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AMERICAN Journal of Epidemiology Formeib AMERICAN JOURNAL OF HYGIENE VOL. 97 MARCH, 1973 NO. 3 REVIEWS AND COMMENTARY With this issue, the section entitled "Commentary" is broadened to include reviews of topics of epidemic-logic interest. The "Reviews and Commentary" section will include both articles solicited by the editors and appropriate articles submitted for consideration, as well as brief re- ports and letters to the Editor. EPIDEMIOLOGY OF INFECTIOUS AND NON-INFECTIOUS DISEASE: SOME COMPARISONS THE FIRST WADE HAMPTON FROST LECTURE 1 ABRAHAM M. LILIENFELD 1 At the start, I would like to express my feeling of tremendous honor and pleasure at having been selected by the Council of the Epidemiology Section to deliver the first Wade Hampton Frost lecture. To whatever extent my epidemiological work has been responsible for this, certainly this honor must be shared with my colleagues, many of whom are among you in the audience and with whom I have collaborated on many studies, Alexander D. Langmuir, Warren Winkelstein, Jr., Milton Terris, Leonard M. Schuman, Philip E. Sartwell, to name a 1 Presented before the Epidemiology Section at the annual meeting of the American Public Health Association, November 13, 1972. * Chairman, Department of Epidemiology, the Johns Hopkins University School of Hygiene and Public Health, 616 North Wolfe Street, Baltimore, Maryland 21205. Dr. Lilienfeld holds a Research Career Award from the National Institutes of Health (No. K 06 GM 13,901). Work reported in this paper was sup- ported in part by Grants No. 11489 and No. 5166 from the National Cancer Institute. few, as well as past and current members and students of my department. Those of us who have been engaged in epidemiological investigations during the past 20 to 30 years are well aware of the profound influence of Wade Hampton Frost on our discipline. That this influence still permeates epidemiological thought today was brought home to me while I prepared this lecture and reviewed many of Frost's publications, noting, with few exceptions, how au courant was his mode of reasoning, particularly concerning the derivation of inferences from epidemiological data. I will not attempt to review in detail the various contributions made by Frost. This has been ably presented in the preface to a select collection of Frost's papers by Maxcy, Papers of Wade Hampton Frost: A Con- tribution to Epidemiological Method (1), which I highly recommend to those who have not as yet read them. A clear state- ment of what Frost exemplified was ex- pressed by Maxcy in commenting on Frost's 135

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AMERICAN

Journal of EpidemiologyFormeib AMERICAN JOURNAL OF HYGIENE

VOL. 97 MARCH, 1973 NO. 3

REVIEWS AND COMMENTARY

With this issue, the section entitled "Commentary" is broadened to include reviews of topicsof epidemic-logic interest. The "Reviews and Commentary" section will include both articlessolicited by the editors and appropriate articles submitted for consideration, as well as brief re-ports and letters to the Editor.

EPIDEMIOLOGY OF INFECTIOUS AND NON-INFECTIOUSDISEASE: SOME COMPARISONS

THE FIRST WADE HAMPTON FROST LECTURE1

ABRAHAM M. LILIENFELD1

At the start, I would like to express myfeeling of tremendous honor and pleasure athaving been selected by the Council of theEpidemiology Section to deliver the firstWade Hampton Frost lecture. To whateverextent my epidemiological work has beenresponsible for this, certainly this honormust be shared with my colleagues, manyof whom are among you in the audience andwith whom I have collaborated on manystudies, Alexander D. Langmuir, WarrenWinkelstein, Jr., Milton Terris, Leonard M.Schuman, Philip E. Sartwell, to name a

1 Presented before the Epidemiology Section atthe annual meeting of the American Public HealthAssociation, November 13, 1972.

* Chairman, Department of Epidemiology, theJohns Hopkins University School of Hygiene andPublic Health, 616 North Wolfe Street, Baltimore,Maryland 21205.

Dr. Lilienfeld holds a Research Career Awardfrom the National Institutes of Health (No. K 06GM 13,901). Work reported in this paper was sup-ported in part by Grants No. 11489 and No. 5166from the National Cancer Institute.

few, as well as past and current membersand students of my department.

Those of us who have been engaged inepidemiological investigations during thepast 20 to 30 years are well aware of theprofound influence of Wade Hampton Froston our discipline. That this influence stillpermeates epidemiological thought todaywas brought home to me while I preparedthis lecture and reviewed many of Frost'spublications, noting, with few exceptions,how au courant was his mode of reasoning,particularly concerning the derivation ofinferences from epidemiological data.

