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Warner Collection; Biomedical Informatics Collection","title_t":"A Mathematical Approach to Medical Diagnosis: Application to Congenital Heart Disease","journal_title_t":"M.D. computing : computers in medical practice","id":712982,"publication_type_t":"journal article","parent_i":0,"type_t":"Text","thumb_s":"/55/e7/55e71664dc375228ddf2867e08d89cad35df774c.jpg","last_page_t":"50","oldid_t":"uspace 10999","metadata_cataloger_t":"AMT","format_t":"application/pdf","subject_mesh_t":"Epidemiologic Methods; Mathematics; Diagnosis, Computer-Assisted; Diagnosis, Differential; Heart Defects, Congenital; Signs and Symptoms","modified_tdt":"2016-06-23T00:00:00Z","school_or_college_t":"School of Medicine","language_t":"eng","issue_t":"1","file_s":"/e2/fe/e2fed20c052291b6fc8650c73c067ec16dec2359.pdf","citatation_issn_t":"0724-6811 (Print) 0724-6811 (Linking","other_author_t":"Toronto, Alan F.; Veasey, L. George; Stephenson, Robert","created_tdt":"2015-04-15T00:00:00Z","_version_":1664094557738893312,"ocr_t":"CLASSIC ARTICLES An editorial on this Classic Article in medical computing appears elsewhere in this issue. A MATHEMATICAL APPROACH TO MEDICAL DIAGNOSIS: APPLICATION TO CONGENITAL HEART DISEASE HOMER R. WARNER, M.D., Ph.D., ALAN F. TORONTO, M.D., L. GEORGE VEASEY, M.D., AND ROBERT STEPHENSON, Ph.D. An equation of conditional p-robability is derived to express the logical process used by a clinician in making a diagnosis based on clinical data. Solutions of this equation take the form of a differential diagnosis. The probability that each disease represents the correct diagnosis in any particular patient can be calculated. Sufficient statistical data regarding the incidence of clin·ical signs, symptoms, and electrocardiographic findings in patients with congenital heart disease have been assembled to allow application of this approach to differential diagnosis in this field. This approach p-rovides a means by which electronic computing equipment can be used to advantage in clin-ical medicine. D iagnosis of disease on the basis of clinical data is considered by the medical profession to be a subtle art that can be mastered only after years of careful study and extensive personal experience. Although rapid advances are being made in the development of new and improved methods for acquiring objective information from a patient concerning an illness, similar progress has not been made in analyzing and improving the logical process by which a diagnosis is deduced from this information. The present study was undertaken to find an explicit mathematical expression for this logical process, with the hope that such an expression might improve the accuracy of diagnosis in certain fields of medicine, lead to a more scientific approach to the teaching of medical diagnosis, and provide a means, with the help of an electronic computer, for relieving the physician of the task of storing and- recalling for practical use in diagnosis an ever-increasing mass of statistical data. The derivation of such an equation is herein presented and its useful-ness illustrated in its application to the diagnosis of congenital heart disease on the basis of clinical data. Theory That the logical process involved in medical diagnosis could be expressed as a problem in conditional probability (1) was suggested by Ledley and Lusted (2). The problem consists of estimating the likelihood or probability of event y1 occurring in the presence of another event, x. In this paper the event y 1 is one disease among a series of diseases y1, y2 , .. . Yk• assumed to be mutually exclusive, and the event x is a set of clinical findings x 1, x2 , ..