tefor various d iseases or canc er forms. In the case of breas t canc er screening, for in-s tance , i t i s obv ious ly mu ch mor e im por t an t no t to t ake So as the uppe r l imi t, i .e .the en try in to the cl in ical ly man ifes t s tage, but the p oint in t ime of metas tat iclymph n ode a f fec t ion . Howe ver , th i s time i s then no longer co r re la ted wi th a un i -fo rm tum or s ize, as as sumed in F ig . 1, bu t , wi th som e fo rm s o f deve lopm en t , canbe p resen t w i th as l i tt le as a few mi ll imetres o f tumo r d iameter , ye t wi th o therfo rms , l a rge tumor s me asur ing severa l cen t imet res do no t exh ib i t any lymp h nod eaffect ion (Heuser e t a l . 1979; Duncan and Kerr 1976). This considerat ion aloneshows tha t set t ing the screening in terval a t 1 year , as is the case und er the legal pro-g ram me o f ear ly de tec t ion o f cancer in the Federa l Repub l ic o f Germ any , i s l a rge lyan a rb i t ra r y measure . There fo re , in the case o f b reas t cancer , Heuser e t a l. (1979)advoc a te ind iv idua l se t t ing o f the in te rva ls accord ing to the pa t ien t s ' r i sk fac to rsand earl ier suspect f indings , a l though, and th is must be emphasized , a c lear con-cep t o f d i st inguish ing w ome n w i th the r isk o f rap id ly g rowing tum ors wou ld f i rs thave to be deve loped 2.

All these consider at ions show how diff icul t real ist ic es t ima t ion of sensit iv i ty iswhen app ly ing the me thod o f in te rva l cases to cance r sc reen ing . Never the less , th i sme tho d i s pop u lar because an e f f ic ien t def in ite d iagnos t ic re fe rence tes t, w h ichcou ld be app l ied to a sc reen ing popu la t ion , i s no t ava i lab le here (Cham ber la in e tal. 1979). W here as a ser ies of s tudies on bre as t can cer pursues th is appr oac h in arelat ively s imple way (e .g . Fo x et a l . 1978; Heu ser e t a l. 1979; C ham ber lain et a l.1979), Kirch and Klein (1978) t r ied to examine the relat ionships between in tervalcases and vary ing per iod ic examina t ions in a quan t i t a t ive model . Us ing da ta o f ex -tens ive Amer ica n s tud ies , they a r r ived a t the resu lt tha t the p rop or t io n o f in te rva l1 F or 95 of the 141 cases, the study presents data on rectal palpation findings at the most recentroutine examination. Seventy-tbur(77%) of these were inconspicuous. Obviously, the remainingpalpation findings were no t interpreted as indicating the possibility of carcinomas; otherwise, theterm incidental carcinoma could not be applied purposefully.2 Gautherie and Gros (1980) proposed the use o f thermography o distinguish risk groups for rapidneoplasms


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33 6Table 2. Expected proportion of interval case s in peri-odic programsProportion.of falsenegatives

Interexaminafion interval (months)3 6 12 24

A. Physical examination programs0 01 07 29 5710 02 11 34 6120 03 16 40 6630 04 20 46 7040 06 24 52 74

B. Joint physical-mam mographic exam inations a0 - - 04 18 4210 - - 07 23 4720 - - 10 27 5230 - - 12 32 5740 - - 15 37 62

" 50% of cancers detected by each mod ality; (cf.Kirch and Klein 1978)

F. W. Schwartz

c a s e s r is e s a l m o s t l i n e a r l y w i t h t h e i n c r e a s e o f t h e f a l se n e g a t i v e s ( i n se n s i v it y ) a n da l m o s t l i n e a r ly w i t h t h e i n c re a s e o f th e i n t e r e x a m i n a t i o n i n t er v a l s ( T a b l e 2 ). T h ee x a m p l e a p p l i e s t o b r e a s t c a n c e r s c r e e n i n g .T h i s t a b l e m a k e s i t p o s s i b l e t o e s t im a t e t h e s en s i ti v it y ( l - e ) a t k n o w n v a l u e s f o ri n t e r v a l c a s e s a n d g i v e n s c r e e n i n g p e r i o d i c i t y . I f t h e s e n s i ti v i t y is k n o w n , t h i s t a b l ec a n a l s o b e u s e d t o d e t e r m i n e t h e p r o p o r t i o n o f i n t e r v a l c a s e s w h i c h e n t e re d t h ed e t e c t a b l e p h a s e o n l y a f t e r t h e p r e v i o u s s c r e e n i n g d a te . F o r a g i v e n i nt e r v al , I c a l-c u l a t e t h e d i ff e r e nc e b e t w e e n t h e v a lu e s o f m y k n o w n s e n s it iv i ty a n d t h o s e o f as c r e e n i n g w i t h t h e h y p o t h e t i c a l s e n s i t iv i t y o f 1 (c~ = 0 ).

