Methods for classification of two thyroid follicular tumour classes
S. K . P A R U I tJ , U. J U E T T IN G J and G . B U R G E R *
The goal o f the present paper is to show that certain cytometric (morphological, photometric and textural) features of isolated cell nuclei can be useful for discrimi
nation and classification of two thyroid tumour classes, namely, follicular adenoma and follicular carcinoma which cannot in general be visually discriminated in cytological smears. Several linear classifiers both at cell and specimen levels are proposed. In order to estimate the true error rate of these classifiers, a ‘hold one specimen out’ scheme is employed.
Im p o rtan t g o als in clinical cytology are cancer diagnosis, cancer typing, p ro g nostic g rad in g , etc. These tasks are p atien t oriented and final decision m aking refers to specimens a n d n o t to cells. O ne ap p ro ach to these tasks is th ro u g h certain q u a n ti
tative features o f isolated cell nuclei (B urger et al. 1985, B urger an d Juetting 1986).
In this case, first the cell images in a specim en are segm ented and then a set o f morphological, p h o to m e tric and tex tu ral features are ex tracted from the nucleus o f each cell. S pecim en classification m ay then be a tw o-stage schem e. In the first stage, each of th e cells in a specimen is classified into one o f the m em ber classes. In the second stage, o n th e basis o f the first stage classification results, th e specim en itself is classified in to o n e o f the specim en classes. The tw o-stage specim en classification problem h a s b een considered first by C astlem an and W hite (1980, 1981) an d later by several o th e rs (B u rg er and Ju ettin g 1986, Tim m ers 1987, Sm eulders 1986). T he present p a p e r d e a ls w ith tw o cytopathologically relevant th y ro id tu m o u r classes where a fine n eed le asp ira te specim en is to be classified into o ne o f them . It is assum ed that there a re tw o classes a t cell level also. W e em ploy statistical linear discrim inant analysis to o b ta in a n o p tim al classifier a t the cell level and o n th e basis o f th a t devise a specimen classifier w hich is n o t necessarily optim al a t the specim en level.
Also p ro p o s e d is a specim en classification app ro ach th a t does n o t involve cell classification b u t is based only on the cell features m entioned above. T he tw o thyroid classes th a t a re d e a lt w ith here are follicular adenom a an d follicular carcinom a which in general a re n o t visually distinguishable in cytological sm ears. It is assum ed th a t an overwhelming m a jo rity o f cells in the carcinom a specim ens are carcinom a cells, though they c a n n o t be identified. N ow , since a pu re carcinom a cell class can n o t be formed, th e p o o le d cells from all carcin o m a specim ens are tre a te d as th e carcin o m a cell class. T h is is la te r p roved to be n o t so unreasonable by th e results o f a ‘ho ld one specimen o u t’ sch em e w here a cell classifier is devised using all b u t on e specim en an d then the cells in th a t specim en are classified by the classifier. T he cells th a t are classified as ‘c a rc in o m a ’ are called positive. Specimen classification is d o n e o n the basis of the p o sitiv e cells. T h e a d en o m a cell class is form ed by p o o lin g all the cells from all a d e n o m a specim ens.
Received 27 M arch 1990.
t Guest Scientist from the Electronics and Communication Sciences Unit, Indian Statistical Institute, 203 B.T. R oad, Calcutta, 700035, India.
t Institut fur Strahlenschutz, G. S. F. Munchen, D-8042 Neuherberg, Germany.
It is well know n th at if the training set is used as a testing set f o r a c lassifier, the estim ate o f the m isclassilication rate is optim istically biased (H a n d 1 9 8 1). I n order to solve this problem the ‘hold one specim en o u t’ scheme is em ployed t o a c h i e v e a more reliable estim ate o f the m isclassilication rate. It is finally show n t h r o u g h numerical results how reduction in dim ensionality m ay lead to reduced tr u e m isclassification rates.
2. Cytological material and feature set
The present analysis is based on 27 follicular adenom a an d 20 f o l l i c u l a r carcinoma specimens w hich were obtained by line needle asp iratio n before s u r g e r y a n d on the diagnosis th a t w as done by a pathologist after surgery. T he sm ears w e r e a i r d ried and pappenheim stained. F rom each specim en, a b o u t 100 iso lated w e ll p r e s e r v e d cell nuclei were visually selected for analysis w ithout any pathological b i a s i n g . T h e images o f the cells were captured by a TV cam era with m icroscopical o b je c tiv e m agnification o f 100 X (oil) using a narrow band optical filter at 500 nm w a v e le n g th , a n d digitized.