I will not attempt to review in detail thevarious contributions made by Frost. Thishas been ably presented in the preface to aselect collection of Frost's papers by Maxcy,Papers of Wade Hampton Frost: A Con-tribution to Epidemiological Method (1),which I highly recommend to those whohave not as yet read them. A clear state-ment of what Frost exemplified was ex-pressed by Maxcy in commenting on Frost's

135

136 ABRAHAM M. LILIENFELD

Wade Hampton Frost, 1880-1938

studies of diphtheria: "They are splendid•examples of orderly and logical statementderived from carefully collected material,a considerable part of which is quantitative,concerning factors affecting the prevalenceof an endemic acute infectious disease."

The great influence of Frost on our dis-cipline has been best described by Gordonin his review of American epidemiology inthe twentieth century (2). He points outthat, "In 1921, Wade Hampton Frost be-came the first professor of epidemiology inAmerica. He remains the first among allwho have followed, for no one has donemore to further epidemiology as a scientificdiscipline." He further comments that, "Theaccumulating knowledge of epidemiologicaltheory and the increasing use of statisticalmethods led progressively to a turn ofepidemiology from a descriptive and com-parative procedure to an analytical dis-cipline. If one American is to be singled outas contributing most forcefully to thischange, he is W. H. Frost. In his teaching,through his students, and by his own con-

tributions, Frost developed means for quan-titating mass phenomena of disease and formeasuring the biologic attributes of diseaseas evidenced in populations of people. Onceestablished as an analytical discipline, theway was clear for epidemiology to make fulluse of the technical methods originating fromother medical and biological sciences, andto perfect field methods of study." Gordonspecifies a few of Frost's contributions:"Wade Hampton Frost contributed more toquantitative method than any other Amer-ican epidemiologist, through his studies onpoliomyelitis (1913), the common cold(1932), and tuberculosis (1933); andthrough developing the modified life tabletechnic and the index case concept." Tothese we must add the cohort analysis ofmortality data, the use of morbidity sur-veys, the importance of the study of thefamilial distribution of disease and theconcept of using the community as, whattoday is popularly labeled, "a human popu-lation laboratory."

Frost also had a continued interest in theapplication of epidemiology to the practiceof public health of his day. As stated byMaxcy (1), " . . .he was cognizant at alltimes of the usefulness of this tool (ofepidemiology) for the improvement of pub-lic health practice." Thus, Frost presentedpapers on "Rendering Account in PublicHealth," "Authoritative Standards and As-sociation Policy," and his oft-quoted clas-sical "How Much Control of Tuberculo-sis?" (1). He integrated epidemiological in-vestigation, public health practice, medicalscience and public health teaching. Thisholistic viewpoint could well serve as anexample today to those in our disciplinewho seek to separate the science from prac-tice.

His only attempt at a systematic ex-position of the scope, principles and methodsof epidemiology is contained in an articleprepared in 1927 that summarized the think-ing of that time (3). He stated that epide-miology is "essentially a collective science,

EPIDEMIOLOGY OF INFECTIOUS AND NON-INFECTIOUS DISEASE 137

and its progress is largely dependent uponthat which has been made in other fields.For example, since description of the diseasein a population obviously requires that thedisease must be recognized when it occurs,the development of epidemiology must fol-low and be limited by that of clinical diag-nosis, and of the rather complex machineryrequired for the systematic collection ofmorbidity and mortality statistics. Epide-miology must also draw upon statisticalmethod and theory, because even the sim-plest of quantitative descriptions must bestated statistically; and more minute de-scriptions, involving perhaps the demon-stration of complex associations, may re-quire the application of quite elaboratestatistical technique. Moreover, quantitativeepidemiological descriptions, in terms of thefrequencies of diseases in different popu-lation groups, require, as part of their data,more or less detailed statistics of population,implying the prior development of demog-raphy; and for descriptions of the relationsof disease to climate and weather, sys-tematic meteorological records are nec-essary."

" . . . Usage has extended the meaning ofepidemiology beyond its original limits, todenote not merely the doctrine of epidemicsbut a science of broader scope in relation tothe mass-phenomena of diseases in theirusual or endemic as well as their epidemicoccurrences. Although it is clear from cur-rent usage that the definition of epide-miology has been thus extended beyond itsoriginal sense, it is not clear just how far ithas been extended. It is certain that itsscope is not usually limited to the diseasesin which epidemics are characteristic, sinceit is entirely in conformity with good usageto speak of the epidemiology of tuberculosis;and it seems customary also to apply theterm to the mass-phenomena of such non-infectious diseases as scurvy, but not tothose of the so-called constitutional diseases,such as arteriosclerosis and nephritis. There-fore, in view of the latitude which the un-

certainty of usage allows, epidemiology willbe considered here as referring exclusivelyto the diseases of man which are classed asspecific infections, since this will permit ofa more coherent discussion."

