Clinical biostatistics XXXIII. On teaching statistics to medical students
Alvan R. Feinstein, M.O: West Haven, Conn. The Cooperative Studies Program Support Center and the Department of Medicine of the West Haven Veterans Administration Hospital, and the Departments of Medicine and Epidemiology of the Yale University School of Medicine
For more than 80 years, statisticians have been conducting discussions, symposia, and debates in an effort to answer a series of persistent questions about the teaching of statistics. 1, 2, 4, 10, 13, 16-18, 21-24 Was the subject important enough to be incorporated into general education? If so, at what level of education-secondary school, university, or graduate school? What topics should be included and how should the illustrative examples be chosen? How should the instruction be oriented-mainly toward "theory" or toward "applications"? How should the students be regarded-as potential professional statisticians or as informed users of statistical techniques? What should be the instructor's background-intensive accomplishment in mathematical statIstIcs or experienced familiarity with statistical applications? Some of these questions are not too difficult to answer with respect to the role of statistics in medical education. Everyone seems to agree that medical doctors ought to know about statistics. Practitioners need it as an act of selfdefense, to be able to comprehend a medical literature that has become increasingly statistiSupported by Public Health Service Grant No. HS 00408 from the National Center for Health Services Research and Development. 'Professor of Medicine and Epidemiology, Yale University School of Medicine, New Haven, Conn.; Senior Biostatistician, Cooperative Studies Program Support Center, Veterans Administration Hospital, West Haven, Conn.
cal both in the citatIOn and in the analysis of data. 8 Investigators need it as an act of selfenlightenment, to improve the methods used for designing research, evaluating results, impressing granting agencies, and convincing editors. Consequently, a teacher of medical statistics should not ordinarily have to face a group of students whose skepticism must first be overcome about the value or importance of the subject. A teacher of medical statistics should also have a relatively easy time in choosing an orientation, topics, and illustrations. Unlike university students or secondary school students, whose goals may be variegated or ill-defined, a medical student usually has a clearly marked objective. By entering medical school, the student has indicated a reasonably specific career goal, which in most instances is the practice of medicine. From knowing that goal and from examining the types of statistical procedures that appear in general medical literature, the teacher should easily be able to determine what should be taught. He should also be able to find a plethora of suitable illustrative examples. Despite these apparent advantages over colleagues who work in non-medical enclaves, the faculty members who try to teach statistics to medical students have not been particularly successful. In a recent survey performed by Theodore Colton6 , 35% of the instructors in 121
American medical schools reported that the "majority of students" viewed the statistics course with either "dislike" or "abhorrence". The ennui of the students also appears to be shared by their teachers. In a summary of a Medical Statistical Conference held in England in 1971, I. D. Hill12 reported that "an audience consisting largely of statisticians ... seemed to reach the surprising conclusion . . . that the answer to 'How should statistics be taught to medical students?' was 'It should not'''. According to Hill, "Experience has shown that (medical students) will learn little from it, other than a distaste for the subject. What little they may learn of statistical techniques will almost invariably be misapplied, if ever used at all" . At that same meeting, R. F. J. Withers reported "experiments that had been conducted in teaching ~tatistics to undergraduates at the Middlesex Hospital' '. He concluded that "students who had had lectures would have preferred small tutorial classes, while those who had had these would have preferred lectures" . The conclusion that seems to emerge from these discouraging comments is that medical students will not enjoy learning about statistics, no matter how it is taught; and whatever they manage to learn will later be either abused or forgotten. There are several important reasons, however, for not accepting the hopelessness of this prognosis. The first reason is that in the general pedagogic malaise of modem medical education, the ailments of statistics are not at all unique. Medical students today are usually much more disdainful about many of the other courses they receive in the "basic sciences" than they are about statistics. If the disenchantment for statistics can be stipulated or quantified, it is mainly because teachers of statistics have made an effort to get and publish the data. Had similar surveys been performed for contemporary courses in "basic science", an even worse set of scholastic maladies might have been identified. The second reason is that the natural advantages that should help a teacher of medical statistics have been destroyed by several externally imposed handicaps in chronology and pedagogy. These handicaps, which are not