The nom inal local resolution o f the digitized im ages was 0-25 /m i a n d t h e nominal gray value range 256. Using IL IA D procedures (E riksson et al. 1 9 8 2 ) w hich are interfaced w ith a VAX 11 /750 (G ais and R odcnacker 1987), 43 f e a tu r e s a r e extracted from each cell image. These features include («) m orphological f e a tu r e s s u c h a s area and perim eter, (b) photom etric features such as integrated o p tic a l d e n s i t y and (c) textural features describing the staining p attern o f a cell. D etails o f t h e f e a t u r e s are available elsewhere (R odenacker 1987)
A t the cell level the set o f cells pooled from all 27 ad en o m a s p e c i m e n s fo r m the sample adenom a cells. The sam ple set o f carcinom a cells is fo rm e d s i m i l a r l y . These tw o sam ple sets were used to devise the cell level classifier. T h e c l a s s i f i c a t i o n here is supervised an d uses linear discrim inant analysis.
3. Feature reduction and cell classification
T o use all the 43 features in discrim ination and classification is n o t p ra c tic a l f°r two reasons. F irst, to com pute all the 43 features for each cell in a n unknown specimen is very expensive in term s o f com puting time. Second, th e a c c u r a c y of®
classifier m ay, beyond a level, decrease with increasing n u m b er o f f e a t u r e s ; this|S know n as B ellm an’s ‘curse o f dim ensionality’ (H an d 1981). T h is c u r s e o f dirt611' sionality is dem onstrated in a later section.
It is seen th a t there is a high am o u n t o f redundancy in the set o f 4 3 f e a tu r e s wit*1 respect to discrim inatory pow er. As a first step to reducing the n u m b e r o f features in the classifier, a sm aller num ber o f features from the original set o f 4 3 f e a tu r e s wefe selected. F o r this purpose, a stepwise discrim inant analysis w as e m p l o y e d .
T he stepwise m ethod selects only the features w ith significant e x tr a d i s c r i m i n a t e d pow er and the num ber o f com p u tatio n al steps involved in the p ro c e ss d e p e n d s on W d a ta set. The m ethod starts w ith no features in the m odel. A t each s t e p , i f th e mo&e is non-em pty, the feature in it th a t contributes least to the d is c r im in a to r y pow er0 the m odel as m easured by W ilks’s lam bda is considered. If this c o n t r i b u t i o n is not significant (in term s o f a preassigned value) the feature is rem o v ed f r o m t h e mow ■ O therw ise, irrespective o f w hether the model is em pty, the fe a tu r e n o t in it contributes m o st to the discrim inatory pow er o f the m odel is c o n s i d e r e d . I f ltS co n trib u tio n is significant (again in term s o f a pre-assigned value), t h e n t h e featurelS included in to the m odel. W hen each feature in the m odel c o n trib u te s sig n ific a n tly t0
Total (%) (a) Using all 43 features. The misdassilication rale is; 33-21% (1494)
Adenoma 1673 843 2516
(66 44) (33-51) (100)
Carcinoma 651 1331 1982
(32-X5) (67-15) (100)
(b) Using only 13 best features. The misclassificalion rate is 34-17% (1537)
Adenoma 1624 887 2516
(64-75) (35-25) (100)
Carcinoma 650 1332 1982
(32 SO) (67-20) (100)
(c) Results using only the canonical variable are the same as in (b)
Table 1. Cell level reclassification results using linear discriminant analysis with equal a priori probabilities. There are .V, = 2516 cells in 27 adenoma specimens and N2 = 1982 cells in 20 carcinom a specimens.
the discrim inatory po w er o f the m odel an d no feature o utside th e m odel does so, the stepwise selectio n p ro ced u re stops.
In the p re s e n t case, both the criteria above are m ade strin g en t so th a t n o t too many features a re finally selected in the m odel. In te r n s o f th e F test the significance level is taken to b e as low as 0 005 in bo th cases. T he final m odel obtained through this stepwise selectio n consisted o f only 13 features. T he loss in the classification results a t the cell level due to the rem oval o f 30 features is insignificant and shown in Table 1.