• xj, which will here be called symptoms even though physical signs and electrocardiographic findings are included. The probability of y 1 is defined by Ny, Equation 1: Py, = N ( y,, Y2 • • · -Yk) CLASSIC ARTICLES where NY is the number of times disease y~ would occur in a large random sample of N(y,, y2, • •. Ykl patients with diseases y 1, y2 , ••• Yk· (P y,) is simply the incidence of disease y 1 in this subpopulation consisting only of people having one of these diseases. The probability of symptoms x occurring in a patient with disease y 1 is given by where N xy is the number of patients witfi. disease y 1 also having symptoms x. Dividing the numerator and denominator of the right-hand term by the size of the population N20 yr BW l ~ = cyanosis; mild BW x . 5 = cyanosis, severe (with clubbing) BW Xfi = cyanosis, intermittent BW ~ = cyanosis, differential BW Xg = squatting BW , ~ . = dyspnea BW · :x1() = easy fatigue BW x11 = orthopnea BW :x1~ = chest pain BW. x13 = repeated respiratory infections ,BW xu = syncope BW x15 = systolic murmur loudest at apex B . :x16 = qiastolic murmur loudest at apex B { x17 = systolic murmur loudest in left 4th interspace B .x18 = diastolic murmur loudest in left 4th interspace BW x19 = continuous murmur loudest in left 4th interspace B l :xro = systolic munnur with thrill loudest in left 2nd interspace ; · .... B ~. 1 = ~ystolic m. urmur without thrill loudest in left 2nd ·.; ... · . : mterspace · ·. · BW ~ = diastolic murmur loudest in left 2nd interspace , · · BW ~ = continuous murmur loudest in left 2nd interspace · · · .. BW -~ = systolic murmur loudest in right 2nd interspace · BW ~ = diastolic murmur loudest in right 2nd interspace BW ~ -~. =systolic murmur heard best over posten.·or ch. est . : BW Xz7 = continuous murmur heard best over posterior chest ~' ·. ·. BW ~ = accentuated 2nd heart sound in left 2nd interspace : · . . BW ~ = diminished 2nd heart sound in left 2nd interspace · BW · Xao = right ventricular hyperactivity by palpation · :SW · Xa1 = forceful apical thrust BW x~2 = pulsatile liver BW x33 = absent or diminished femoral pulsation BW { x34 = E. CG axis more than 110\" BW Xss = ECG axis less than 0\" BW { Xae = R wave greater than 1.2 m V in lead V 1 BW . x37 = R' or qR pattern in lead V 1 BW Xss = R wave greater than 2.0 m V in lead V 6 BW x39 = T wave in lead V 6 inverted (no digitalis) W { ~0 = early diastolic murmur loudest at apex W x 41 = late diastolic murmur loudest at apex W { ~42 = holosystolic murmur loudest in left 4th in1ter:sp;;~oee · W x43 = midsystolic murmur loudest in left 4th inf·.,. ...... .,....\"', W { \"« = holodiastolic murmur loudest in left 4th W x~ = early diastolic murmur loudest in left 4th in1tersm~ W I :?C46 = midsystolic murmur with thrill loudest in 2nd interspace W ~7 = holosystolic murmur with thrill loudest in 2nd interspace W x48 = midsystolic murmur without thrill loudest in interspace W ~9 = holosystolic murmur without thrill loudest in interspace BW Xso = murmur louder than gr 3/6 \"'B indicates that the symptom was used on the brown Chl~cJ\\:.\"OJl W indicates that the symptom was used on the white ChleCI4~-oll .S1 tSymptoms within braces are mutually exclusive and must be,:. handled as special cases (see text). ~{I)ISEASES INCLUDED IN DIFFERENTIAL ~'.DIAGNOSIS .; .. Ji -~~ Table 2 \\\\ ~t·~~ : ~:J::t!eptal defect without pulmonary stenosis or ~~. pulmonary hypertension* .• ~.-.·:~ •.-• !•• ••.•. ' Y:Ya 4 = atrial septal defect with pulmonary stenosis .:- = atrial septal defect with pulmonary hypertension • ~; y5 =complete endocardial cushion defect (A·V commune) ~~- y6 =partial anomalous pulmonary venous connections ',, (without atrial septal defect) ~~· y7 = total anomalous pulmonary venous connections , ': (supradiaphragmatic) :\\; y8 = tricuspid atresia without transposition .· y9 = Ebstein's anomaly of tricuspid valve '.·. y10 =ventricular septal defect with valvular pulmonary .\\ · stenosis :'.;· y11 =ventricular septal defect with infundibular stenosis i:'. y12 =pulmonary stenosis, valvular (with or without probe-patent foramen ovale) y13 =pulmonary stenosis, infundibular (with or without .