Computer diagnosis in jaundice

Journal of Hepatology, 1986;3:154-163 Elsevier

154 HEP 00206

Computer Diagnosis in Jaundice Bayes' Rule Founded on 1002 Consecutive Cases Axel Malchow-M011er, Carsten Thomsen, Peter Matzen, Linda Mindeholm, Beth Bjerregaard, Stewart Bryant, J0rgen Hilden, JOrgen Holst-Christensen, Torben Stmhr Johansen and Erik Juhl Department of Medicine, Divisions of Hepatology and Gastroenterology, and Department of Surgical Gastroenterology, Hvidovre Hospital, Departmentof Biostatistics, Instituteof Medical Genetics, Universityof Copenhagen, Copenhagen (Denmark) (Received 3 December, 1986) (Accepted 26 February, 1986)

Summary Extensive clinical and clinical cher0ical information was collected from 1002 consecutive jaundiced patients. Initial selection of variables based on Chi2-tests or Mann-Whitney U-test allowed the removal of 64 of the 107 variables originally collected. A further selection of variables was carried out using a modified version of Bayes' rule thus reducing the number of variables from 43 to 22. Of the 982 patients with a final diagnosis 743 patients (76%) could be classified correctly into one of 13 diagnostic categories. The Bayes' rule was also applied to a test group of a further 110 jaundiced patients and found to perform equally well: of 108 patients with a final diagnosis 81 (75%) were correctly classified. A comparison between the clinician's diagnosis and the computer-aided diagnosis according to Bayes' rule demonstrated agreement with regard to one of the 13 diagnostic alternatives in 734 patients (75%), of whom 81 patients were wrongly diagnosed. In the test group agreement upon diagnosis was found in 80 patients (74%). By plausibly combining the computer-aided and the clinician's preliminary diagnoses, more correct classifications were obtained than with either method alone. Many diagnostic modalities such as ultrasound examination, CT-scan, and direct cholangiography are at hand today for the differential diagnosis of jaundice. Computer-aided diagnosis using Bayes' rule has proved a reliable tool for the clinician and can be used in the planning of a diagnostic strategy for the individual jaundiced patient.

This work was supported by grants 512-7138, 512-8969, 512-8766, 512-10276, 12-9350, and 12-3567 from the Danish Medical Research Council. Correspondence and reprint requests to: Axel Malchow-M011er,M.D., Department of Medicine B, Frederiksborg Central Hospital, DK-3400HiUer0d, Denmark, Tel. (2) 261500, ext. 6115. 0168-8278/86/$03.50© 1986Elsevier SciencePublishers B.V. (BiomedicalDivision)

BAYES' RULE IN JAUNDICE Introduction

Computerized or computer-aided diagnosis was introduced many years ago and has covered a variety of clinical aspects [1-5]. Differential diagnosis of jaundice by use of computer has been studied, first of all by American, English, and Swedish groups [6-8]. A comprehensive review on the subject was published in 1978 by Goldberg and Ellis [9]. During the last decade a broad spectrum of new diagnostic methods have appeared for the differentiation of obstructive and non-obstructive jaundice, such as ultrasound examination, computed tomography scan, direct cholangiography, and hepatitis serology [10,11], all of which will lead to a diagnosis in the majority of cases [12,13]. Consequently, few patients today will run the risk of serious consequences of an incorrect diagnosis, the classic example being laparotomy in suspected obstructive jaundice which turns out to be cholestatic hepatitis. However, patients may run a risk of complications due to diagnostic manoeuvres if the advanced tests are applied indiscriminately. They should be used with due regard to risks, cost, and informativity. Therefore, we advocate that a thorough history and clinical examination together with a few and quickly available laboratory tests remain the foundation for the initial management of the jaundiced patient, i.e. for the selection of a confirmatory test strategy that will involve minimum risks and costs and provide maximum diagnostic information. This initial phase, with its traditional multitude of symptoms and signs and its lack of confirmatory evidence, seems ideal for a computerized, statistical approach. A computer would be required primarily for sifting out a suitably large data base to get rid of useless or redundant variables, and for establishing a probabilistic diagnosis rule to be applied to future cases. A probabilistic approach to diagnosis seems of particular value when taken as a guideline for the selection of necessary diagnostic investigations, because only probability statements can convey the amount (and nature) of residual uncertainty as to the cause of jaundice and hence justify the choice of further diagnostic strategy, or transition to treatment.