Frost's views were somewhat limited bythe perspectives of his time. However,Frost's methodological contributions to thestudy of tuberculosis have been applied toother chronic diseases. It seems fair toassume that had Frost lived beyond 1938,the year of his death, his conceptualizationof epidemiology would no doubt have ex-tended to include all the diseases and con-ditions which concern us today.

Since this is the first lecture in this series,it appeared appropriate to review a broadarea in epidemiology. More specifically,I thought it would be interesting to comparesome of the similarities and differences ofthe infectious and non-infectious diseases,to indicate some of the concepts in the in-fectious diseases that might be applicableto the non-infectious diseases and to brieflyconsider a few specific related topics. In amodest way, such discussion might serve asa bridge between Frost's times and currentareas of activity. I should like to discussthese in some detail within the followingdifferent areas of epidemiological activities:

1) Observations of occurrence of diseasein man

2) "Natural" experiments3) Experimental epidemiology—random-

ized controlled experiments4) Theoretical epidemiology (mathemat-

ical-statistical)a) Modelsb) Computer simulation

Most epidemiological research consistsof observational studies on the occurrenceof disease in man; it is to this area thatFrost devoted much of his intellectual en-ergy. An important difference between in-fectious and non-infectious diseases is theelement of time. This is clearly observedby comparing the incubation period of adefinitely infectious disease (figure 1) with

138 ABRAHAM M. LILIENTELD

one of a non-infectious disease (4). For thenon-infectious disease, which may very wellprove to be a misnomer in terms of somecurrent thinking, figure 2 presents some dataon radiogenic leukemia which Cobb an-alyzed a few years ago (5). It is of morethan just passing interest that the pooling

4 8 12 16 20 24 28INCUBATION PERIOD IN WEEKS

SERUM HEPATITISFIGURE 1. Frequency distributions of incubation

periods in cases of serum hepatitis after admin-istration of icterogenic lots of yellow fever vaccine.(From Sartwell, Am J Hyg 51: 311, 1950.)

of such data on incubation periods forleukemia was based on the infectious diseaseanalogue. In fact, Cobb attempted to esti-mate possible incubation periods for whatwere essentially single exposure epidemicsof leukemia in order to identify that timeperiod prior to the occurrence of the diseasewhich should be studied in searching forother potential etiological agents.

The incubation period is much shorter ininfectious diseases than in radiogenic leu-kemia ; the former is measured in weeks andthe latter in years. It is of interest to specu-late on possible explanations for this dif-ference. In infectious diseases, the incuba-tion period is the time interval betweenreceipt of the infection and onset of illnessand depends largely on the growth rate of

the particular infectious agent and to alesser extent, on the portal of entry anddegree to which the host can mobilize hisdefenses. In infectious diseases, these in-tervals generally are relatively short.

In non-infectious diseases, one cannotattribute the long latent period to the timerequired for the growth of organisms. Onepossible explanation for the length of the

-6 -12 -18 24 -30 -36-42-48 -54-60-66 -72 -78 -84 -90 -96-W2-C6

Incubation Period tn Months

FIGUBE 2. The distribution of incubation periods of leukemia cases following irradiationfor ankylosing spondylitis. (From Cobb et al., J Chron Dis 9: 388, 1959.)

EPIDEMIOLOGY OF INFECTIOUS AND NON-INFECTIOUS DISEASE 139

latent period which has received some at-tention, particularly with respect to radia-tion effects, is the influence of independentmultiple etiological factors, which has beentermed the "multi-hit" theory of leukemo-genesis or carcinogenesis (6). Basically thisconcept suggests that for clinical disease todevelop, a sequence of cellular changes musttake place; in fact, estimates have beenmade on the number of multiple hits nec-essary before clinical disease occurs. Thesesteps are often equated with somatic muta-tions, but this presupposes knowledge, pres-ently unavailable, regarding the mechanismof cellular changes. If such multiple in-dependent steps are necessary, one wouldexpect a lengthening of the incubation pe-riod.

This biological concept is an importantreminder to the epidemiologist in his searchfor possible etiological factors that he mustattempt to ascertain multiple factors andtheir possible interrelationships; this be-comes an integral part of his researchstrategy.

As an illustration, I would like to presentsome data on childhood leukemia from theTri-State Leukemia Study, a cooperativeventure in which all patients with leukemiadiagnosed between 1959 and 1962 in Up-state New York counties, Baltimore andMinneapolis-St. Paul were interviewed aswere probability samples (1:3000) of thepopulation in these areas. The methodologicdetails have been presented elsewhere (7).