~ probe-patent foramen ovale) Yt• =pulmonary atresia y 15 = pulmonary artery stenosis (peripheral) •. . •JI6 = pulmonary hypertension, • isolated Yt7 =aortic-pulmonary window y18 =patent ductus arteriosus without pulmonary hypertension* y19 = pulmonary arteriovenous fistula y20 = mitral stenosis Y2 t =primary myocardial disease \\ YP2. = anomalous origin of left coronary artery y23 =aortic valvular stenosis y24 = subaortic stenosis yP.l) = coarctation of aorta Y26 =truncus arteriosus Y?:T = transposed great vessels y28 = corrected transposition Y29 =absent aortic arch y80 =ventricular septal defect without pulmonary hypertension • y31 =ventricular septal defect with pulmonary hypertension* y32 =patent ductus arteriosus with pulmonary hypertension* y33 =tricuspid atresia with transposition *Pulmonary hypertension is defined as pulmonary artery pressure ~ systemic arterial pressue~ al probability (P xly ) of symptom complex x occurring in disease y1 must be the product of the probabilities of the individual symptoms that make up the set occurring in disease y1 • This is expressed in Equation 7: In order to clarify the meaning of independence of individual symptoms let us consider the case of two symptoms, Xa and xb. It might be argued that for xa to be truly independent of xb, the probability of Xa must not be influenced by the presence of xb; that is Equation 8: P x.'x.. = P x •. However, this can be true only if xb is uniformly distributed throughout the population. This means that P \"\"'Y• = P \"\"'Y• = P Xb'Y• = 1 and that xb is of no diagnostic value. For this reason Equation 8 must be an inequality. In spite of this, these symptoms for present purposes are truly independent of each other as long as this inequality is due only to the non-uniform distribution of xh in diseases y1 , y2, •.. Yk and not due to a direct causal relationship between Xa and xb. In the selection of symptoms to be used in a particular field, care must be taken to adhere to this criterion as closely as possible. With use of Equation 7, we may rewrite Equation 6 in an expanded form as Equation 9: With this expression it is possible to calculate the probability (Pyllx,. x2, . • • x;) t~at ~ach disease Y1• Y2· ... Yk extsts rn the presence of symptoms x1 , x2 , ••• xj from statistical information concerning the incidence of each disease P Y in the population under conside~ation and the incidence of each of the patients' symptoms in each of these diseases (P x 1y , P x 'Y , etc.). These statistical' d'ata, 2 required for the righthand term of Equation 9, may be compiled and stored in a form (punched cards, punched paper tape, or magnetic tape) that will make them readily available for an electronic digital computer to extract the pertinent numbers (depending on the symptoms presented by the patient) for carrying out the calculation called for by the equation. Because Equation 9 uses only probabilities involving the symptoms actually present in the patient under consideration, the absence of a particular symptom does not influence the diagnosis. Thus, in order to make use of the fact that the absence CLASSIC ARTICLES of a symptom may have a bear- in disease YI> its complement (1 ization and/or findings at sur-ing on the probability of a given - P x81y;) must represent the prob- gery, and because relatively ob-disease being present, Equation ability of symptom x8 not occur- jective clinical findings can easi- 9 is modified to give ring in a patient with disease y 1. ly be obtained, this field was Thus, the absence of a symptom chosen for a pilot study. The list Equation 10: is treated as a discrete event of symptoms and diseases used p - when Equation 10 is used, and in this study, with their corre-y 11(x1,x8, ••• xJ) the probability that a symptom sponding symbols, is shown in p y,P x,ly,(1 - p J~~<;'Y• is absent can be obtained direct- Tables 1 and 2. Statistical infor-ly from the probability figure for mation concerning the incidence L Py.Px,ly.