155 The present paper is one of a series in which we apply several standard statistical techniques to a large and carefully collected data base, elucidating their relative performance in terms of the quality of guidance they can provide and the ease with which they can be applied at the bedside. The technique employed in this paper is the rule named after Thomas Bayes [14], whereas that of Matzen et al. [15] is a logistic discrimination model and that of MalchowMoiler et al. [16] is a simple flow-chart (decision tree). Bayes' rule is the potentially most powerful method of the three, in particular when a fine subdivision is desired (13 diagnostic categories in the present case), while the logistic and the flow-chart approach are suited for coarse grouping only. A price is paid in terms of computational complexity: Bayes' rule calls for a microcomputer for easy and safe use, whereas the other two methods require a pencil and a postcard-size chart only.

Patients and Methods Data base

All adult (>15 years) patients admitted to a 1000bed university hospital (Hvidovre Hospital, Copenhagen) during a 5-year period from 1976 to 1981 and clinically considered jaundiced were included in the study. Patients developing jaundice during their stay in hospital were included as well. After exclusion of patients in whom the clinical suspicion of jaundice proved false (s-bilirubin <18/xmoles/l), our material comprises 1002 patients. Information was obtained about history (59 variables), clinical examination (33 variables), and clinical chemical tests (15 variables) available within 48 h. This was carried out by aid of a questionnaire, and a total of 107 variables was recorded. Symptoms and signs were defined in cooperation with study groups in the U.K. [7,17] and Sweden [8]. Diagnoses were established according to the usual procedures of the departments. After a minimum observation period of 3 months, all records were reviewed by the authors in order to achieve a final diagnosis in each particular case. For further details, see references [12,13]. Six

156

A. MALCHOW-M~LLER et al.

TABLE 1 DISTRIBUTION AND TYPE OF VERIFICATION OF 982 JAUNDICED PATIENTS IN 13 DIAGNOSTIC GROUPS The composition of the test sample is also given. Final diagnosis

Number of patients in data base

Verification procedure

195 26

151 (77%) 18 (69%)

25

23 (92%)

54 51

33 (61%) 28 (55%)

155

112 (72%)

15

19

17 (89%)

2

50

37 (74%)"

10

5 (50%)

Liver biopsy, laparotomy, autopsy (% of patients)

Direct cholangiography, laparotomy, autopsy (% of patients)

Number of patients in test sample

Acute non obstructive

Viral hepatitis Toxic hepatitis Acute alcoholic liver disease (alcoholic hepatitis, fatty liver) Postoperative jaundice, septicaemia Liver congestion

23 3

Chronic non-obstructive

Alcoholic cirrhosis without hepatoma Alcoholic cirrhosis with hepatoma Non-alcoholic chronic liver disease (chronic active hepatitis, postinfectious or cryptogenic cirrhosis, primary biliary cirrhosis) Congenital hyperbilirubinaemia (Gilbert's syndrome) Benign obstruction

Gallstones or cholangitis Pancreatitis

148 28

133 (90%) 20 (71%)

23 3

150 ( 9 9 % )

19 7

Malignant obstruction

Carcinoma of the pancreas or bile ducts Liver metastases Total

151 70

-

982

475 (48%)

51 (73%)

per cent of the patients had multiple diagnoses (~<3), but only one, i.e. the most likely cause of jaundice, was chosen. O f the total material, 20 patients were withdrawn in the present analysis: 17 with jaundice of unknown origin, and 3 patients with rare and (in our

303 (31%)

108

material) isolated causes of jaundice: a m o e b i c abscess of liver, B u d d - C h i a r i s y n d r o m e , and recurrent jaundice of pregnancy. This leaves 982 patients in our data base. Table i shows the distribution of patients in 4 main

157

B A Y E S ' R U L E IN J A U N D I C E

categories of jaundice, which are further divided into 13 diagnostic groups. In 475 (48%), the diagnosis was based on pathological criteria (percutaneous liver biopsy, operative findings, or autopsy), and in 303 patients (31%), it was based on either pathoanatomical criteria or the results of direct cholangiography. In the remaining 204 patients (21%), the diagnosis was mainly founded on the clinical course.