A s s u m i n g t h a t , a t t h e t i m e o f d e t e c t i o n o r o f fi rs t tr e a t m e n t , a li n e a r re l a t i o n -s h i p c a n b e s e en b e t w e e n t h e p r o p o r t i o n o f p a t i e n t s w i t h a x i l l a ry l y m p h n o d e a f -f e c ti o n a n d t h e n u m b e r o f t u m o r d o u b l i n g s f r o m a g iv e n ba s ic t u m o r s iz e, K i r c ha n d K l e i n ( 19 7 8) h a v e c o m p o s e d a c o r r e s p o n d i n g t a b l e f o r t h e e x p e c te d p r o p o r t i o no f p o s it iv e l y m p h n o d e c a s es ( T a b le 3). H o w e v e r , D u n c a n a n d K e r r ( 19 7 6) h a v ep r o v e d t h a t t h is n o l o n g e r a p pl i es t o t u m o r s a b o v e 6 c m d i a m e t e r .

T a b l e 2 c a n b e u s e d t o e s t i m a t e t h e s e n s i ti v i ty , w h e r e a s T a b l e 3 n o t o n l y f u l fi ll st h e s a m e p u r p o s e u s i n g a d i ff e r en t o b s e r v a t i o n m e t h o d , b u t a l so p r o v i d e s a m e d i -c a l ly r e l e v a n t c r i t e r i o n o f d e c i s io n f o r t h e d e s i r e d s e n s it i vi t y a n d p e r i o d i c i t y o f as c r e e n i n g . T h u s , e . g. , i t b e c o m e s o b v i o u s t h a t e v e n u n d e r d i f f e r e n t s e n s i ti v i t y a s -s u m p t i o n s a p h y s i c a l e x a m i n a t i o n a t 3 - m o n t h l y in t e r v a ls s e em s t o h a v e t h e s a m eu s e fu l n es s 3 a s a sc r e en i n g c o m b i n e d w i t h m a m m o g r a p h y , w h i c h i s c a r r i e d o u t e v -e r y 1 2 m o n t h s .3 The authors use the proportio n o f "lymphatic node negative" patients to define the "prim ary ben-efits" o f a screening program which is contrasted to different cost assumptions. It is presum ed tha tthis m easure'~is accepted t o be a p rognostically su fficient parame ter


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Sensitivity Determination of Cancer Screening Programmes with the Aid of "Interval Cases" 337

Table 3. Expected proportion of positive node cases inperiodic programsProportionof falsenegatives

Interexamination interval (months)

3 6 12 24A. Physical examinations

0 33 35 37 3910 34 36 38 4020 34 36 38 4030 34 37 39 4040 35 37 39 40B. Joint physical-mammographic examinations~

0 - - 29 32 3610 - - 30 33 3720 - - 31 34 3730 - - 32 35 3840 - - 32 35 38a 50% of cancers detected by each modali ty; (cf.Kirch and Klein 1978)

These considerations show that the concept o f sensi tivity est imation by m eansof interval cases is product ive i f appl ied w ith approp ria te considerat ion. How ever,it can only be app lied successfully in cases where sufficient empirical da ta on tum orkinetics and sojourn time in a detectable preclinical phase are available and, fur-thermore, on the relationships between tumor size and detectability by the exam-ination method applied. In this connection, the "length-sampling bias" has to beregarded m ore crit ically than i t used to be because, with morphological ly orientedmethods of discovery, i t ignores the increasing detectability of tumors in lapse oftime. A rational screening strategy today dem ands a detailed knowled ge of ex-perimental, clinical and epidemiological data.ReferencesChamberlain J, Clifford RR, Nathan BE et al. (1979) Error rates in screening for breast cancer by clini-cal examination and mammography. Clin OncolDohm G, Hautumm B (1979) Die Morphologie des kiinischen Stadiums 0 des Prostatacarcinoms (in-cidental carcinoma). Urologe A 14:105-111Duncan W, Kerr GR (1976) The curability of breast cancer. Br Med J 2:781-783Fox SH, Moskowitz M, Saenger EL (1978) Benefit/risk analysis of aggressive mammographic screen-ing. Radiology 128:359-365Gautherie M, Gros CM (1980) Breast thermography and cancer risk prediction. Cancer 45:51-56Heuser L, Spratt JS, Hisam C et al. (1979) Relation between mammary cancer groth kinetics and theintervals between screenings. Cancer 43:857-862K itch RLA, Klein M (1978) Prospective evaluation o f periodic breast examination programs. Cancer41:728-736Zelen M, Feinleib M (1969) On the theory of screening for chronic diseases. Biometrika 59:601-614

Received July 8, 1980/Accepted April 25, 1981

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Sensitivity Determination of cancer screening with the aid of interval cases F W Schwartz