In the analysis, it was suggested thatseveral factors were related to the occur-rence of leukemia in children: 1) precon-ceptional radiation; 2) maternal reproduc-tive wastage; 3) history of childhood virusdiseases; and 4) intra-uterine radiation (8);these risk factors for leukemia are classifiedand defined as follows:

Pathologic

History of childhood virus diseases—Measles, rubella, chickenpox, mumps,polio, herpes zoster, encephalitis and in-

TABLE l

Pattern of eslimaltd relative risks for leukemia inchildren t-4 years of age by combination of

risk factors

No. of pathologicfactors

None12

No. of radiologic factors:

None 1 2

Relative risk

1.01.11.2

1.01.63.4*

1.62.7*4.6*

* Significant at 0.05 level.Adapted from Gibson et al.. N Engl J Med 279:

909, 1968.

fectious mononucleosis more than 12months before diagnosis of leukemia.Reproductive wastage—Mother's histoiyof miscarriages and stillbirths before con-ception of subject.

Radiologic

Preconceptional radiation of mother be-fore conception of subject.In utero radiation of mother while preg-nant with subject.

Initial analyses were limited to the effectof each factor separately. Then, the datawere analyzed in combinations of multiplerisk factors, grouped according to whetherthe factors were radiologic or pathologic; theresults are presented in table 1. The patternshown in this table does not support thenotion that the risk for leukemia increasesmerely by the addition of other risk factors.Whenever there is only one factor, therelative risks are low. The addition of twosingle factors increases the risk somewhat, to1.6. However, when there is a combinationof multiple factors, the risk increases mark-edly.

It occurred to me that a different ap-proach might be preferable. These factorsshould not be combined according to theradiologic and pathologic aspects sincethese categories do not consider the tem-poral sequence of events, and it might be

140 ABRAHAM M. LILIENFELD

TABLE 2

Pattern of estimated relalive risks for levkemia inchildren 1-4 years of age by risk factors re-

arranged by order of occurrence

No. ofpreconceptional

factors

None12

No.

None

1.01.21.9

of postconccptional

1

Relative risk

1.11.63.1

Factors:

2

1.82.74.6

useful to view the matter, crudely of course,in just such terms. One could classify theindividual risk factors for leukemia aspreconceptional and postconceptional fac-tors, as follows:

Preconceptional

Reproductive wastagePreconceptional radiation

Postconceptional

In utero radiationHistory of childhood virus diseases

The relative risks for these groups werecomputed and are presented in table 2; theyare not strikingly different from those pre-sented in table 1. The relative risks for com-binations of factors are practically un-changed. The major difference is that therenow appears a sharper gradient of relativerisks for each class of risk factors—precon-ceptional and postconceptional—which wasnot present in table 1. This can only beconsidered as suggesting that the temporalsequence might be of importance.

One might even consider adding anotherdimension to this two-dimensional pattern,that of dose for each factor. Then, onecould speculate that an increased dose foran individual factor might be equivalentto the combined effects of several factors.

I present these data to indicate that thefinding of a low relative risk for an in-dividual factor of etiological interest shouldnot deter us from further consideration of

that factor. All of us have experienced thefrustration of finding such low order asso-ciations with individual factors. However, itis quite conceivable that these may still beimportant when considered together withother possible etiological factors. Of course,such a possibility makes investigative lifea bit more difficult.

As many of you know, all lengthy in-cubation periods are not necessarily the re-sult of multiple factors. In some instances,they may reflect a cumulative lifetime ex-posure to one or more factors. In others,they may be related to chronologic age,with the aging process per se, having someeffect. As an aside, I might point out thatthe process of aging has not received theepidemiological attention it deserves. It isa virgin research area with many potentialdividends, such as ascertaining in humanpopulation groups whether some character-istics determine differential risks of aging,whether there are methods of measuringbiologic age in contrast to chronologic age,and whether biologic age has an independenteffect on disease causation.

In searching for etiological factors, theepidemiologist should have some notion towhat extent the disease under investigationcan be explained by or attributed to definiteor possible etiological factors that havealready been ascertained. One statistic thatis of considerable value but not widely usedin this area is the attributable risk as de-rived by Morton Levin in 1953 (9). Attrib-utable risk means the following: given apopulation with a certain rate of occurrenceof a disease, what proportion of the cases ofthat disease can be attributed to one ormore specific etiological factors? This isexpressed by the formula:

Attributable risk (AR) = - 1)b(r - 1) + 1

b = Proportion of population with char-acteristic that is being consideredas an etiological factor

r = Relative risk

EPIDEMIOLOGY OF INFECTIOUS AND NON-INFECTIOUS DISEASE 141

It should be pointed out that this definitionfor attributable risks differs from that usedby MacMahon and Pugh (10) by takinginto account the frequency of the popula-tion with the characteristic (6).