Test group In the test group, data were collected from 110 consecutive patients with jaundice. The final diagnosis in these patients (Table 1) was established in the same way as described for the patients in the data base.

for one of the 43 variables mentioned earlier. So, is the estimated probability of the symptom or sign Xr given the disease category D i. P{Dj} is the a priori probability of the disease category D i which can be calculated from the data base. The adjustable quantities b and ci were chosen as mentioned in the Discussion. A stepwise-forward selection of variables was carried out by picking the most promising variable and adding one variable to X at a time using at each step a quadratic scoring rule, Q (18), which measures agreement between the output from Bayes' rule and the final diagnoses of the patient sample. The formula for Q is:

P{XrlDj}

O = average

To guarantee stability of the modified Bayes' rule, to be described below, the number of variables (symptoms, signs, clinical chemical tests) should be well under the number of patients in a typical category, and care should be taken to retain only truly discriminatory variables. A variable screening was therefore performed by tabulating each variable against the presence or absence of each of the 13 medical conditions and calculating a Chi2-test or Mann-Whitney U-test as appropriate. Consideration was also given to likelihood ratios, i.e. the factors by which a finding changes the odds of a disease, either up or down. This screening procedure allowed us to sort out variables that seemed of little or no value with regard to discrimination between the 13 diagnostic jaundice categories, thus reducing the 107 variables to 43. A modified Bayes' rule was used in later computations: //'r ( l b ( X r l D j } ) b" P(Dj) • c i

P(DilX}

{Pi,final- 1/2 ~j ( e i j ) 2 + 1/2}

i

Statistics

=

^

where Pi,final is the assigned probability of the final diagnosis of patient i and ~. (Pij) 2 is the sum of the J squared diagnostic probabilities of all diagnoses. Thus, Q measures the quadratic deviation from the situation of perfect diagnostic ability, in which case Q = 1. The worst.possible value for Q is zero. Figure 1

O

08

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o

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05 5

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with ib for estimated probability. Here Dj is the j'th jaundice category (j = 1..... 13) and X the contents of a patient's record consisting of the individual symptoms and signs X~,X2 ..... X~.... ; each Xr is the value

Fig. I. The increase in diagnostic performance, measured by the quadratic score Q (see text), as more variables are taken into account. The star marks the chosen cut-off; the 22 variables thereby selected are listed in Table 2. S-AP = serum alkaline phosphatases, S-ASAT = serum aspartate aminotransferases, S-LDH = serum lactate dehydrogenases, C H F = congestive heart failure, HBsAg = hepatitis B surface antigen.

158

A. MALCHOW-MOLLER et al.

shows the gradual increase in Q as variables are introduced. The final selection of variables was d o n e by cutting away the last 21 of the 43 variables found in the initial screening. The cut-off point, m a r k e d by a star in Fig. 1, was estimated from the slope of the curve. T a b l e 2 lists the 22 finally selected variables. Results

Reclassification o f patients in data base Table 3 shows the reclassification of the 982 patients in the d a t a base using Bayes' rule. T h e term reclassification refers to the application of the rule to the very patients on whose d a t a it was constructed.

Thus, each patient has been classified according to the highest probability as calculated by the formula. F o r example, of the 195 patients with a final diagnosis of acute viral hepatitis (first row), this was found the most p r o b a b l e diagnosis in 174, whereas in the remaining 21 patients o t h e r diagnoses were given higher probability (4 patients toxic hepatitis, 3 patients acute alcoholic liver disease etc.). Conversely, in 30 o t h e r cases (first column), acute viral hepatitis was found most likely according to Bayes' rule, but this later p r o v e d to be incorrect. In all, 743 patients (73%) were correctly allocated. If one were to accept only diagnoses with diagnostic probabilities (Pmax) of 0.80 or higher, relatively fewer patients would have been classified. In 495 pa-