(1- P\"siY) · · .PxJIYt the presence of the symptom. of each of these symptoms in all k each of these diseases is present- Application to Congenital Heart ed in Table 3. The numbers in where the bar above x8 in the the first column represent the initial term indicates that symp- Disease incidence of each disease (P y) in tom x8 is not present in the pa- Because the accuracy of a diag- the subpopulation made up of tient under consideration. Be- nosis of congenital heart disease patients referred to this labora-cause P>~~~~ X1s x17 Y,············ 0.,100 01 49 50 01 00 01 00 01 01 10 03 05 05 03 05 01 70 02 Y2··········~ .081 10 50 50 02 01 02 00 01 35 50 05 02 40 01 02 02 30 20 Ya············ .005 30 60 10 20 10 20 00 01 60 70 05 02 10 10 02 02 05 05 Y4····· .. •··•• .001 10 20 70 30 10 25 00 01 80 90 05 05 15 10 02 02 15 20 Y6······ ...... .027 20 50 30 15 05 10 00 01 40 50 05 05 30 05 60 15 90 40 Ys············ .005 10 40 50 01 01 01 00 01 15 20 01 05 05 01 02 02 20 02 Y7············ .00~ 20. 70 10 65 10 05 00 01 70 80 05 05 20 05 02 02 10 15 Ys············ .. 018 50 48 02 30 65 01 00 10 80 90 20 05 15 10 02 05 65 05 y9 ............ .001 10 45 45 22 44 01 00 22 80 80 10 30 15 22 05 25 95 25 Yto··· .. •···· .054 40 55 05 25 25 10 00 30 75 90 05 05 10 20 02 02 20 02 Yu .. ····••·· .063 40 55 05 30 30 10 00 40 75 90 05 05 10 25 02 02 20 02 Y12 ...... : ... .045 20 70 10 01 01 01 00 01 50 65 01 01 01 10 02 02 10 02 Y1a·-······· .013 20 70 10 01 01 01 00 01 50 65 01 01 01 10 02 02 10 02 Y14·········· .014 90 09 01 10 90 00 00 80 90 99 05 10 05 35 02 02 40 05 Y1s·········· .001 05 45 50 01 01 01 00 01 01 01 01 01 01 01 04 01 02 01 Yt.s·········· . . 013 10 45 45 01 01 01 00 01 70 95 40 10 10 10 01 01 30 05 Yt7·········· .001 3.0 60 10 05 01 01 00 01 10 10 05 01 10 01 05 10 20 05 Y1s······· .. • .07~ 20 40• 40 01 01 01 00 01 20 20 10 01 10 05 05 15 10 02 YI9··· ....... .002 20 30 50 45 45 01 00 01 10 20 05 01 01 10 05 02 10 02 Yzo·········· .008 20 50 30 01 01 01 00 01 50 50 40 05 10 10 80 20 10 I{) Y21 :··· ...... .013 70 29 01 01 01 01 00 01 40 50 20 01 05 05 15 02 05 02 Y22-····-·· .001 70 29 01 01 01 01 00 01 30 30 30 80 15 20 05 01 01 01 Y2a··· .. ·•··· .036 10 80 10 01 01 01 00 01 20 30 20 15 01 35 20 02 20 10 Yu .......... . 009 10 80 10 01 01 01 00 01 20 30 20 15 01 35 20 02 20 10: . Y26·········· . 054 10 70 20 01 01 01 00 01 20 30 20 01 01 05 05 01 20 .10 . Y2s·········· .005 50 40 10 30 60 01 00 15 15 30 05 . 01 20 10 02 02 70 02· Y27 ·-······· .. 063 90 10 00 20 60 05 10 05 60 70 20 u~. 10 05 02 50 02 Y2B····-···· .. 001 30 30 30 30 05 10 ()() 01 10 20 01 01 05 02 70 Q2, y~ ............ .001 60 39 01 01 01 01 80 30 10 50 05 20 01 20 05 02 50 02 ,- Y3o·.······· .. ~52 15 70 15 01 01 0.1 00 01 20 30 05 01 15 05 05 20 95 05 >. Y:u·•····· .. , . _.081 3.0 60 10 30 50 10 00 05 60 70 20 10 20 10 05 01 50 .lQ.;,. -Ya2··· ........ :.- .00~ 30 40 30 01 01 05 50 01 20 30 10 01 10. 05 02 02 10 .to : Y88.·········· ,, ... 06~ . 40 55 05 50 20 10 00 01 80 90 20 01 30 05 05 10 70 0{5 . 46 M.D. COMPUTING .... of Table 3 is a matrix with symptoms along the horizontal axis and diseases listed vertically. For instance, the number 0.02 at the intercept of symptom x , and disease y2 represents P x.1y2 , the probability or incidence of mild cyanosis occurring in a patient with atrial septal defect Vlithout pulmonary hypertension. (In this study pulmonary hypertension is arbitrarily defined as pulmonary artery pressure equal to or greater than aortic pressure.) Several things about this symptom-disease matrix require explanation. Listed among the diseases is a category called normal. The incidence of normal X2s Xz7 X2s x29 Xao X:n Xa2 X sa 01 01 15 05 10 03 01 01 01 01 60 01 80 01 01 01 01 02 30 15 40 01 o5 01 01 01 95 01 50 01 65 01 01 01 70 02 40 10 10 01 10 15 40-. 