T h u s in th e first phase o f feature reduction, a subset o f 13 features from the original feature set is selected. But 13 is considered still to o high fo r th e dim ensionality the cell classifier. In the second phase o f feature reduction, the aim is n o t to reduce the cost of m e a su re m e n t o f features but to increase the accuracy o f the classifier (H and '581). F o r th is p u rp o s e the canonical discrim inant analysis is used which derives a linear com bination o f the 13 features ( t h e first canonical com ponent); this gives the highest betw een class variation. This linear com bination is called the canonical variable. This v a ria b le alone is used in the cell classifier. T he increase in accuracy achieved by re p la c in g 13 features with t h e canonical variable in the cell classifier can
^ seen later (in T a b le s 3 and 4).
Specimen classification Reclassification schem e
far the classificatio n has been confined to the cell level. T he problem now is to Ossify a specim en o n the basis o f its classified cells. H ere it is assum ed th a t each sPecimen class is ch aracterized by the p ro p o rtio n p o f positive cells present in a sPecimen and th a t th e n u m b er o f these cells follows a binom ial d istrib u tio n Bin (n, p)
" 'W n is th e to ta l n u m b er o f cells in the specimen. Let p, be the p o p u latio n Paranieter fo r th is p ro p o rtio n in the ad en o m a specim ens an d p 2f o r this p ro p o rtio n ln [he carcinom a specim ens. Let p* be the ra tio o f the to tal n u m b e r o f positive cells Present in 27 a d e n o m a specim ens to th e to tal num ber o f cells in them . Sim ilarly, p f
c°mputed o n th e b asis o f 20 carcin o m a specimens, p f an d p f are the m axim um 1 e**hood e s tim a to rs o f />, an d p2, respectively. It can be show n th a t p f follow s an A p to tic norm al d istrib u tio n w ith m ean /?, and v a ria n c e/?f(l - p f ) j N x. Similarly,
Adenoma Carcinoma Unclear T o tal (a) Using all the 43 features. Number of correctly classified specimens is 33 (78-57%).
Number of incorrectly classified specimens is 4 (2143%)
Adenoma 18 6 3 27
Carcinoma 3 15 2 20
(b) Using the best 13 features. Number of correctly classified specimens is 32 (78-05%).
Number of incorrectly classified specimens is (21 95°o)
Adenoma 17 6 4 27
Carcinoma 3 15 2 20
(c) Results with only the canonical variable are the same as in (A).
Table 2. Specimen level classification results with reclassification scheme corresponding to the cell level classification results shown in Table I. The percentages exclude unclear specimens.
p f follows an asym ptotic norm al d istrib u tio n w ith m ean p 2 a n d v ariance p*(] — p * ) l N2 • (A^, an d N 2 are th e to tal num bers o f cells present in the a d e n o m a a n d c a rc in o m a specimens, respectively). Let these tw o d istrib u tio n s be d e n o te d by / , a n d f 2, re s p e c t
ively (p , and p 2 being replaced by sam ples />* and /?*, respectively). L et t b e th e threshold value for the positive cell p ro p o rtio n such th a t / , ( / ) = f 2(t) a n d t lies betw eenp, a n dp 2. N ow the specimen classification problem reduces to decid in g w h ic h o f th e above two popu latio n s a specim en with n cells (am o n g w hich x a re p o s itiv e cells) is com ing from . Let p be the p o p u latio n ratio o f positive cells in such a sp ecim en . T h en p* follows an asym ptotic norm al d istrib u tio n w ith m ean p a n d v a ria n c e p*( 1 — p*)/n where p* = x)n.
N ote th a t the 90% confidence interval for p is (p* — 1-645N/(^ * (1 — p * )/n ), p* + l-645v/(p * (l - p*) j n) ) . l f p* -I- l- 6 4 .\( /> * ( | - p*)/n) is less th a n /, th e n th e specimen is classified as adenom a. On the oilier h and, i f />* — 1 - 6 4 5 j( p * ( \ — p * )/n ) is greater than r, then the specimen is classified as carcinom a. O therw ise, th e sp e c im e n is n o t classified b u t left as unclear. T h a t is. a spccimcn is n o t classified if t falls in sid e the above confidence interval. The spccim cn level classification results u sin g th is scheme are shown in T able 2.