TABLE 2 FINALLY SELECTED VARIABLES IN THE DIFFERENTIAL DIAGNOSIS OF JAUNDICED PATIENTS BY USE OF BAYES' RULE Alcohol consumption was graded into nil, 1-4 drinks (<50 g) per day, ~>5 drinks per day for less than 5 years, and ~>5 drinks per day for 5 years or more. Examination of the gallbladder region was recorded as no palpable gallbladder a soft palpable mass, or a firm and possibly tender palpable mass. For further definitions, see [8,17]. Variable

Scale (number of alternatives)

Selected as number (cf. Fig. 1)

continuousa binary binary binary nominal (3) ordinal (7) binary ordinal (3) binary binary ordinal (4)

1 22 20 21 8 17 12 11 13 16 7

ordinal (3) nominal (3) nominal (3) binary

2 18 14 15

continuous continuous continuous continuous continuous continuous binary

5 3 4 6 9 10 19

History Age Hereditary jaundice Previous gallstone disease Previous jaundice due to cirrhosis Previous malignancy Duration of present history Intermittency of jaundice Fever with or without chills Hepatotoxic drugs In treatment for congestive heart failure Alcohol consumption

Clinical signs Spider naevi Liver surface Gallbladder examination Ascites

Clinical chemical data Serum bilirubin Serum alkaline phosphatases Serum aspartate aminotransferases Serum lactate dehydrogenases Clotting factor 2, 7, 10 White blood count HBsAg

a The label 'continuous' refers to a grouping into some 10 intervals.

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159

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TABLE 4 CLASSIFICATION OF 982 JAUNDICED PATIENTS ACCORDING TO BAYES' RULE Pmax denotes the probability of most likely diagnosis, and patients are separated into high (2->80%) or low (<80%) probability of diagnosis. Number of patients

Final diagnosis

Prnax~ 0.080

Pmax< 0.80

Correctly classified N (%) Acute hepatitis Toxic hepatitis Acute alcoholic liver disease Postoperative jaundice, septicaemia Liver congestion Alcoholic cirrhosis without hepatoma Alcoholic cirrhosis with hepatoma Non-alcoholic chronic liver disease Congenital hyperbilirubinaemia Gallstones or cholangitis Pancreatitis Carcinoma of the pancreas or bile ducts Liver metastases

148(76) 3 (12) 0(0) 4(7) 19 (37) 115 (74) 0(0) 5 (10) 3 (30) 71 (48) 0(0) 58(38) 27 (39)

Total

453 (46)

tients (half of the data base), one diagnostic category or another was given a probability of 0.80 or higher as illustrated in Table 4. Out of these patients, 453 (92%) were correctly classified and 42 patients (8%) turned out to be incorrectly classified. The remaining 487 patients had diagnostic probabilities below 0.80 (socalled 'grey zone area'). Figure 2 shows the effect of varying threshold lev-

Incorrectly classified N (%) 4(2) 4 (15) 4(16) 3 (6) 3 (6) 3 (2) 4 (2) 6 (12) 0(0) 1 (1) 3 (11) 6(4) 1 (1) 42(4)

N (%) 43 (22) 19(73) 21 (84) 47(87) 29 (57) 37 (24) 15 (79) 39(78) 7(70) 76(51) 25 (89) 87 (58) 42(60) 487 (50)

els for Pmax upon the classification of patients. As the required probability threshold is lowered, more patients will be classified, but the n u m b e r of wrongly "classified cases increases also. Pmax cannot be lower than 1:13 = 0.07, so with this threshold all patients receive a classification: 743 patients (76%) are correctly classified and 239 patients (24%) wrongly so (the first of the 6 columns in Fig. 2).

Classification of patients in test group Proporlion of totol %

IE

1008060-

Patients incor-

rectly classified Patients not classified

40Patients correctly classified

200

0.07 0.40

I 0.50

0.60

0.70

0.80

~ox

Fig. 2. The impact of varying probability thresholds on the classification of 982 jaundiced patients using Bayes' rule. Pmaxis the probability of the most likely of 13 diagnostic alternatives.

There was no statistically significant difference in disease frequencies when comparing the test group with the data base. In 2 patients the diagnosis as to the cause of jaundice remained unknown. Of the 108 patients with a final diagnosis, 81 (75%) were given a correct diagnosis. This figure agrees with the value of 76% obtained by reclassifying the data base. Fifty-one patients (47%) had diagnostic probabilities of 0.80 or higher, and only 5 of these were misclassifications. The remaining 59 patients had Pmax-values below 0.80, and this group also included the 2 patients in whom a final diagnosis could not be reached.