02 10 01 01 01 10 15 85 02 80 01 01 01 '01 01 02 60 01 20 30 01 01 01 02 35 ro 20 10 01 10 15 10 00 20 01 02 01 10 15 10 60 20 01 02 01 01 01 10 60 20 01 05 01 01 01 10 60 20 01 05 01 10 10 01 90 20 01 02 01 50 05 10 02 10 01 01 01 02 02 95 00 30 01 10 01 . 02 02 70 01 20 40 01 01 03 05 50 01 20 40 02 01 05 70 05 05 20 01 01 01 ' 01 01 50 01 20 05 02 Oi 01 01 20 02 10 50 02 01 01 01 20 02 01 05 oi 01 01 01 20 10 01 40 01 05 01 01 20 10 01 40 01 05 80 ' 15 10 10 01 30 01 99 05 10 40 10 30 05 01 01 01 01 20 10 20 20 02 02 01 01 20 10 10 10 01 oi 01 01 90 02 40 05 01 10 01 01 30 0~ 05 30 01 01 01 01 90 02 30 05 05 01 02 02 90 02 30 05 05 01 01 01 30 10 01 20 30 01 (P Y ) in this study is 0.10, since 10% of the patients referred to this laboratory for heart catheterization are normal by physiologic studies, which include dyedilution curves. The figures in the incidence column and symptoms x 1, x2 , and Xa (age) may vary from one population to the next, while the other data, which express the probability of each symptom in each disease, should remain constant from one laboratory to the next. Each of the probabilities in the matrix was determined by us from a careful review of published data of others, particularly Keith and coworkers, 3 review of data ob-xs,, X as x36 Xa7 X as Xag X..o X.u Xu 01 02 02 02 02 02 01 00 02 70 05 05 85 02 02 -'ni 02 01 85 05 20 70 02 02 . 01 ·01 01 85 05 20 70 02 02 - 01 02 01 05 70 05 85 02 02 15 01 85 tained from 1035 patients referred to this laboratory for diagnostic catheterization, and estimates based on the pathologic physiology of the defect in the case of rare defects in which adequate statistics were not available. Notice that each patient is classified according to age into one of three categories-! month to 1 year, 1 year to 20 years, and over 20 years of age. The patient's age is treated as a symptom. For instance, the number 0. 70 occurring at the intercept of x 2 and y 13 indicates that this symptom (age, 1 to 20 years) will occur in 70 of 100 patients with X4a x\"\" X.ts X4s X47 X\"s X49 x50 70 04 03 00 00 80 05 10 30 02 20 05 01 90 01 60 05' Ql 05 60 01 38 01 70 15 20 · 02 05 01 40 01 40 05 02 20 02 20 20 20 80 15 02 02 15 02 02 02 02 02 . 20 02 02 02 02 60 02 30 90 02 25 75 o2 . 02 0~ 02 30 10 01 ' 30 05 01 80 02 70 02 90 02 02 90 ·10 05 02 50 . 15 o5 02 20 20 20 20 50 10 02 02 60 02 02 25 25 45 45 25 25 15 15 05 05 50 95 02 85 10 02 02 02 02 20 05 02 02 60 05 25 05 90 95 02 85 10 02 _02 02 02 20 o5 02 02 60 05 25 05 90 95 02 85 10 02 02 01 01 01 .10 02 02 68 01 25 01 80 95 02 85 10 02 02 01 01 01 10 01 01 68 01 25 01 80 95 02 85 10 02 02 02 01 30 40 02 05 01 01 02 02 20 10 02 10 02 02 02 tn 01 02 02 ()1 00 02 01 25 02 60 95 02 90 05 02 02 01 01 01 30 15 05 02 02 05 02 20 . 01 15 02 02 60 05 10 02 10 20 05 02 02 02 10 05 75 02 10 02 02 50 05 ' 10 02 05 10 02 02 05 02 . 20 10 85 05 05 02 02 02 02 02 . 02 H) io 02 02 02 02 . 10 10 30 50 02 10 40 02 02 20 20 10 10 •10 10 05 05 10 10 7o 05 io 05 0,5 40 90 02 02 10 10 02 02 .92 02 05 05 10 05 10 05 05 20 .90 . 01 01 01 oi 01 01 · 01 01 01 01 10 05 15 02 02 70 15 02 02 02 20 10 02 05 01 05 01 90 ' 05 15 02 02 70 ' 15 02 02 02 20 10 02 05 Oi .05 01 . 90 05 05 02 02 40 04 01 01 05 20 ; 1(} 02 0~ ' 02 iO 05 . E>5 30 10 40 10 20 05 ·o2 02 40 40 02 ' 02 10 10 . 10 10 40 40 20 30 05 20 05 02 02 30' 30 . 02 62: 03 03 . 10 10 50 20 10 10 10 10 10 02 . 02 30 30 . 02 02 . 05 05 30 30 60 70 05 80 05 10 05 o2 02 3o 30 ' 02 '02 ' 10 l'o 30 30 20 30 10 05 05 . 15 05 20 02 92 o5: 05 01 01 10 01 10 85 70 05 75 15 10 05 01 01· 30 . 30 iu 02 01 05 01 A~O 70 05 75 15 10 . 05 02 02 . 10 . 10· 02 02 02 02 20 20 0 02 90 02 02 90 10 10 02 30 30 05 05 10 10' 30 30 50 VOL. 9, NO. 1. 1992 47 CLASSIC ARTICLES ·1]EtwS TO BE-USED IN EQUATION 10 IN . '.CASES OF MUTUALLY EXCLUSIVE SYMPTOMS .., _, _ . · .. - ' . . . Table 4 .~heck ·, ·tlheet ' - ~ ' ~ .. B/W B!W . B/W B . B w w. w Sym.p~ ~cxs - 48 M.D. COMPUTING Symptom prettent xl ~ . Xs none X26 Xir neither :x28 ~ neither x34 Xso neither Xs6 Xs7 neither xl7 :x18 Xtg none Xl7• Xts Xzo X21 x22 x23 ~o,Xzz x2 ~, x 22 , ,J:Wne X19 X42 ~s x.u ~5 ~.x.u ~.