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inherent in the content of statistics itself, arise from a series of decisions and indecisions by the statistician's faculty colleagues. One outstanding chronologic problem is the amount of time allotted for the course. According to Colton's survey6, less than half of American medical schools require students to receive a separate, distinct course in statistics. In the schools that provide some sort of formal exposure to statistics, the median amount of time for the course is 21 hours; and in about a fourth of the schools, the course receives less than 13 hours. Colton did not obtain any comparative data about the time allotted for other "basic science" activities, but anyone familiar with current curricular patterns could quickly show that contemporary medical students spend many more hours learning about aspects of electron microscopy and molecular mechanisms, which they may never need to consider in clinical practice, than they do in learning about statistical procedures, which will confront them almost every time they open a general medical journal. Furthermore, it is obviously unfair to ask a statistician to do a good job of teaching if he is given either no opportunity to do so or is asked to work in a time span that is so brief or so fragmented that he cannot plan a well-organized course. A second chronologic problem is in timing, rather than time. Most statistics courses are taught in the first year of medical school. The presumptive rationale for this chronologic location is either that no other suitable time can be found, or that a knowledge of statistics should be acquired as soon as possible, since it offers a guide to all the research procedures and data to be encountered later in the medical school curriculum. This choice of timing, however, places statistics in the educational company of the many unattractive non-clinical courses that medical students must frequently endure before being allowed to meet patients and learn about clinical phenomena. Immersed in what is often called the "irrelevance of the basic sciences" , a medical student may ascribe guilt by association and begin to regard statistics as also irrelevant. In the past few years, however, members of the clinical faculty have begun coming to
Volume 18 Number 1
the rescue of their non-clinical colleagues. By providing supplementary lectures on "clinical correlations", the clinicians have upgraded the "relevance" of the "basic science" material and have helped it evoke interest, if not necessarily enthusiasm, in the students. A different kind of stimulus that students receive for learning basic biochemistry, physiology, and microbiology is the overt realistic threat of having to answer questions about these topics in order to pass the licensure examinations conducted by the National Board or other agencies. The teaching of medical statistics is not currently aided by either of these positive stimuli. I know of no medical schools in which the biostatistics courses are accompanied by clinical correlation sessions that are planned and conducted by clinicians, rather than by statisticians. Statistics has also been omitted as a distinctive discipline whose mastery is to be tested for medical licensure. Despite the many allegations that practicing doctors are incompetent to evaluate the statistical reports appearing in medical literature and that the doctors, instead, get brainwashed by the advertising of the pharmaceutical industry or by the blandishments of the academic-federal complex, the guardians of medical licensure examinations have not included specific sections concerned with evaluating biostatistical reports in medical literature. Questions about statistics, when they appear at all in the licensure examinations, are usually included as a minor part of the topics concerned with public health, epidemiology, or preventive medicine. As a result of these handicaps, an instructor in medical statistics must often overcome a much greater set of obstacles than those faced by his counterparts who teach either "basic science" in medical school or general statistics elsewhere. Having neither the carrot of a collaborating clinician nor the stick of a licensure threat, the statistician must work wholly on his own to capture the medical students' interest. He must create his own approach to clinical correlation, with all of the attendant difficulties produced by the frequent absence of medical training in his own general education and by the frequent absence of realistic attention to clinical biostatistics in his statistical education.