BAYES' RULE IN JAUNDICE

161

TABLE 5 OUTCOME FOR DATA BASE PATIENTS OF A STRATEGY OF TRUSTING THE CONFIDENT PARTY: i.e. A 'CERTAIN' DIAGNOSTIC SUGGESTION MADE BY THE EXAMINING CLINICIAN AND/OR A COMPUTER DIAGNOSIS OF HIGH DIAGNOSTIC PROBABILITY (Pmax~>0.80) Reply pattern

Correct (%)

Wrong (%)

Unclassified

Total

Both confident and agreeing (same diagnostic alternative) Both confident, but disagreeing One confident (Bayes)

371 (96%) 76 (78%) 235 (77%) -

17 (4%) 21 (22%) 69 (23%) -

-

388

682 (86%)

107 (14%)

One confident (clinician) Neither confident

Total

Comparisons between cfinician and computer The participating clinicians (two internists and two surgeons, all senior registrars with long experience in differential diagnosis of jaundice) were asked to state their clinical diagnosis when they examined the patient and filled in the entry questionnaire; in some cases they did not yet know the results of clinical chemical tests. For the purpose of the present analysis, the clinician's diagnosis was considered certain if only one diagnostic suggestion had been made. Any combination of diagnoses from different diagnostic categories as well as no diagnostic suggestion at all were treated as uncertain. A comparison between the clinical diagnosis and the computer diagnosis according to Bayes' rule showed an almost equal number of correct diagnoses in either situation: 760 of the data base patients were correctly diagnosed by the clinician, and 743 patients by the computer (n.s.). Overall agreement with regard to one of the 13 diagnostic alternatives was demonstrated in 734 patients (75%) of whom only 81 patients were wrongly diagnosed. Mutual agreement and also agreement with the final diagnoses declined, when the clinician was uncertain or Pmax according to Bayes' rule was below 0.80. Table 5 shows the outcome of relying on the confident party, be it the clinician or the computer. If both were confident, i.e. certain clinical diagnosis and Pmax ~> 0.80, very few misclassifications occurred. If

-

10

10 97

-

304

183

183

193

982

only one was confident it is seen that the percentage of correct classifications in both situations was very similar, but the clinician tended to make more certain diagnoses than did the computer. By way of comparison, recall that Bayes' rule employed alone had 92% correct answers out of 495 confident ones. The clinicians had 87% correct suggestions out of 702 'certain' ones. In the test group agreement between clinician and Bayes' rule was found in 80 patients (73%), of whom 11 patients proved to be incorrectly diagnosed in the light of the final diagnoses.

Discussion

Overall achievements of the statistical rule In other studies on computer-assisted diagnosis in jaundice, 85% to 95% correct diagnoses have been reported [6-8]. The number of patients in these studies, however, was rather limited, data bases comprising 50 patients (U.S.A.) [6], 145 patients (Sweden) [8] or just over 300 patients (U.K.) [7]. When reclassification is carried out upon small patient samples, one would expect high percentages of correct allocations. It is therefore essential to test any proposed rule on a separate series of test cases. When the English rule was evaluated on new patients, 66% to 90% were classified correctly [19,20]. However, when it was applied to the Swedish data, only 50%