The most outstanding attributable riskamong diseases of current interest is thatof cigarette smoking in lung cancer. Giventhe frequency of smoking in the appropriateage groups of the U.S. population and arelative risk of 10, it is estimated that 80-85 per cent of lung cancer in the UnitedStates can be attributed to cigarette smok-ing. This estimate is not only important tothe public health administrator but also tothe epidemiologist, since it identifies ciga-rette smoking as a major factor, and indi-cates that other environmental factors prob-ably play a relatively minor independentrole. This observation can influence the re-search strategy of an investigator as hepursues the ascertainment of additionalpossible etiological factors; for example, asan initial approach, he may decide to limithis studies to nonsmoking lung cancer pa-tients.

To further illustrate the use of the at-tributable risk, I have taken the childhoodleukemia data from the Tri-State Studypresented earlier and have computed theattributable in addition to the relative risksfor each individual factor and the proportionof the study population (the one- to four-year old children) exposed to these factors(table 3).

It is evident that only between 9 and 17per cent of the leukemia cases can be at-tributed to each individual factor. However,when one views the cumulative effect, thatis, the presence of one or more of the riskfactors, one obtains a relative risk of only1.54, but the attributable risk is 30 percent, indicating that 30 per cent of thecases are now explained. The reason forthe increase in attributable risk is clear; 81per cent of the population is exposed to oneor more of these factors. This combinationof a rather low attributable risk with a

TABLE 3

RekUive and aitribviable risks for leukemia inchildren 1-^ years of age for each of fmir risk

factors

Risk factor

Individual:Preconoeptional radiationReproductive wastageIn utero radiationChildhood virus diseases

Cumulative:1 or more risk factors

%among

controls

w

52182831

81

Rel-ativeriskW

1.391.831.G01.32

1.54

Attrib-utible

risk(%)

16.713.014.49.0

30.0

large segment of a population suggests thatthere are other factors involved but theyare principally found among those individ-uals already exposed to these four risk fac-tors. This requires a different research strat-egy from that proposed for lung cancer. Ido not think that a consideration of therelative risks alone would provide similarsuggestions.

The complexities imposed by time andmultiple factors are not limited to the non-infectious diseases. Similar considerationsexist with regard to some infectious diseases,particularly those that are due to the "slow"viruses. It is also possible that some of thenon-infectious diseases may have simpleunifactorial etiologies. I hope, however, thatthis discussion will stimulate an increaseduse of the attributable risk in evaluatingepidemiological data.

I would now like to turn to an area ofcurrent epidemiological interest. Given thepossibility that some forms of cancer, morespecifically leukemia and the lymphomas,are of infectious origin, perhaps even com-municable, what would be the most produc-tive epidemiological test of this hypothesis?Those who have tried to answer this ques-tion over the past several years have at-tempted to evaluate the hypothesis bydetermining the clustering of cases in time,space or in both time and space. A varietyof elaborate statistical methods have been

142 ABRAHAM M. LILIENFELD

developed to decide whether the degree ofclustering is more than would be expectedby chance. A critical assessment of theseapproaches suggests that the data are notconsistent with the communicable hypoth-esis (11,12).

An epidemiological problem in clusteranalysis is that it is usually limited to thedistribution of cases. One strong and last-ing impression early in my career was madeby Alexander Langmuir, who pointed outthat clinicians are interested in cases withthe disease, the statisticians with the popu-lation from which the cases are derived,and the epidemiologist is interested in therelationship between cases and the popula-tion in the form of a rate with the cases rep-resented in the numerator and the popula-tion in the donominator.

When the epidemiologist is interested indetermining communicability or infectious-ness in studying an infectious disease andrequires a rate, he uses the family as theunit or perhaps some larger populationaggregate to compute an attack rate; thespecific rate would be some form of thesecondary attack rate.

It is a source of some curiosity that thoseconcerned with the communicable or in-fectious hypothesis in cancer have not bor-rowed a page from infectious disease epide-miology and conducted a study to estimatethe secondary attack rate for various socialaggregates of exposed population groups,including families. Admittedly, such a studywould be more difficult to carry out than inan acute disease because of the lower fre-quency of diseases such as leukemia and thelonger incubation periods, so that studieswould be needed over longer periods of timeand in larger population groups. However,the likelihood of obtaining a clear-cut an-swer as to infectiousness is considerably in-creased. I think that if Frost were heretoday, he would support this for we knowthat after Chapin developed and introducedthe secondary attack rate, Frost broadened

its applicability and used it widely in manyof his own studies (13).

There are other areas where studies offamilial aggregation might provide usefulleads, such as studying the relationshipbetween different disease entities. There isevidence, for example, that suggests a re-lationship between some forms of benignbreast disease and female breast cancer (14,15). It would be worth knowing whetherthe frequency of breast cancer among rela-tives of those with benign breast diseasediffers from that of the general population.An area of current research activity con-cerns the cerebrovascular diseases. It wouldbe helpful to determine whether there isfamilial aggregation not only of each formof cerebrovascular disease but also of defi-nite or related risk factors, such as elevatedblood pressure, cholesterol level and otherforms of vascular disease.