To these handicaps is added yet another burden, arising from a general scientific "copout" by the rest of the medical faculty. Despite the time that the faculty members spend in research and in trying to teach students to become "clinical scientists", most medical school curricula contain no specific instruction devoted to issues in scientific philosophy, to the general architecture of scientific methods, to the design of clinical research, or to the evaluation of research. The principles of scientific investigation are seldom considered during courses in either "basic science" or clinical science, because the members of the faculty are themselves often untrained in these principles and may be discomfited when asked to discuss them. Many of the triumphs of biomedical science during the past few decades have arisen not from creative scientific thought, but from major advances in technologic devices and from the financial support that enabled large numbers of Ph.D. and M.D. personnel to use those devices for research. Although certain leaders in the field have been talented connoisseurs of creative science, the key to success for many other investigators was not a knowledge of scientific principles in designing experiments or surveys, but a technologic skill in using an ultra-centrifuge, an electron microscope, or an immunochemical electrophoresis apparatus. Before the flow of federal money recently began to ebb, the main prerequisite for getting funds to do biomedical research was often an appropriate academic degree, a suitable period of technologic apprenticeship, and the choice of a topic devoted to fashionable issues in basic mechanisms of biology or disease. In such an atmosphere, the faculties of medical schools tended to become more expert in technologic research than in scientific reasoning; more devoted to laboratory activities than to clinical or epidemiologic problems; and more concerned with publicational quantity than with scientific quality. Consequently a medical student today seldom learns the principles of scientific research from either the "basic" or the clinical faculty. The members of the clinical faculty rarely discuss these principles because they may feel un-
qualified to do so or because the subject has presumably been amply covered by the "basic" faculty. The members of the "basic" faculty, however, usually discuss their own specialized interests and data, rather than general strategies of research. Even when the general methods of "basic" research are specifically contemplated, the methods are pertinent only for the human fragments, animals, or inanimate materials studied in the investigator's laboratory. The methods cannot be directly applied when the material of the research is an intact person or group of people. The medical-school statistician is thus often left with an extraordinarily difficult dilemma. His uniquely expert knowledge is in the various strategies and tactics of the mathematics of statistical inference. These procedures constitute a kind of gravy for the meat of scientific clinical research. For the gravy to be tasty and alpreciated, someone must provide the meat; but no one else may do so. If the statistician decides to provide it himself, he runs the risk of substantial professional and intellectual discomfort. He may be ill at ease in trying to teach the design of many forms of research in which he has not participated and with which he feels unfamiliar; he may receive opprobrium from his biometric colleagues for having descended into mundane, "applied" levels of non-mathematical discussion instead of creating the abstract esoterica that are often encouraged and published as biometric research 9; and he may feel disgruntled at having to teach scientific alphabet and grammar rather than statistical poetry. Conversely, if he decides to confine his teaching to the statistical "gravy", he runs the risk of rejection from medical students who find the gravy tasteless, excessively rich, or "irrelevant" without the meat. There are several ways out of this dilemma. One approach is to remove the chronologic barriers in both timing and time. Medical school admission committees could insist that statistics (rather than courses such as the calculus, which is clinically useless) be made part of the mathematical pre-requisites for entrance to medical school. The addition of statistics to undergraduate university education could also have a salubrious effect on the teaching of
