{"responseHeader":{"status":0,"QTime":6,"params":{"q":"{!q.op=AND}id:\"712955\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"volume_t":"2","ark_t":"ark:/87278/s6h73qzz","setname_s":"ir_uspace","restricted_i":0,"department_t":"Biomedical Informatics","format_medium_t":"application/pdf","creator_t":"Warner, Homer R.","date_t":"1969","mass_i":1515011812,"publisher_t":"Elsevier","description_t":"Biomedical Informatics","first_page_t":"486","rights_management_t":"Copyright © Elsevier 1969","relation_is_part_of_t":"Homer R. Warner Collection; Biomedical Informatics Collection","title_t":"A Mathematical Approach to Medical Diagnosis: Application to Polycythemic States Utilizing Clinical Findings with Values Continuously Distributed","journal_title_t":"Computers and Biomedical Research","id":712955,"publication_type_t":"journal article","parent_i":0,"type_t":"Text","thumb_s":"/55/e7/55e71664dc375228ddf2867e08d89cad35df774c.jpg","last_page_t":"493","oldid_t":"uspace 10972","metadata_cataloger_t":"AMT","format_t":"application/pdf","subject_mesh_t":"Bayes Theorem; Probability; Computers; Likelihood Functions; Hematologic Diseases; Polycythemia Vera; Diagnosis, Computer-Assisted; Normal Distribution; Statistical Distributions; Hemoglobins","modified_tdt":"2016-06-22T00:00:00Z","school_or_college_t":"School of Medicine","language_t":"eng","issue_t":"5","file_s":"/9b/d2/9bd29c9828828df8674eeea762b93e8ebdd4bdd7.pdf","citatation_issn_t":"0010-4809 (Print) 0010-4809 (Linking)","other_author_t":"Bishop, Carter R.","created_tdt":"2015-04-15T00:00:00Z","_version_":1679953790342529024,"ocr_t":"COMPUTERS AND BIOMEDICAL RESEARCH 2, 486-493 (1969) A Mathematical Approach to Medical Diagnosis: Application to Polycythemic States Utilizing Clinical Findings with Values Continuously Distributed * CARTER R. BISHOP AND HOMER R. WARNER Department of Medicine and Department of Biophysics and Bioengineering, University of Uta/z, Salt Lake City, Utah 84112 Received May 12, 1969 Certain clinical findings, largely laboratory data, which help to distinguish the various polycythemic states, are continuously distributed. These continuous distributions were used as probability functions from which elements of Bayes' formula for conditional probability were derived. This formula was written into a computer program which calculates a probability value for each of the diagnostic possibilities. A preliminary trial of the program employing this technique was applied to 103 cases that were either normal or known to have polycythemia rubra vera. When presented with the initial patient data the mathematical probability diagnosis was correct 95% of the time. Three hematologists were 76% correct whereas three general practitioners were correct in 65% of the same cases. In the process of making a medical diagnosis the physician must recall a great deal of past information against which the new patient is compared. This recollection is always subject to human error. Even with the best recollection, the physician would be unlikely to compare each case equally and he might be influenced by findings which have little bearing on the diagnosis. The computer has been employed to provide perfect recollection and impose internal consistency. Several workers have proposed conditional probability as a means of accomplishing these goals using Bayes' formula for conditional probability.1 •2·\"··'· 5 These programs have dealt with clinical findings that could be classified in a given patient as being present or absent. When clinical findings which present as a continuous function were utilized, probability values were assigned to certain ranges of the continuous function and often such data have been reduced to a binary function by setting a dividing line, one side of which was considered \"'This investigation was supported by a postdoctoral research fellow~hip (1-F2-GM- 29,729) from the National Institute of General Medical Science~ and by grants from the Division of Research Facilities and Resources (FR-00012) and the Nationallnstitute of Arthritis and Metabolic Diseases (AM-04489), National Institutes of Health, Bethesda, Maryland. 