CONCEPT, MEASUREMENT, AND DATA IN MIGRATION ANALYSIS
WILLIAM HAENSZEL'"
RESUMEN
Se discute dos metodo« para computar tasas de migraci6n, uno relaciona el desplazamiento conla poblaci6n someiida al riesgo en ellugar de origen y el otro que usa como denominador el productocruzado de la poblaci6n en los lugares de origen y de destino. Se concluye que el segundo asumeimplicitamente que los desplazamientos se originan y terminan como una variable poblacionalfortuita.
Se senalan algunas dificultades con este modele particular y el autor sugiere que deben buscarseotras perspectivas analiticas para tratar datos sobre migraci6n y en conecci6n con esto se refiere a laliteratura sobre la teoria matemdtica de las epidemias.
SUMMARY
Two metlwds of computing migration rates-one relating moves to population at risk in place oforigin and the other using as a denominator the cross-product of population in places of origin anddestination-are discussed. It is concluded that the second assumes implicitly that moves originate and terminate as a random population variable.
Some difficulties with this particular model are pointed out and the author suggests that otheranalytical approaches to migration data be sought and in this connection refers to the literature on themathematical theory of epidemics.
or, more generally,
M··r.cu,«:» Pi I
when several places of destination are involved.
of measurement for this rate can be expressed as time/population"; the timedimension is introduced by specificationof the interval in which the count ofmoves was made.
A second approach follows conventional vital statistics practice in which therate estimates the probability of the eventin question. The migration rate in thisform is based on the familiar triad ofevent, population at risk (population atplace of origin), and period of observation.The corresponding units of measurementare time/population-s
Rate = Pr( obability) (M ii) = ~:i (2)
2 B. MacMahon, T. F. Pugh, and J. Ipsen,Epidemiologic Methods (Boston: Little, Brown &Co., 1960); M. Spiegelman, Introduction toDemography (Chicago: Society of Actuaries,1955).
253
(1)
The literature on migration presents anambivalent position with respect to thecomputation and presentation of migration rates. One frequently used methodrelates the number of moves (net or gross)between places of origin and destinationto the product of the respective populations:'
R _Mii±Miiate- PiP
i'
where M represents the number of moves,the direction being indicated by the orderof subscripts, and Pi and Pi the populations at origin and destination. The units
* National Cancer Institute, Bethesda, Maryland.
1 T. R. Anderson, "Intermetropolitan Migration: A Comparison of the Hypotheses of Zipf andStouffer," American Sociological Review, XX(1955), 287-91; J. Q. Stewart, "The Gravitationor Geographic Drawing Power of a College,"Bulletin of the American Association of UniversityProfessors, XXVII (1941), 70-75; H. ter Heide,"Migration Models and Their Significance forPopulation Forecasts," Milbank Memorial FundQuarterly, XLI (1963), 56-76; G. K. Zipf, "TheP1P./D Hypothesis: On the Intercity Movementof Persons," American Sociological Review, XI(1946), 677-86.
254 DEMOGRAPHY
Eldridge" has stressed the need tocalculate migration rates that relate thecount of moves to a population exposedto risk. Thomlinson4 subscribed to thislatter usage in his discussion of migrationrates, although he qualified his remarksby stating that "two base populations arenecessary when using a gravitational approach or when measuring the stream ofmovement-i.e., when emphasis is on themove rather than on an area." Price" alsoaccepts the position that rate of migrationshould be expressed as a probability statement; the purpose of his proposed mathematical model would be to estimate bymultivariate techniques the contributionsof various components to the force ofmigration.
Their structure and substantive applications clearly show the two rates tohave different properties, and it seemssurprising that no one has discussed therationale underlying the two divergentapproaches. The views presented herehave been shaped by work in vital statistics and epidemiology, and this predisposes me to favor equation (2) and to regard equation (1) with reserve. I amunder no illusion that my comments willgain acceptance from all investigators, forthe purpose is to provoke discussionwhich may cast some light on the issues.
We may begin by noting that the label"migration" had been applied to two related, but different, universes of discourse-a population of "moves" and a population of "people who move." A universe of"moves" can be generated by simultaneous classification of individuals by initialand subsequent place of residence, and the
3 H. T. Eldridge, "Primary, Secondary, andReturn Migration in the United States," Demography, II (1965), 444-55.
4 R. Thomlinson, "The Determination of aBase Population for Computing MigrationRates," Milbank Memorial Fund Quarterly, XL(1962), 356-66.