~ x42.~ x43, x45 none ~0 ~1 neither Xzz ~6 X47 ~ JC..tg :le..t6• X22 JC..t7,Xzz JC,jg, x22 ~g, Xzz ~ none Term to Be Used infundibular pulmonary stenosis who come to this laboratory. In this way, then, the fact is recognized that the age of the patient does influence the probability of a given diagnosis . Since the patient can belong in only one of the three age groups, these three \"symptoms\" cannot be considered independent of one another. Thus, if the patient's age is between 1 and 20 years, P x 2 is used in Equation 10 but the complement of the probability for the other two age groups is not used in this case. Furthermore, it is important that care be taken not to include in the list of symptoms any two symptoms that invariably occur together, since this strongly suggests interdependence and a causal relationship between them. For instance, clubbing of the fingers was not included as a separate symptom since it occurs in the same patients with congenital heart disease who have evidence of severe cyanosis. Instead, it is included as part of the definition of severe cyanosis. Inclusion of redundant (interdependent) symptoms would result in an unreal increase in the probability of those diseases having a high incidence of these symptoms when these symptoms are present, and a falsely low probability when these symptoms are absent. There are other symptoms in the list that are mutually exclusive. For instance, the existence of x5 excludes by definition x4, Xt;, and x7 • Thus, it would be an error to consider the absence of x4, :xs, and x7 as additional pieces of information once-.x5 is known to be present. On the 1 other hand, the absence of x4 through x7 in a particular case (no cyanosis) is an important fact and must be recognized by using in Equation 10 the complement of the sum of the probabilities of each of these symptoms occurring in the disease in question, which is 1 - Px41y1 -Px51y1 -Px,;ly1 -Px7jy1• Groups of mutually exclusive symptoms are indicated by braces in Table 1, and a complete list :TEST CASE ILLUSTRATING EFFECT OF INCLUDING NEGATIVE INFORMATION Table 5 Diagnosis with Equation 9 Diagnosis with Equation 10 . Symptom Disease Probability Disease Probability . Xs .......... . · xlO Xu X29 Xa4 X as X43 X4s Yu Y1o Y1e Y12 Yl3 of mutually exclusive symptoms, together with instructions about what data should be used in solving Equation 10 in any particular case, is given in Table 4. Use of the Computer Because of the large number of calculations required to make each diagnosis in the example (congenital heart disease) used in this paper, it is necessary to use a digital computer if Equation 10 is to be solved in a practical way. This equation can be solved by almost any generalpurpose electronic digital computer that has the capability of \"floating decimal point\" operation. The incidence of each symptom in each disease shown in the matrix is transferred to punch cards. These disease cards, together with cards that contain the program telling the computer what operations to perform, are transferred into the computer memory by a card-reading machine. Another punched card is prepared from a check-off list of symptoms on which the physician, after examination of the patient, has marked the symptoms presented by the patient. (X-ray data are not presented in this paper but are being evaluated for inclusion in the symptom list at the present time.) From this information, the computer then calculates, with use of Equation 9 or 10, the probability of each of the 33 congenital heart diseases being present in the patient under consideration. The diseases with probabil- 0.33 Y12 0.62 0.28 Y1a 0.21 0.11 Y10 0.07 0.14 Yu 0.04 . 