thinking in numbers
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Prevention of SmallpoxSMALLPOX is continuing in South Wales; and, though
deaths from this disease are few, they are particularlydistressing because they are felt to be preventable.Prevention, however, is a complex task, dependingalike on screening of immigrants, prompt detectionof cases and of contacts, and a high rate of immunity inthe indigenous population. Screening of those whoreach this country, however ardently practised, cannotbe assuredly effective : as Dr. S. C. ROGERS points outin his letter on p. 587, an international certificate ofvaccination may not mean what it says; and, even if itdoes, the holder may not be immunised. Our public-health service being highly developed, most cases
arriving in this country are detected, and contacts
traced, with reasonable dispatch. It is in the third
requirement-routine vaccination-that our defence isweakest.
Primary vaccination is best, and most safely, under-taken below the age of 1 year: the Ministry of Healthsuggests that for a thriving infant the age of choice isprobably 4 months. 1 Yet, though the primary-vaccination rate of infants under 1 year of age has
latterly been rising, in 1959-60 it was still only 41.3%.2Last month it was reported that, of 21 recent cases ofsmallpox in this country, only 13 had been vaccinatedat any time; of these 13, only 9 had been vaccinated inthe past seven years-and these 9 included 4 vaccinatedafter contact with smallpox.3 One way to raise the
primary-vaccination rate might be to reintroduce anelement of compulsion as regards infants; but a PrivateMember’s Bill which would have had this effect hasbeen rejected by the House of Commons.4 Mostworkers would probably agree that the House was
right. The legal compulsion of the Vaccination Actswas never effective; and indeed in many areas thevaccination-rate rose after its repeal under the NationalHealth Service. Furthermore, any attempt at com-
pulsion might reasonably be regarded as unjustifiedinterference with personal freedom, particularly becausevaccination is itself not devoid of risk. In England andWales in 1960, 2 patients died of generalised vaccinia,and 8 cases of postvaccinial encephalomyelitis (ofwhich apparently 5 proved fatal) were reported.2 Theseare disturbing figures-but by no means as disturb-
ing as the likely total of deaths from smallpox if thepopulation were wholly unvaccinated. The sensiblecourse seems to be to pursue voluntary vaccination withgreater vigour, while making clear to the public theextent of the risks it still carries. At the same time weshould do all we can to reduce these risks; and in timeimprovement may appear.
Unhappily, successful primary vaccination does notensure continuing immunity: " The duration of
immunity conferred by vaccination against smallpox ininfancy is known to be of variable extent, and the
presence of a good vaccination scar does not mean that1. Ministry of Health: Memorandum on Vaccination against Smallpox.
H.M. Stationery Office, 1956.2. Report of the Ministry of Health, 1960. Part II: On the State of the
Public Health; p. 53. H.M. Stationery Office, 1961.3. See Lancet, Feb 24, 1962, p. 436.4. ibid. p. 439.
the person possessing it will not contract the disease." 5In the Middle East in the 1939-45 war, immunitycommonly lasted less than two years.6 No averagefigure can be relied on: many years ago STEVENSON,’director of the Government Lymph Establishment, drewattention to the fact " that the degree and the duration ofthe protection varies in individuals and that in exceptionalcases it falls very short of the average." In MadrasDOWNIE et al. have shown that of a group of adults,mostly aged 20-30, with good scars from infant vaccina-tion, about 10% had little or no neutralising antibody inthe serum. Thus periodic revaccination is essential-forchildren, the Ministry suggests,l on entry to and againon leaving school, and in adult life at intervals that
may be as short as three years for those at special risk.Where an outbreak does occur, protection of the non-immunised is aided by two factors. First, cases are
rarely infective in the prodromal stage; in MadrasDOWNIE et awl. isolated no virus from mouth washingsand garglings of patients in the first two days of illness.Secondly, vaccination of contacts is usually effective ifcarried out within three days after exposure, using apotent vaccine and proper technique; and here we mayrecall the Ministry of Health’s insistence 1 that, whenvaccinating or revaccinating in the face of possibleexposure to smallpox infection, the vaccine should beintroduced (either by the scratch method or by " mul-tiple pressure ") in two separate areas at least one inchapart. Another possible means of protecting contacts,in an outbreak, is to give them immune y-globulinfrom the sera of recently vaccinated adults 10; but theplace of this prophylactic is not yet entirely clear.World-wide eradication of smallpox is something to
which we can look forward confidently. But the diseasewill not be permanently eradicated, even from this
country, so long as the vaccination-rate remains as low asit is at present. Besides greater effort in this direction,there is still room, as the Madras studies show, for muchfurther research on methods both of prevention and oftreatment.
Thinking in NumbersMEDICAL statistics is by no means an exclusive
specialty, but has attracted hygienists, physicians,pathologists, and many others who find its methods
productive of new knowledge and (even more) of newquestions. Among them Prof. ROBERT CRUICKSHANKhas been both a practitioner (with his studies of infectionwithin the family) and a source of encouragement toothers; and as Lister fellow of the Royal College ofPhysicians of Edinburgh he has been able to display hisenthusiasm to a wider audience." The examples which5. Wld Hlth Org. Chron. 1962, 16, 13.6. Illingworth, R. S., Oliver, W. A. Lancet, 1944, ii, 681. Easton, J. H. L.
Publ. Hlth, Lond. 1945, 58, 110.7. Stevenson, W. D. H. Lancet, 1944, ii, 697.8. Downie, A. W., Hobday, T. L., St. Vincent, L., Kempe, C. H. Bull.