In reviewing the epidemiological studiesof non-infectious diseases, one becomes im-mediately aware that many studies reportan association of a disease with a verygeneral variable. For example, disease fre-quency by social class is frequently an-alyzed as well as the differential frequencyof a disease between states or regions of thecountry or even between different countries.But, after obtaining such results, no effort ismade to determine the underlying reasonfor such relationships. I would like to stressthe importance and need for our field studiesto go beyond these broad relationships andinto as many specific ones as possible. Table4 illustrates a possible sequential pattern ofrelationships with regard to social class. Ifone can modify the general populationvariable, such as social class, to prevent thesequence of events leading to the disease—if one could for instance eliminate poverty—it is possible that the disease would de-crease in frequency and negate the need forfurther studies. However, such a direct at-tack on a variable is usually not feasibleand it then becomes necessary for the epide-miologist to explore the specific components

EPIDEMIOLOGY OF INFECTIOUS AND NON-INFECTIOUS DISEASE 143

General populationvariable

Social class

Relationships

Possible specificpopulation variable

Medical careDietWorking conditionsPsychosocial stressOther

TABLE 4

among sets of variables related to social class

Examples of specificcomponents

Specific therapyVitaminsSpecific occupational

exposuresOther components

Physiological or cellularvariables

Specific biochem-ical mechanism

End result

Specific disease orcause of death

of the general variable and search for a fac-tor that can be altered to permit disease con-trol, as is suggested in table 4. In manyepidemiological studies, it would appearhighly desirable to include measurementsof physiological or biochemical variablestogether with the specific population com-ponents.

THEORETICAL OH MATHEMATICALEPIDEMIOLOGY

An area of epidemiology which has al-ways evoked considerable interest is oneI term theoretical or mathematical epide-miology; here the focus has been on thedescription of the epidemic occurrence inmathematical terms, that is, as a mathe-matical model.

In infectious diseases, there is a continu-ing effort to develop mathematical modelsto describe epidemics; we know this asepidemic theory and, in fact, Frost, col-laborating with Reed, contributed to thisdevelopment. What we know as the Reed-Frost model is included among some un-published lectures used in his courses (16,17). More recently, these methods have beenextended to include computer simulationof epidemics under varying conditions.

The development of mathematical modelshas also been of some interest in the non-in-fectious diseases, particularly in consider-ing the effects of radiation and carcinogen-esis. (6). Models have been developed torepresent various types of theories, e.g., the2-hit theory, meaning that cancer resultsfrom a sequence of exposure of the cell to

two events, separated in time, which finallyresult in a malignant transformation; thishas been extended to a multi-hit theory,with the malignant transformation result-ing from a sequence of series of multipleexposures. From these probability concepts,one can derive equations regarding the age-specific incidence rates of cancer and deter-mine whether the rates resulting from thetheoretical model are consistent with ob-served data.

My primary purpose in mentioning thesedevelopments is to illustrate the similaritiesbetween the infectious and non-infectiousdiseases. The Reed-Frost model presentedbelow has a relatively simple interpretation:

Cm = 5,(1 -qCl)

C — Cases.5 = Susceptibles.q = Probability of individuals not having

contact.1 — q" = Probability of having con-

tact with at least one case.t = Time.When a susceptible has a contact with acase, he will develop into a case and theoccurrence of cases over time is a functionof susceptibles and probabilities of havingcontact with cases. The equation can mathe-matically be reduced to the following:

Ct+i = - e~rc')

r = Proportionality constant

One of the multi-hit models which hasbeen developed to fit the age distribution

144 ABRAHAM M. LILIENFELD

of several specific forms of cancer is theone proposed by Burch:

P r i l = S0(l - e*'*)

PTi t = Age-specific prevalence at age tyears of condition initiated by rrandom events.

So = Per cent population genetically pre-disposed.

kr = LmT; L = Number of cells.m = Mutation rate per cell/year.

It is most striking that the form of themodel is essentially the same as in theepidemic theory; I must admit to havingbeen unprepared for this result. However,upon reflection, the biological similaritiesbecome evident. A hit is similar to a con-tact; a conversion from a susceptible to acase ia similar to a mutation which convertsa normal cell to a malignant one. I haveno desire to overstate the similarity of thesespecific models since other models whichhave been developed are not as similar.However, it is clear that in both the in-fectious and non-infectious diseases thisparticular approach has been used in similarways.

The mathematization of biological or ofnatural phenomena has considerable appealto man in his effort to understand and con-trol nature. Although such approaches havebeen powerful in other disciplines, it is notclear what they have contributed to epide-miology. My personal feeling is that theirrole thus far has been a limited one; al-though I must admit that it may be tooearly to pass judgment. This type of theoret-ical model building should be assessed interms of its ability to stimulate and influencea change in direction or methods in a disci-pline; frankly, I do not believe it has hadthis influence in epidemiology. True, it hasled to increased precision in the thinkingand defining of some ideas and concepts andfrequently has been of assistance in theteaching of concepts and perhaps that isall that one can expect.