0.04 Y1e 0.03 ity greater than 1% are printed out at the end of the calculation, together with their respective probabilities. Two symptom lists are checked off by the clinician after examination of each patient. On one list (brown sheet) murmurs are described only as to timing and location, while on the other list (white sheet) the time course of intensity of the murmurs is included (Table 1). Equation 10 is solved with each of these sets of symptoms, and the resulting differential diagnoses are compared. Although the calculation based on the white sheet often gave a higher probability to the correct diagnosis, this was not consistently the case, particularly in instances in which classification of the time course of murmur intensity was difficult even with the help of a phonocardiogram. The point to be made here is that in applying this approach to diagnosis a compromise must be reached between two alternatives: the desirability of using as much information as possible, and the limitations in accuracy with which the more detailed information can be observed in the patient and the necessary statistical data can be obtained. Example The case shown in Table 5 illustrates the effect of using both positive and negative information in making a diagnosis. The list of symptoms indicates that the patient was over 20 years of age and complained of easy fatigue and orthopnea; his pulmo- Diagnosis ·with Equation 10 and without ::&1 Y12 Y1a Yro . Probability 0.73 0.24 0..02 I nary second sound was diminished; his electrocardiogram exhibited an axis greater than 110° and an R wave greater than 1.2 m V in lead V 1 ; and by phonocardiogram he had a midsystolic murmur, without a thrill, which was of equal intensity in the pulmonary (second left interspace) and the precordial (fourth left interspace) area. Calculation of the probabilities for each disease with use only of the positive information (Equation 9) resulted in a higher probability for tetralogy of Fallot (y10 and y11) than for isolated pulmonary stenosis (y12 and y 13). However, when both positive information and negative information were taken into account, as when Equation 10 is used, the probability of isolated pulmonary stenosis became 0.83, while the probability of tetralogy of Fallot was only 0.11. This patient was later found to have y12 both by physiologic studies and at surgery. Also illustrated in Table 5 is the way in which this approach can be used to evaluate the contribution made toward a diagnosis by any given symptom. Here the calculation has been carried out with and without the symptom of art.hopnea (x11). Had this patient not complained of orthopnea the probability of isolated pulmonary stenosis (y12 and y 13) would have been 0.97, as compared with 0.83 when orthopnea was considered present. This, of course, results from the fact that orthopnea rarely occurs in patients with Y12 or Y1a· Since the presence or absence of VOL. 9, NO. 1, 1992 49 CLASSIC ARTICLES just one symptom may make a real difference in the differential diagnosis, as in this instance, it is apparent that each symptom on the list must be accurately evaluated in every case if the correct probabilities are to be calculated. For this reason, only the most objective symptoms should be included in the definition of the original list for any study, even if this must be done at some sacrifice of detail. In the case of the present study we are under the impression from our experience to date that symptoms 10 through 14 detract from the accuracy of diagnosis as often as they contribute, because of the difficulty involved in assessing their actual presence or absence in many cases, as well as the inaccuracy of the available statistical data regarding the incidence of these symptoms in each of these diseases. These five symptoms might well be eliminated from the list. Evaluation of Experience to Date Because the differential diagnosis obtained with this approach represents an estimation of probabilities in which the statistical data of Table 3 are used, it is impossible from a limited number of cases to evaluate its accuracy. However, it is apparent from