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college biology, where the important roles of variation and other cogent statistical phenomena are still commonly neglected. By demanding that basic statistics be a premedical subject, the medical faculty would be liberated from having to deal with the problems of teaching it. The liberation could be advantageous if the time that is thereby freed in medical education is put to other good uses, such as studying the architecture of clinical research, the operation of some higher powered statistical tools (such as the analysis of multiple variables), and decisions about when those tools should be employed. The liberation could be disastrous if it is converted into evasion, with the medical faculty concluding that statistics requires no further attention and denying medical students any further instruction in the many uniquely and distinctively clinical aspects of statistics and statistical research. Alternatively, the teaching of statistics could be moved into the last year of medical school, when students have had enough clinical exposure to understand the value of statistics for appraising clinical literature and for making clinical or investigative decisions. If no other chronologic improvements can be carried out, this approach might be the most desirable. The number of hours needed for the course will depend on what is chosen as the appropriate content, who teaches it, and how much classroom time is saved by the use of modem pedagogic adjuncts. These adjuncts-which can allow students to teach themselves 19 • 20 a great many entities that were formerly transmitted by didactic lectures-include programmed texts, 14a "correspondence courses" ,3 "slide-tape shows" , and diverse forms of computer-aided instruction. 7 • 11. 14 There is one fundamental point to be borne in mind when time is allotted for a medical statistics course. Unlike many of the molecular esoterica of "basic science", the strategies and tactics of statistics will appear recurrently to challenge a medical doctor in his daily practice and in his reading of general medical literature. s For a medical student to receive suitable preparation for those challenges, the foci of the medical curriculum should be adjusted accordingly. Another important improvement might be
Volume 18 Number I
attained by changing some of the personnel who now act as teachers. In suggesting that statistical instruction "permeate the whole of undergraduate training" for medical students, Lowe 14b lamented "the shortage of suitably qualified teachers" who can relate statistical material "closely, forcefully, and convincingly to (the students') laboratory and clinical interests. " Lowe also suggested that the teaching responsibility might "rest with the department of social medicine." A more striking complaint, addressed by two prominent biostatisticians 24 to their colleagues, was as follows: "The professional statisticians employed by the university statistics departments fail to expound the subject in a sufficiently down-to-earth and realistic manner to be intelligible to their audience ... Let us confess it, so many (teachers) are so little aware of practical problems or of the correct methods of handling them, that even when intelligible they are a source of confusion rather than enlightenment". With appropriate pedagogic substitutes in materials and personnel, medical students would be freed from the unappealing aspects of conventional textbooks and lectures. The time spent with a live instructor could be devoted to challenges in problem-solving, in research design, or in the appropriate selection and use of statistical procedures. Ultimately, however, the main issues in the teaching of medical statistics depend upon the content of the course, not upon changes in chronologic location, pedagogic adjuncts, or charisma of the instructors. Improvements in these features can provide substantial help in making an attractive intellectual content more appealing, but neither the timing and vehicles of the instruction nor the dramaturgy of the instructor will salvage a course in which the topics themselves are chosen and presented ineffectually. In 1958, a Committee on the Teaching of Biometry reported 5 that the most "common request" received from statistics teachers was "for the publication of the contents of good courses of biometry, as a guide to teachers of the subject". Several years ago, another committee was appointed and charged with outlining such a list of contents for medical stu-
dents. The committee's report 15 is presented in the accompanying paper in this issue. The committee has compiled what may strike many readers as an inordinately broad scope of topics, ranging from the architecture of clinical research (a subject that almost never appears in traditional biostatistics courses) to discriminant function analysis (a subject that is usually relegated to advanced statistical instruction). By adding a discussion of research architecture to the traditional contents of biostatistics, the committee hoped to call attention to the preeminence of non-mathematical reasoning in making scientific plans for clinical and epidemiologic investigation. By including a broad variety of statistical topics, the committee acknowledged the diversity of procedures that appear in general medical literature. 