4.2. H old one specimen out scheme
In Tables 1 and 2, the results are o f reclassification in th e sense th a t th e sa m e set is used for b o th learning and testing. T o o b tain the true e rro r (o r m isclassification) ra te one should use a different testing set from the learning set. B ut in the p re se n t case (an d in the medical field in general), n o t enough specim ens are n orm ally a v a ila b le w hich can be divided into a learning set an d a testing set. F o r this reason, a h o ld o n e specim en o u t scheme is em ployed. T h a t is, w hen a specim en is being classified, it is excluded from the learning set while all o th e r specim ens are included, a n d th e excluded specimen becom es the testing set. T h is is repeated fo r each specim en a n d th e average p ro p o rtio n o f misclassified cases is an estim ate fo r th e tru e m isclassification rate. B ut is should be noted th a t tw o things are learn t on the basis o f all the specim ens together: first, the set o f 13 m ost discrim inatory features a n d second, the coefficients o f the canonical variable. These are learnt only once and le a rn t before em ploying th e ho ld o ne specimen o u t scheme. The results o f three different classifiers a t b o th cell level an d specimen level using this schem e are given in T ables 3 a n d 4, respectively.
In specimen level classification also, the fact th a t less n u m b er o f features can be m o re accu rate is evident. F o r the classifier w ith all 43 features, results w ith th e h o ld
Adenoma Carcinoma Total
(%) (%) (%)
(a) Using all 43 features. The misclassitication rate is 45-40% (2042)
Adenoma 1398 1118 2516
(55 56) (44-44) (100)
Carcinoma 924 1058 1982
(46 62) (53-38) (100)
(6) Using 13 best features. The misclassitication rate is 42-49% (1911)
Adenoma 1447 1069 2516
(57-51) (42-49) (100)
Carcinoma 842 1140 1982
(42-48) (57-52) (100)
(c) Using only the: canonical variable. The misclassification rate is 34-24% (1540)
Adenoma 1627 889 2516
(64 67) (35-33) (100)
Carcinoma 651 1331 1982
(32-85) (67-15) (100)
Table 3. Cell level classification results with hold one specimen out scheme using linear discriminant analysis. All three tables below show true error rates. The results demonstrate how a classifier with more features can sometimes be less accurate (Bellman’s curse of dimensionality).
o n e o u t scheme are far worse than those with the reclassification scheme. F o r the classifier with 13 features, the difference is less. Finally with the canonical variable the difference is nil. T hus, the instability o f a classifier increases w ith larger num ber o f fe a tu re s an d this can be explained in the follow ing way. F o r a classifer w ith m ore fe a tu re s, m ore num ber o f p aram eters are to be estim ated. But the n u m b er o f obser
v a tio n s on the basis o f which this estim ation is to be m ade rem ains the sam e. In other w o rd s , the sam e set o f observations if seen in a h igher dim ensional space is quite likely to b e sparsely distributed an d hence will lead to un stab le a n d unreliable estim ates o f th e param eters. C onsequently, the perform ance o f a classifier w ith m ore features b e c o m e s worse.
T h e specim en classifier above classifies each cell o f a specim en. A n alternative way is n o t to classify the cells w hich lie very close to the b o u n d ary between the tw o classes.
Adenoma Carcinoma Unclear Total
(a) Using all the 43 features. Number of correctly classified specimens is 24 (61-54%).
Number o f incorrectly classified specimens is 15 (38-46%)
Adenom a 12 11 4 27
Carcinom a 4 12 4 20
(b) Using best 13 features. Number of correctly classified specimens is 25 (65 79%).
Number of incorrectly classified specimens is 13 (34-21%)
A denom a 13 9 5 27
C arcinom a 4 12 4 20
(c) Using only the canonical variable. Number o f correctly classified specimens is 32 (78-05%). Number of incorrectly classified specimens is 9 (21-95%)
A denom a 17 6 4 27
C arcinom a 3 15 2 20
T a b le 4. Specimen level classification results with hold one specimen out scheme corresponding to the cell level classification results shown in Table 2. The percentages exclude unclear specimens.
Adenoma Carcinoma Unclcar T o ta l
( % ) <“ u) ( % ) ( % )
(a) Cell level classification results
Adenoma 1431 '41 494 2516
(56-8X) 03-44) (19 63) (100)
Carcinoma 483 n i h 383 1982
(24-37) (S(> 31) (19 32) (100)
(b) Specimen level classification results
Adenoma 20 fo 1 27
Carcinoma 3 16 1 20
Table 5. Cell and specimen level classification re s u lts with hold one specimen out schem e o n the basis of new cell classification approach where only a cell with a posteriori p ro b ab ility more than 0-55 is classified. Only th e c a n o n ic a l variable is used.