our experience to date with 36 cases that the most probable diagnosis estimated with Equation 10 agrees with the actual diagnosis made by physiologic studies and observation at surgery at least as often as does the most probable diagnosis estimated by three experienced cardiologists from the same clinical information. Furthermore, the differential diagnosis resulting from solution of the equation is frequently more complete and, in retrospect, often appears more logical to the clinicians than the differential diagnosis listed by each of them before seeing the equation's prediction. It must be emphasized that Equation 10 was derived directly from the definition of conditional probability. Thus, any evalua- 50 M.D. COMPUTING tion of the accuracy of the predictions made by this approach should be considered as testing the adequacy of the matrix of statistical data and not of the equation. Given the correct original data matrix and accurate observations of the patient, the calculated probabilities will be correct. Final refinement of the present data matrix must await the accumulation of sufficient data for calculation of new probabilities (P xJIYo Since the presence or absence of each symptom is determined in each case, and follow- up information almost invariably yields the diagnosis with certainty, the data for satisfactory recalculation of symptom incidence are routinely accumulating. The computer will be used to recalculate its own data matrix when the amount of data is sufficient. Aids to Teaching That an explicit expression of the logic used in medical diagnosis has potential usefulness as a tool for teaching diagnosis to medical students and physicians seems apparent. The approach here presented provides a framework within which any diagnostic problem can be formulated and critically analyzed. Often the very act of attempting to formulate the problem in terms required for application of Equation 10 results in new insight by providing answers to such questions as: 1. What is the exact definition of each symptom and each disease? 2. Are certain symptoms interdependent and others mutually exclusive? 3. What symptoms are important determinants of the diagnosis and what symptoms are unimportant? A solution of Equation 10 for any given set of symptoms provides an objective, reproducible standard against which students can check the accuracy of their own deductions from these symptoms. How modifying the symptom set in any desired fash-ion affects the differential diagnosis can be readily observed. This approach to the teaching of diagnosis of congenital heart disease is in current use at this hospital and has met with enthusiastic acceptance by medical students. Appendix To illustrate the use of Equation 10, consider the simple case of a population consisting of just two diseases (y1 and y2) and three independent symptoms (x11 x2, and x3). The relative incidence of these two diseases and the probability of each symptom in each disease are shown in the matrix below. Incidence x 1 0.23 0.77 0.1 0.8 0.7 0.6 0.2 0.5 If the patient to be diagnosed presents with symptoms x 1 and x3 , Equation 10 would be solved with use of the following numbers to make the diagnosis: Py11(x1,x2,x3J = 0.23(0.1)(1 - 0.7)(0.6) 0.23(0.1)(1 - 0.7)(0.6) + 0.77(0.8)(1 - 0.2)(0.5) =0.01-~ and 0.77(0.8)(1 - .2)(0.5) 0.23(0.1){1 - 0.7)(0.6) + 0.77{0.8)(1 - 0.2)(0.5) = 0.984 [Adapted from JAMA (1961; 177(3): 177-183) with the permission of the publisher.] References L Feller, W., An Introduction to Probability Theory and Its Application, New York: John Wiley & Sons, Inc., 1960. 2. Ledley, R.S., and Lusted, L.B., Use of Electronic Computers to Aid in Medical Diagnosis, Proc Inst Radio Engineers 47: 1970-1977 (Nov.) 1959. 3. Keith, J.D., and others: Heart Disease in Infancy and Childhood, New York: The Macmillan Co., 1958."}]},"highlighting":{"712982":{"ocr_t":[]}}}
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