486 MATHEMATICAL DIAGNOSIS TABLE 1 LIST OF CLINICAL FINDINGS EVALUATED FROM THE HISTORY, PHYSICAL EXAM AND THE LABORATORY Volume of Packed Red Cells Red Blood Cell Count Hemoglobin Concentration White Blood Cell Count Granulocyte Count Platelet Count Leukocyte Alkaline Phosphatase Age at the Onset of the Disease Basophilia Splenomegaly Ph 1 Chromosome Sex Race Altitude of Patient's Place of Residence 487 abnormaP•4 • 0 • It is the purpose of this paper to present an approach to such clinical findings which treats the continuous distribution as a probability function and thus permits the data to speak more sensitively for themselves. The polycythemic states were divided into five disease categories; normal, polycythemia rubra vera [PRV], secondary polycythemia (A) [2° (A)], secondary polycythemia (B) [2 ° (B)], and chronic myelocytic leukemia [CML]. For the purposes of this preliminary report only normal and PRV are considered. Thus the probability space is made up of patients referred to a hematologist because of polycythemia who were proved to be normal or have PRY. The records of 250 cases of polycythemia were examined at the Division of Experimental Medicine, University of Oregon College of Medicine, Portland, Oregon.* The clinical findings recorded at the patients' initial visits to the University of Oregon Medical Center were used. If prior therapy might have altered any of the findings, no recording of that value was made. Clinical findings used in this study are listed in Table 1. For those findings that were binary in character (e.g. Ph1 - chromosome, splenomegaly, sex and basophilia), the incidence of that finding in the two disease categories was calculated. A histogram of the frequency distribution was prepared in each of the disease categories for each of the eight clinical findings that were continuously distributed. The frequency distribution of the laboratory findings which were continuous functions were well described by a lagged-normal distribution. f(x) = _1 ; - e-!(\":r- T . f'(x), 11y 27r (1) * The records were made available by Dr. E. E. Osgood and his associates. 488 BISHOP AND WARNER where f (x) is d f(x)jdx. An essential property of this equation is that the variance of f(x) is a function of u and T, so that S.D. ~ = rr' + T'. The best fitting lagged-normal distribution 7 was found for each histogram (Fig. 1). From the mean, standard deviation, and tau parameter of each of these distributions the probability of any given value for a particular test in each disease category can be determined. Table 2 shows the mean CtL), standard deviation (u) and tau (T) values for these eight tests in the two disease categories. In the normal group, each of the variables was normally distributed, so no entry is made for 'T which is zero. In Table 3 the incidence of the Ph1 chromosome, basophilia, spelenomegaly and male sex are depicted. The probability for the Ph1 chromosome in the normal and polycythemia rubra vera patients is assumed to be near 0.0, although this figure was not derived from the 250 records reviewed. Basophilia is only very roughly measured here as the presence of any basophils in a count of 200 cells. Splenomegaly is considered present if the spleen is felt below the costal margin and absent if not palpable. 20 A 15 10 ;;; <\"\"n <( u u. 0 ci -:z >- u 50 c z \"::\"> a \"\" 40 ~ 30 20 10 ~ ' 17.3 • ' I. 5 T ' 2. 5 13 14 15 16 17 18 19 20 21 22 23 24 25 HEMOGLOBIN CONCENTRATION 5 6 7 8 9 10 RED BLOOD CELL COUNT !millionsl ~ ' 6.5 • ' .5 T ' I.Q >u z ~ 40l 0 ~ 3o I 20 10 40 50 60 70 VOLUME OF PACKED REO CELLS 8 14 20 ~ ' 8 .4 • ' 2.7 T ' 6.0 WHITE BLOOD CELL COUNT !Jhousondsl FIG. 1. Histogram showing the frequency of various blood determinations in polycythemia Rubra Vera with the Best Fitting Lagged-Normal Distribution. The bar graph is a simple frequency plot of tbe blood determination. The smooth curve is the best fitting lagged-normal distribution. MATHEMATICAL DIAGNOSIS TABLE 2 MEAN (p), STANDARD DEVIATION (cr) AND SKEW FACTOR (r) OF THE CLINICAL FINDINGS IN THE DISEASE CATEGORIES; NORMAL AND PoLYCYTHEMIA RUBRA VERA PRV Normal• PRV Clinical findings I' j= I m n :2:: Pen;> · II PcsJ I Di> J=l j=l .0001 .52 .66 .575 (2) where D, is one of a set of 'm' diseases which are mutually exclusive, Si is one of a set of 'n' clinical findings. The P J · a; + (1 - Pes; [ n;J) (l - a;)] P I -___ i=l (Di SjJ = 111 n (3) I: [PcviJ II !Pes; I D1) • a;+ (1 + Pu;; In;,) (1 - a;)J] i-1 j=l 490 BISHOP AND WARNER The 'a' is a factor which is assigned a value of 1.0 if the clinical finding is prestnt and 0.0 if the finding is absent. This tem1 can be used to weight the importance of some of clinical signs as was done in this program with the basophil count. Since basophilia is only grossly quantitative, its presence or absence as defined should not carry the weight that the volume of packed red cells does . For that reason 'a' is 0.6 if basophilia were present and 0.4 if absent. Figure 2 shows the distribution of hemoglobin values in the two disease categories. If a hypothetical case had a hemoglobin concentration of 18.0 gm %, the probability that a hemoglobin value would be in that range in each of the five disease categories (P ~~- I I \"[\" = 2.5 u I I z LLI I :::0 I 0 LLI I ~~