One of the most succinct statements onthis type of model building was made by

Robert Solo, in a critical assessment ofeconometric models, which represents asimilar approach in economics (18). Hestated: "Ultimately, the mode of expressionthat will most conform to the scientific idealwill not be the image-free symbols of mathe-matics but rather the imagery of normalcommunication and intercourse with itsreference base in the specifics of experience,for only if the general statement is soframed can it be continuously bridged intodirect observations and contrasted with on-going experiences." This judgment, it seemsto me, applies equally well to epidemiology.

EXPERIMENTAL EPIDEMIOLOGY

The last area we shall consider is that ofexperimental epidemiology, broadly definedto include experimentation in both animalsand man. For the past two decades, this hasbecome a major area of epidemiological ac-tivity. As far as I have been able to deter-mine, Frost did not consider either ani-mal or human experiments within the realmof epidemiology. Perhaps, he consideredexperiments in the infectious diseases to bean appropriate concern of microbiology andexperimentation in the non-infectious dis-eases the concern of that clinical specialtyor laboratory discipline dealing with thespecific problem. There is no indication inhis writings as to the role of experimenta-tion within the inference-making frameworkof epidemiology, except of course for the"natural" experiment, which, although oc-curring naturally, closely approximates theconditions of a randomized controlled ex-periment such as John Snow's studies oncholera in London, which Frost resurrectedfrom obscurity.

A comparison of the types of epide-miological experiments in these two cate-gories is shown in table 5. We can considerthe experimental work in animals withvarious etiological agents in non-infectiousdiseases as a form of experimental epide-miology, conceptually equivalent to similarexperimental work in animals in the infec-tious diseases. However, very few non-in-

EPIDEMIOLOGY OF INFECTIOUS AND NON-INFECTIOUS DISEASE 145

fectious disease epidemiologists do actuallyengage in such experimental work. Thistype of research is complex, requiring adifferent set of skills and disciplines; per-haps, it should not even be considered withinthe scope of epidemiology. In any event,such experimental work does make im-portant contributions to our understandingof the biology of specific diseases. Theseanimal studies provide a means for deter-mining the possible pathogenetic mecha-nisms by which an exposure to a particularetiological agent produces the disease. Theymay also provide information on the se-quence of the intermediate pathological,biochemical or physiological steps betweenexposure and disease. Once these have beenascertained, it may then be possible to re-turn to the human situation in observationalstudies to determine whether these steps infact do pertain. The converse is also truein that human observational studies leadto animal experiments.

It is not necessary to elaborate upon theproblems encountered in generalizing fromthe results of animal experiments to man.Although they exist for both the infectiousand non-infectious diseases, extrapolationis somewhat more difficult for the non-in-fectious diseases. For example, one of theproblems encountered in experimental car-cinogenesis and atherogenesis is that of thespecific metabolism of the animal speciesin the experiment which may determinewhether a particular agent produces thedisease. As an example, in the experimentson aniline dyes and bladder cancer, theaniline dyes were not carcinogenic in rats,rabbits, cats or in several other species (19).It was not until dogs were used as the ex-perimental animal that bladder cancer wasexperimentally produced. Apparently, dogmetabolism, at least with respect to anilinedyes, is similar to that of humans and dif-ferent from other species. The converse isalso often true, and in many diseases thehuman situation may be unique and not re-producible in any animals, which leaves uscompletely dependent upon observational

TABLE 5

Experimental epidemiology

Infectious diseases Non-infectious diseases

Animal

Epidemics in animalsVaccine studies

Experimental carcinogenflsiAExperimental atherosclerosisExperimental virology

M a n

Vaccine trialsVolunteer studies: actual pro-

duction of disease in humans

Trial of etiological agentaTreatment of riak factorsCessation studies

studies. This type of situation is obviouslymuch different from Webster's and Wilson'sexperiments on the progress of an epidemicin colonies of mice in which herd immunityand susceptibility were investigated (20,21). Those experiments were not dependenton metabolic differences between species,etc., and generalization of behavioral prin-ciples of epidemics from animal colonies tohumans would appear to be more reason-able. Realistically, however, it will probablynever be possible to generalize from ani-mals to humans except in a very limitedway. For practical purposes, the signifi-cance of positive results from animal ex-periments, without data on human popula-tions, is that such results do indicate apos^ib'e human risk which can be taken onlyat the possible cost of human lives.