162 correct answers were obtained, in contrast to the 90% obtained by reclassification in Sweden [8]. On this background the present results with a data base comprising 1000 patients and a test group of 110 patients are very satisfactory: 3 out of 4 patients were correctly allocated to one of 13 diagnostic alternatives solely by means of statistical handling of probabilities, even in the test group. Not unexpectedly, most diagnostic errors occurred in the small diagnostic categories (Tables 3 and 4). There is one remarkable exception to this rule: 9 of 10 patients with Gilbert's syndrome were correctly classified. This is due to the characteristic and almost pathognomonical appearance of such patients presenting with monosymptomatic hyperbilirubinaemia. Clearly, one cannot have reliable estimates of the symptom probabilities with such a small sample. Still, since the class is sUfficiently well separated from the rest of the data base, it turned out to be possible to discriminate it successfully. Patients with pancreatitis were extremely difficult to diagnose, partly because of the lack of discriminatory value of S-amylase determinations. We have also demonstrated that, for the present purpose of making preliminary diagnoses, one needs only about 20 variables rather than the 50-100 variables more or less routinely, though selectively, recorded by hepatologists. Further remarks on statistical aspects We previously discussed the dangers of overfitting, which accounts for the tendency for good reclassification results to be followed by disappointing testsample performance [21]. Overfitting is avoided by resisting the temptation to include all variables that appear promising on a conventional level of significance. The fact that the curve in Fig. 1 begins to decrease, rather than just flattening out, when more variables than desired are included, is a well-known manifestation of overfitting [18,21]. If b and cj's are deleted in the formula given in the Methods section, we have the version of Bayes' rule that arises by assuming variables to be conditionally independent given the true condition (D j). The adjustable exponent b, equal to 0.71 in our study, and

A. MALCHOW-MOLLER et al. the adjustable multipliers ci serve to eliminate a major portion of the bias that arises because symptoms and signs are in fact interdependent, and partly also because the 13 diagnostic categories are of widely different size. The values for b and cj were chosen so as to maximize the reliability of P (DjlX} in the sense of agreement between cumulative diagnostic hits and cumulative expected hits [22], and at the same time so as to eliminate 'size-bias' [23]. Before introducing cj, we saw typical 'negative size-bias', i.e. the probability of rare causes of jaundice was overestimated and that of more common causes underestimated. We must refer the reader to other studies [18,22,23] for a detailed discussion of these concepts. Clinical impact Previous studies on computer-assisted diagnosis in jaundice showed no marked superiority of the computer when compared to the clinicians' diagnoses [15,19,20]. In the present study, 76% of the patients were correctly classified by the computer as compared with 77% by the experienced clinician. Of course, these figures do not differ significantly, but it must be stressed that there are methodological difficulties in comparing the two. The skills of a clinician "are hard to measure, not to mention the difficulty of comparing the skills of several doctors [17,24]. The clinician may have used information not included in the questionnaire, and he may have paid attention to other points from the known history and to the relative timing of past events, an aspect which the questionnaire cannot convey. However, as seen in Table 5, the clinician was more often 'confident' than Bayes' rule, yet he was equally often right. In that sense he did outperform the statistical rule. But in real life the computer serves as an aid and not as a competitor. Table 5 illustrates the effect of the two parties supplementing one another. The table cannot tell us the precise extent to which the computer would have corrected the clinician's opinion as to the most likely jaundice causes. The fast development of new, highly specialized and costly diagnostic tests creates a need for a wellchosen diagnostic strategy in each case of jaundice. Therefore, the preliminary clinical assessment is very

163

BAYES' RULE IN JAUNDICE important, and should, if possible, be supported by

a system that can render this service.

methods that increase its reliability. In this assessment, what matters is not whether the patient's true

In another study [16] we compared the present rule with the two manual diagnostic aids we have devel-

condition is rated most probable, but rather whether

oped, cf. Introduction. Though superior to its m a n u a l competitors, we would not yet r e c o m m e n d invest-

the top 2 or 3 diagnostic alternatives point to a diagnostic strategy that would lead straight to diagnostic confirmation. Ultimately, Bayes' rule - - and statistical diagnosis in general - - should be able to provide such support. In particular, it would help the clinician sorting out clearcut cases and referring these to one or two confirmatory diagnostic tests as appropriate. In not so clearcut cases precise diagnostic odds would also held the medical team plan a rational diagnostic workup. With our large and carefully analysed data base we feel that we are coming as close as possible to