8 As noted in the report, "not all of these topics need to be discussed in detail" , and many topics should be noted either briefly or very briefly. The objective is to allow a student to become acquainted rather than to develop an intimate friendship, with the diverse statistical techniques that will be encountered in clinical pUblications. Because the work emerged from one committee and had to be approved by a parent organization, the report represents a compromise of different viewpoints and emphases. Nevertheless, the compromises were not major or difficult; the consensus was reached with surprising ease; and the proposal allows for flexible adaptation of the contents. The main challenge now is to arrange for implementation of the proposal. Reprints will be sent to all deans of North American medical schools and to other appropriate people in medical education. Readers of the report and of these papers in clinical biostatistics can help advance the cause by calling it to the attention of their deans, chairpersons of curriculum committees, and biometric faculty; and by suitable forms of effective exhortation toward action. As chairman of the committee, I want to express my deep gratitude for the efforts made by its members and for the pleasure of both working with them and learning from them. The committee would also like to thank Dr. Edward N. Brandt (now Dean of the University
of Texas Medical Branch at Galveston), who instigated our work, and the officers of the American Statistical Association Subsection on Teaching of Statistics in the Health Sciences, who will help disseminate it. References 1. Bancroft, T. A., and Huntsberger, D. V.: Some papers concerning the teaching of statistics, Statistical Laboratory, Iowa State University, 1961. 2. Bartlett, M.. J.: Teaching and education in biometry, Biometrics 6:85-98, 1950. 3. Bissell, A. F., and Hobson, T. F. J.: Learning and teaching statistics by correspondence, The Statistician 18:237-244, 1968. 4. Cavalli-Sforza, L.: Teaching of biometry in secondary schools, Biometrics 24:736-740, 1968. 5. Cochran, W. G. (Ch.), Bliss, C. 1., BuzzatiTraverso, A., Darmois, G., and Mather, K.: Report of the committee on the teaching of biometry, Biometrics 9:518-519, 1953. 6. Colton, T.: An inventory of biostatistics teaching in American and Canadian medical schools. In press, J. Med. Educ. 7. Evans, D. A.: The influence of computers on the teaching of statistics (with discussion), J. Roy. Stat. Soc. Assn. 136:153-190; 205-225, 1973. 8. Feinstein, A. R.: Clinical biostatistics. XXV. A survey of the statistical procedures in general medical journals, CUN. PHARMACOL. THER. 15:97-107, 1974. 9. Feinstein, A. R.: Clinical biostatistics. XXIX. On the biologic content of biometric literature, CUN. PHARMACOL. THER. 16(Part 1):526-540, 1974. 10. Finney, D. J.: Teaching biometry in the university, Biometrics 24:1-12, 1968. 11. Foster, F. G., and Smith, T. M. F.: The computer as an aid in teaching statistics, Appl. Stat. 18:264-270, 1969. 12. Hill, 1. D.: Report on a medical statistical conference, Appl. Stat. 20:319-321, 1971. 13. Hogg, R. V.: On statistical education, Amer. Stat. 26:8-11, June, 1972.
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14. Kossack, C. F., and Henschke-Mason, C.: The role of computer programming in teaching statistics, Biometrics 29:841, 1973. (Abst.) 14a.Leaverton, P. E.: A review of biostatistics. A program for self-instruction, Iowa City, 1972, University of Iowa Press. 14b.Lowe, C. R.: On the teaching of statistics to medical students, Lancet 1:985-987, 1963. 15. Report of a Committee of the American Statistical Association Subsection on Teaching of Statistics in Health Sciences. Proposal for a core curriculum in medical biostatistics, CUN. PHARMACOL. THER. 18:127-131, 1975. 16. Report of the Joint Committee on the teaching of statistics in colleges, J. Roy. Stat. Soc. Assn. 137:412-427, 1974. 17. Report of the Panel on Statistics: Introductory statistics without calculus. Committee on the Undergraduate Program in Mathematics, Mathematical Association of America, P. O. Box 1024, Berkeley, Calif., 1972. 18. Spicer, C. C.: The training of medical statisticians, J. Roy Stat. Soc. Assn. 127:219-221, 1964. 19. Stahl, S. M., and Hennes, J. D.: Biostatistics: An experiment with self-learning in the health sciences, J. Med. Educ. 48:271-275, 1973. 20. Stahl, S. M., Hennes, J. D., and Fleischli, G.: Progress on self-learning in biostatistics, J. Med. Educ. 50:294-296, 1975. 21. Walker, H. M.: Studies in the history of statistical method. With special reference to certain educational problems, Baltimore, 1929, The Williams & Wilkins Co. 22. Wishart, 1.: Some aspects of the teaching of statistics. With discussion by Greenwood, M., Elderton, W., Fisher, R. A., Allen, R. G. D., Irwin, J. 0., Selwyn, V., and Bowley, A. L.: J. Roy. Stat. Soc. 102:532-564, 1939. 23. Wishart, J.: The teaching of statistics. With discussion by Pearson, E. S., et al.: J. Roy. Stat. Soc. Assn. 111:212-229, 1948. 24. Yates, F., and Healy, M. J. R.: How should we reform the teaching of statistics? J. Roy. Stat. Soc. Assn. 127:199-210, 1964.