The Likelihood Concept in Differential Diagnosis

THE LIKELIHOOD CONCEPT IN DIFFERENTIAL DIAGNOSIS MARTIN LIPKIN, M.D.* During the past ten years, a number ofstudies have tried to systematize certain portions of differential diagnosis. They have attempted to subject the information that enters into differential diagnosis to various analytical treatments and to study some of the fundamental operations that appear to take place during the formation ofa differential diagnosis. The results of the studies reveal certain similarities between the experimental work and the practice ofdifferential diagnosis, and they indicate various directions to be taken in future studies. They also indicate the possibility that automation of certain portions of differential diagnosis may be quite feasible. Thepurpose ofthis paper is to describe some aspects ofthe experimental work in this field. It is hardly necessary to mention that no areas ofsystematics or automation are able to catalogue and correlate data as fluidly and discriminatingly as can the minds ofphysicians. On the other hand, it is equally important to recognize that automated processes contain certain tremendously valuable properties, such as extensive memories, and the ability to perform a large number ofcalculations very rapidly. With these potential advantages and known disadvantages in mind, the various experimental studies have approached certain areas related to differential diagnosis in the following manner: to recognize the relationship—similarity or dissimilarity—that a given pattern of information (hospital case data) has to other patterns (disease criteria); to derive functions that quantitativelyexpress the similarity or dissimilarity between the two patterns; to organize and report the results in a form useful to the physician in making a differential diagnosis. * Associate Professor ofMedicine, Cornell University Medical College, Second (Cornell) Medical Division, BellevueHospital. This article is based on a lecture delivered atthe Symposiumon the Diagnostic Process, sponsored bythe University ofMichigan Schools ofMedicine and Public Health, Ann Arbor, May 9-11, 1963. 485 I. Development ofthe Diagnostic Index Among the early experiments in this field were two data analyses initiated in 1952 1-3. The first measured the likelihood of a diagnosis by comparing the findings in a hospital case to the descriptions ofdiseases and then calculating a numerical value for each diagnosis considered. The list of diagnoses, enumerated with their numerical values in rank order, is called the Diagnostic Index. The diagnosis ofhematologic diseases is ultimately based on objective criteria. For this reason all the data describing 26 hematologic diseases were listed in a master code. A numerical value, or weight, was then assigned to each item ofinformation present in each ofthe diseases. The instructions stated: given a disease description, assign a positive weight to data that contribute to the diagnosis, give a negative weight to data that do not. Let the significance ofthe item in the disease determine the weight. Each item may thus carry a different weight in each disease. Let each disease description have all the items in the master code, and each item in each disease a positive or negative weight. The sum of all the weights in each disease will yield the total positive weight and the total negative weight ofthe disease. In accordance with these instructions 1-3, hospital cases were compared to the data describing the diseases. In attempting to translate hospital case information into the form ofa differential diagnosis, it was found that accuracy of the output—that is, the differential diagnosis—increased or decreased in relation to a wide variety of mathematical approaches that could be employed. For example, ifthe input values (weight ofa patient's symptoms in each disease) were merely added or multiplied or subtracted in a variety of logarithmic and non-logarithmic functions, the resultant differential diagnoses were less accurate than ifthe input values were related to the total weight of each disease. By comparing the sum of the weighted diagnostic criteria ofthe hospital case to the sum ofthe weighted diagnostic criteria ofthe disease, the degree ofidenticalft ofhospital case data in each disease was defined. This measurement was made in its simplest form by determining the weighted average ofa hospital case in each disease , where W.A. = ZwX/Sw, and W.A. = weighted average; w = weight of a given item of data; X = a value of 1 for each item of data present in the hospital case and a...