Wld Hlth Org. 1961, 25, 55.9. Downie, A. W., St. Vincent, L., Meiklejohn, G., Ratnakannan, N. R.,
Rao, A. R., Krishnan, G. N. V., Kempe, C. H. ibid. p. 49.10. Kempe, C. H., Bowles, C., Meiklejohn, G., Berg, T. O., St. Vin-
cent, L., Sundara Babu, B. V., Govindarajan, S., Ratnakannan, N. R.,Downie, A. W., Murthy, V. R. ibid. p. 41.
11. Measurements in Medicine. By ROBERT CRUICKSHANK. Royal College ofPhysicians of Edinburgh, 1961. Pp. 46.
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he gives-of trials of prophylactic agents and the
aetiology of respiratory infections-illustrate the essentiallogic of the method. Nevertheless we fear that morethan his persuasive pen is needed to make such methodsgenerally popular.As a profession we seldom think numerically or indeed
very exactly. We leave this to the administrative depart-ments of the hospital, who can tell us in an instant howmany patients were admitted in January, and the cost oftinct. buchu per patient per annum to a minute fractionof a penny. The machine which sorts the punched cardsis in the finance department. The average medicalcommittee will devote hours to serious and farseeingdebate, but is singularly averse from numerical estimatesof anything at all. Though patients are now examinedmore thoroughly than ever before, the results are
seldom recorded usefully or legibly. The records
department can find the notes of any patient within afew minutes; but to assemble the notes of every patientadmitted with, say, pernicious ansemia may be beyondits powers. We accept the figures sent to us by the bio-chemist without reference to possible errors of methodor chance. (A bookmaker with several medical clientsconfirms that as a profession we are weak on probability.)We use words such as " always " and " rare " without athought that each might be defined more accurately: forexample,
" always " in a biological sense means 19 timesout of 20, or something of that order. In fact we have aweakness for such masterly imprecisions as that famousdiagnosis " a gastropulmonary state of affairs ".A hundred years ago St. Bartholomew’s Hospital (and
no doubt others) used to print in the annual report aclassified list of the reasons for admission and the
occupations of those admitted. These were too illdefined to be much use to a modem statistician but theygave promise of an intelligent purpose. Registrars werefirst appointed with the specific duty of caring for thepatients’ notes, and we suspect that the prime motivewas a wish to draw statistical information from theserecords. Today the purpose of the notes is rather toensure continuity of treatment. They are not analysed:they are stacked. The notification of infectious diseasewas a logical sequel to the statistical fervour of CHADWICKand SIMON; and if the results are now useless for almostevery purpose, this is probably because no-one is reallyinterested in how many, when, and where.The reasons for our dislike or distrust of numerical
methods are not very obvious. No doubt at school,some of the time we ought to have spent on more profit-able branches of mathematics was wasted in working outsums in compound interest. Biology and even chemistrywere largely taught as descriptive sciences. From themoment he crosses the threshold of the medical school,the student is taught that each patient is unique andshould be treated as such-and nobody would have itotherwise. (Any woman would say the same of herunderclothes. All the same, she categorises them in thelaundry list without hesitation.) We rightly distrust" routine tests " and " routine treatment " as evidenceof a sloppy mind; and yet, if this prejudice is carried to
its logical end, the result is empiricism at its worst.
Luckily ours is not a logical profession any more thanan exact one. There are times when we learn more ofhuman disease if we sit back to consider our manyindividuals as a crowd. Most of us do this quite often,and if we do not turn our observations to good purposeit is because we do not define illness and its symptomsand signs accurately enough. There is no call for thestudent to buy a slide-rule when he buys his stethoscope;but he should learn that organs can often be measuredin cubic centimetres (and sometimes, alas, in grammes);that " innumerable red cells " may or may not be true;and that " 12 pints a day " is probably more accuratethan " moderate drinker ". There are limits to these
attempts at accuracy, but they will be pointed out soonenough.We cannot hope that Professor CRUICKSHANK’S
eloquence will bring a spectacular flood of converts tothe Little Bethels of the medical statisticians, but it
may induce some inklings of grace. Those who stillfind a page of The Lancet filled with mathematical
symbols rather boring are in good company. In 1900the council of the Royal Society passed a resolutionasking that in future " mathematics should be kept apartfrom biological applications ".12 MENDEL’S revelations
probably went unheeded because he addressed them tothe botanical society of Brno-and botanists are no
better at sums than doctors.
Annotations
EXAMS
"EXAMINATIONS are the only effective way to make theaverage student take a subject seriously." 13 When he madethis remark in 1955, Dr. Curran was thinking of thereasons why psychiatry stood low in the estimate ofmedical students and doctors; and he concluded that itwould stay there until students were set compulsoryexaminations in psychiatry. But his lament is from timeto time echoed by teachers in other subjects: it has a
simplicity that might have appealed to the Inquisitors(" we don’t really like it but torture is the only answer ")and it can be used to defend the Establishment. Much,however, depends on what is meant by " examinations ";and certainly a mounting pressure of criticism is now
bearing on this country’s present methods of examiningmedical students, and the " only-way " school is hard putto it in defence of its position. Indeed, at an informalmeeting of medical teachers and educationists arranged inLondon last week by the Association for the Study ofMedical Education, its position was continually assailedwithout counterfire.
Changes in the curriculum have had as one of their aimsthe lightening of the student’s examination load 14 ; andthe style of some examinations has been remodelled,notably in the direction of multiple short-answer tests.But the AsivtE meeting often doubted whether we
really knew what we were doing: had we enough datato determine what our present examinations achieved orwhat effect a proposed change was likely to have ? Theanswer is plainly
" no "; and the meeting discussed ways
12. Pearson, K. The Life of Francis Galton; vol. 3a, p. 100. London, 1930.13. Curran, D. Brit. med. J. 1955, ii, 515.14. See Lancet, 1961, ii, 1346.