Let us now turn our attenfion at thispoint to experiments using volunteers. Itis unnecessary to describe the details ofrandomized controlled trials, which is whatI mean by human experimentation, nor theadvantages and general type of problemsencountered in such trials; these are dealtwith in many publications (22, 23). It doesseem worthwhile, however, to focus our at-tention on the three types of studies indi-cated in table 5 and the problems encoun-tered in the non-infectious diseases, particu-larly those having some of the characteristicsmentioned earlier.

The first type of experiment, i.e., the trialof etiological agents, is best illustrated by

146 AHTtATTAM M . TJTTII W.N WH!I.T>

the randomized trial of exposure of new-born infants to varying concentrations ofoxygen in the incubator to determine ifa high concentration of oxygen was of etio-logical importance in retrolental fibroplasia.This type has no special conceptual prob-lems.

The second type is demonstrated by adrug trial for hypercholesterolemia in theprevention of coronary heart disease. If oneis interested in the possible etiological rela-tionship between elevated serum cholesteroland coronary heart disease and if, in arandomized controlled trial, a drug success-fully lowers serum cholesterol which inturn results in a decreased incidence ofcoronary heart disease, a strong link hasbeen successfully added to the chain ofevidence showing a causal association be-tween the two.

The third type, which is slightly differentfrom the first, is the cessation experiment.Let us assume we are interested in the causalassociation between cigarette smoking andlung cancer; we select a group of cigarettesmokers and randomly allocate them to twogroups, one which continues to smoke andone which we convince to stop smoking. Wethen determine that the mortality fromlung cancer in the smoking-cessation groupis lower than in the smoking-continuinggroup. Such a result would considerablystrengthen the etiological interpretation ofthe smoking-lung cancer relationship.

The last two types of experiments havea special problem reflecting the biologicalfeature of some chronic, non-infectious dis-eases. Let us assume that in both examplescited, the coronary disease and lung cancertrials, negative results were obtained. Wouldthis indicate that there was no causalrelationship between the risk factors thatwere experimentally modified and the spe-cific disease? Definitely not, since it isquite conceivable that the underlying patho-logical process leading to the disease may bethe result of the long term effects of theetiological agent and that this pathologicprocess had already reached a nonreversible

stage in our experimental subjects. Thus, itis possible that exposure to an elevatedserum cholesterol may have passed thepoint where the atherosclerotic process isreversible. Similarly with regard to ciga-rette smoking and lung cancer. We maybe left in the unenviable position of obtain-ing a negative finding, from which a con-clusive negative inference cannot legiti-mately be derived.

I do not believe that one can postulateany general rule that would apply to thistype of situation. Each study must be evalu-ated in the light of our knowledge of theepidemiology and biology of the specificdisease.

Another characteristic of the non-infec-tious chronic diseases that may pose a prob-lem in the planning and interpretation ofthe results of human experimentation is thepresence of multiple etiological agents. Thisproblem becomes especially important whenselecting a population or sample study groupfor a particular study. Let us assume, forexample, that we would like to study theeffect of dietary change on coronary heartdisease by means of a controlled humantrial and that the study will be carried outin a single medical center or community.Since multiple factors, many still unknown,are involved in the etiology of coronaryheart disease, the question might be askedhow generalizable are the results obtainedfrom a study in one community. Differentcommunities may be exposed to other etio-logical factors which may interact with thedietary factor. And, it is obviously im-possible to sample all mankind.

In this presentation I have primarilyattempted to emphasize the similaritiesin the epidemiological approach to infec-tious and non-infectious diseases, particu-larly the methods used and the inferencesto be derived. I have also considered severaltypes of differences. Unfortunately, muchtoo often I hear that there are "Two Epide-miologies" and I have therefore tried todemonstrate that investigators dealing with

EPIDEMIOLOGY OF INFECTIOUS AND NON-INFECTIOUS DISEASE 147

one of these disease categories have muchto learn from those dealing with the other.

There is, however, one distinct majordifference in the epidemiological study ofthese two groups of diseases; in infectiousdiseases, there is an underlying germ theoryof disease. It is important to remember that,with the exception of the few brilliantepidemiological observations in the pre-Pasteur era, epidemiology really flourishedafter the germ theory had a firm base. Inthe non-infectious diseases there is no gen-eral all-embracing theory; each diseasegroup has its own underlying biologicalbase, which imposes a serious limitation onepidemiological studies. Despite this, epide-miologic studies and data have contributeddirectly and- significantly to our presentunderstanding of the biologic basis of sev-eral non-infectious diseases. Many of these,20 to 30 years ago regarded as degenerative,constitutional and nonpreventable diseases,are now regarded in whole or in part asenvironmentally determined, preventable orpotentially preventable. Much of this changeis the result of epidemiological studies, animpressive achievement. But, much remainsto be done. I am certain that epidemiologistscan look forward to an active future, as wellas a most productive one.

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