References 1 Lusted LB. Introduction to Medical Decision Making. Charles C. Thomas, Springfield, IL, 1968. 2 Croft DJ. Is computerized diagnosis possible? Comput Biomed Res 1972; 5: 351-367. 3 Patrick EA, Stelmack FP, Shen LYL. Review of pattern recognition in medical diagnosis and consulting relative to a new system model. IEEE Trans Syst Man Cybern SMC 1974; 4: 1-16. 4 Friedman RB, Gustafson DH. Computers in clinical medicine, a critical review. Comput Biomed Res 1977; 10: 199-204. 5 Wagner G, Tautu P, Wolber U. Problems of medical diagn o s i s - a bibliography. Meth Inform Med 1978; 17: 55-74. 6 Burbank FA. A computer diagnostic system for the diagnosis of prolonged, undifferentiated liver disease. Amer J Med 1969;49: 401-415. 7 KnilI-Jones RP, Stern RB, Girmes DH, et al. Use of sequential Bayesian model in diagnosis of jaundice by computer. Brit Med J 1973; I: 530-533. 8 Lindberg G. Studies on Diagnostic Decision Making in Jaundice. Thesis, Stockholm, 1982. 9 Goldberg DM, Ellis G. Mathematical and computer-assisted procedures in the diagnosis of liver and biliary tract disorders. Adv Clin Chem 1978; 20: 49-128. l0 O'Connor KN, Snodgrass PJ, Swonder JE, et al. A blinded prospective study comparing four current non-invasive approaches in the differential diagnosis of medical versus surgical jaundice. Gastroenterology 1983; 84: 1498-1504. 11 Matzen P, Malchow-M¢ller A, Brun B, et al. Ultrasonography, computed tomography and cholescintigraphy in suspected obstructive jaundice - - a prospective study. Gastroenterology 1983; 84: 1492-1497. 12 Malchow-M~ller A, Matzen P, Bjerregaard B, et al. Causes and characteristics of 500 consecutive cases of jaundice. Scand J Gastroenterol 1981; 16: 1-6. 13 Malchow-M¢ller A, Thomsen C, Hilden J, et al. Survival

ment in implementing Bayes' rule on microcomputer, at least not as long as one is primarily interested in a distinction between obstructive and non-obstructive cases, or between the four main jaundice categories of Table 1. However, a diskette containing the approx. 1000 basic probability estimates, etc., that are needed for r u n n i n g the rule on a personal computer will be available on request, along with explicit definitions of symptoms and signs and with directions for local adaptation.

after jaundice: a prospective study of 1000 consecutive cases. Scand J Gastroenterol 1985;20: 155-162. 14 Bayes T. An essay towards solving a problem in the doctrine of chances. Phil Trans Roy Soc Lond 1763; 53: 370-418. 15 Matzen P, Malchow-M~ller A, Hilden J, et al. Differential diagnosis of jaundice: a pocket diagnostic chart. Liver 1984; 4: 360-371. 16 Malchow-M¢ller A, Thomsen C, Hilden J, et al. A decision-tree analysis for the differentiation between obstructive and non-obstructive jaundice, In preparation. 17 Theodossi A, Knill-Jones RP, Skene AM, et al. Inter-observer variation of symptoms and signs in jaundice. Liver 1981; 1: 21-32. 18 Hilden J, Habbema JDF, Bjerregaard B. The measurement of performance in probabilistic diagnosis - - I I I . Methods based on continuous functions of the diagnostic probabilities. Meth Inform Med 1978; 238-246. 19 Stern RB, KniU-Jones RP, Williams R. Use of computer program for diagnosing jaundice in district hospitals and specialized liver unit. Brit Med J 1975; II: 659-662. 20 Wheeler PG, Theodossi A, Pickford R, et al. Non-invasive techniques in the diagnosis of jaundice - - ultrasound and computer. Gut 1979;20: 196-199. 21 Hilden J, Matzen P, Malchow-M~ller A, et al. Precision requirements in a study of computer-aided diagnosis of jaundice (the COMIK-study). Scand J Clin Lab Invest 1980; 40 (Suppl. 155): 125-128. 22 Hilden J, Habbema JDF, Bjerregaard B. The measurement of performance in probabilistic diagnosis - - II. Trustworthiness of the exact values of the diagnostic probabilities. Meth Inform Med 1978; 17: 227-237. 23 Hiiden J, Bjerregaard B. Computer-aided diagnosis and the atypical case. In: FT De Dombal and F Grimy (Eds.), Decision Making and Medical Care, North-Holland Publ. Co., Amsterdam, 1976: 365-374. 24 Malchow-M~UerA, Rasmussen SN, Keiding N, et al. Clinical estimation of liver size. Dan Med Bull 1984; 31:63-68