T his m ay be ap p ro p riate since the overlap between the tw o cell classes is q u ite h ig h . A cell is classified if the m axim um o f the two u posteriori p ro b ab ilities is g re a te r t h a n 0-55. Otherwise, the cell is left unclassified. Then the sam e specim en c la ssific a tio n technique is applied as is described for the first specimen classifier ab o v e b a sed o n th e classified cells o f a specimen. The classification results in the cell an d specim en le v e ls are given in T able 5. It can be seen th at four out o f six specim ens unclassified b e f o r e are now classified correctly.
T he specimen classification discussed so far involves, directly o r indirectly, sin g le cell classification. N ow a specimen classification scheme is p ro p o sed w hich a v o id s single cell classification altogether and is based on the m ean value o f th e c a n o n ic a l variable V w ithin a specimen. It is assum ed th at V is n o rm ally d is trib u te d w ith in adenom a specimen cells and within carcinom a specim en cells w ith different m e a n s b u t equal variance. T hus, the average o f the tw o m eans is taken as th e th re sh o ld v a lu e T . It is seen th a t the adenom a m ean is greater th a n the c a rcin o m a m ean. N o w , s u p p o s e a specimen with n cells an d m ean v is to be classified. T he sta n d a rd e rro r is s" = s /^ fn . T hus, the sam ple o r specimen m ean V is norm ally d istrib u ted w ith m e a n v a n d stan d ard deviation s". If P ro b (K > T ) is greater th an 0-95. th a t is, if v — 1 6 4 5 s " is greater th an T, then the specimen is classified as ad en o m a. O n the o th e r h a n d , if P r o b ( F < T ) is greater than 0-95, th at is. if v + l-645.v" is less th a n T, th e n th e specimen is classified as carcinom a. O therw ise, the specim en is n o t classified a n d is left as unclear. T he specimen level classification results using this a p p ro a c h a r e given in Table 6. It can be seen th a t the specim en classification results b ase d o n th e specimen m ean are m ore o r less the sam e as those based o n single cell c la ssific a tio n (Table 4(c)).
Adenoma Carcinoma Unclear T o tal
(a) Using only the canonical variable. Number of correctly classified specimens (80-49%). Number o f incorrectly classified specimens is 8 (19-51%).
Adenoma 18 5 4 27
Carcinoma 3 15 2 20
Table 6. Specimen level classification results on the basis of the specimen mean o f the canonical variable V. Reclassification and hold one specimen out schemes produce the same results.
5 . Discussion
T he intention o f this p ap er has been to explore the possibility o f using certain cell fe a tu re s for the classification o f som e thyroid tu m o u r classes on th e basis o f sm ears fro m fine needle a sp iratio n w ithout having to go for surgery. T h e results above in d ic a te that the cell features do co n trib u te to the classification. B ut it is to be noted t h a t though the cell level classifiers arc optim al the specim en level classifiers are not necessarily so. T hus, there is a scope lor im provem ent in the specim en classifiers. It h a s been observed th a t w ithin a diagnostic class, the betw een specim en variability is q u ite high though it has been implicitly assum ed th a t a specim en can be treated as a ra n d o m sample from a norm al population (o f the pooled cells from the corresponding d ia g n o stic class). A m o re realistic m odel will possibily be th a t o f a com pound d is trib u tio n where one can assum e one d istrib u tio n w ithin a specim en and an o th er b e tw e e n specimens w ithin a diagnostic class (Tim m ers 1987, B artels 1988). F o r e x a m p le , it can be assum ed that the cell feature vector X follows N (/i, c ,) w ithin a sp e c im e n and n follows N(x. <r,) within a diagnostic class, w here a] reflects the v a ria b ility within a specim en and
a]the variability w ithin a diagnostic class.
F o r the present analysis o f d ata the statistical softw are package SAS (SAS I n s titu te Inc., U .S.A .) has been used on an IBM 4381-2 m achine.
A s m entioned earlier, there is no in form ation on which are the carcinom a cells in th e carcinom a specimens. In case it is in som e way possible to identify the carcinom a c e lls in a carcinom a specim en, the two thyroid tu m o u r classes u nder consideration m a y be discrim inated m ore successfully em ploying the m ethods proposed in the p r e s e n t paper.
Ac k n o w l e d g m e n t s
T h e authors w ould like to thank D r Schenck for providing the fine needle a s p ir a te specimens and D ipl. M ath . R odenacker an d D ipl. Ing. G ais fo r extracting the c y to m e tric features from these specimens.
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