6 Price, D.O., "A Mathematical Model ofMigration Suitable for Simulation on an Electronic Computer: A Progress Report," in Proceedings of the International Population Confernee (1959), pp. 665-73.
data provide useful descriptions of population redistribution. Such results, however, do not lend themselves to probability statements. Probabilities can becomputed only for denumerable populations at risk, whether they be people,telephone poles, or transistors. Derivativedata obtained by classification proceduresdo not necessarily lead to denumerablepopulations, and this would not appear tobe a property of the data normally available on "moves."
If migration data are to be reported inrate form as probability estimates, thesole option is to report on persons makingprescribed moves. The unique relationship between population at risk and direction of move permits consideration ofunidirectional moves only, outward fromPi. Within this framework, the probability of out-migration within a fixed timeperiod from a defined population at risk atplace (Pi), expressed in equation (2), hasas its complement the probability of notmoving:
Pr(Mi , ) +Pr(Mi , ) = 1. (3)
Furthermore, the probabilities of movingfrom i to j, k, l . . . are additive, sinceeach comprises a subset of admissiblemoves:
One may, of course, calculate a pooledexperience for two or more areas by summation of events and population at risk inthe usual manner, taking care to defineM i j and Mji as included or excluded fromthe count of events depending on thestudy objective.
Pr(M)=Mi,+Mj , (5)Pi+Pj
Appropriate definition and estimationof the base population at risk for computation of migration rates of this type havebeen discussed by Thomlinson." No comment is required here other than to note
8 Thomlinson, op, cit.
Concept, Measurement, and Data in Migration Analysis 255
that the distinction drawn between thenumber at risk at the beginning of an observation period and the average numberat risk over a time interval has receivedmeticulous attention in the actuarial literature with reference to measurements offorce of mortality.
If one is concerned with moves ratherthan with a population at risk of migration, the vital statistics approach to rateconstruction offers no escape from theone-way traffic limitation just noted. Thedesire to handle data on two-way trafficand to admit the concept of net migrationundoubtedly motivated the search forother measures. The crces-product-c-Pzl",-was an obvious candidate for denominator of a migration rate, given its symmetryvis-a-vis M i j and ~fji and invariant relationship with direction of move. An important property of PiP j has been statedby ter Heide, who introduces the notionof the universe of messages (moves)." Ifmoves are assumed to originate and terminate as a random population variable, thedistribution of moves originating within iand terminating within j, or vice-versa,will vary in direct proportion to PiP j •
The analytical implications of Pi andPP, for measures of migration can be considered in the context of how observationson migration are collected. The threemethods in general use can be cataloguedas follows:1. In an area of origin, count and trace out
migrants.2. In an area of destination, count and classify
in-migrants by place of origin.3. For a population characterized by census
or register data, distribute individualswithrespect to residence as of two dates.
1. In observations on a source population, the distinction between moves andthe person who moves has little operational significance, and the two will often beidentical. The moves occur in one direction, and study objectives and definitionswill determine the treatment accorded topersons who move away but subsequently
7 ter Heide, op. cit.
return. The base population and subgroups categorized by age, sex, and otherattributes are fixed, so that the proportionate distribution of out-migrants withrespect to destination remains unchanged,whether the data are shown as absolutenumbers (M ih M i k, ••• ) or as rates viadivision by Pi. As stated earlier, Mii/P i
describes the probability of an individualmoving from i to j within a stipulatedtime interval. The observations can beincorporated in new measures by introducing other characteristics linked withthe move, such as distance and population size of the area of destination.
The transformed rates are useful fortests of study hypotheses (migrationvaries inversely with distance of migration, number of migrants attracted to agiven destination is directly proportionalto population at terminus, and so forth).However, they no longer represent descriptive estimators of population parameters, because the latter variables are manifestations of the event (migration) andclassification of individuals becomes possible only after, and not before, the fact.
2. The investigator using place of destination as the vantage point also will notfind the distinction between a "move" and"person moving" to be important in practice. For any destination, the distributionof in-migrants by place of origin can bestated in absolute numbers, as a percent oftotal in-migrants, or as a ratio, Mii/Pj,without disturbing the internal relationships; only the form, not the substance, ofthe data is changed. While the formalarithmetic for calculating Mii/Pj andMii/Pi is the same, they have a differentlogical content. The latter, being linkedwith a population at risk, has been statedto estimate the probability that an individual from i will move to j; the formerconstitutes a relative frequency statement, which must be handled with caution and whose range of permissible inferences is restricted. The difficulties can beillustrated by a parallel problem whichoften arises on review of percentage distributions by disease in autopsy and hos-
256 DEMOGRAPHY
pital-admission series. Does the high (low)frequency of a given disease in a seriesarise from a high (low) risk for this diseasein the underlying population, or does itreflect in part the operation of low (high)risks from other diseases?
Relative frequency ratios have descriptive properties in the sense that the results are derived from observations onindividuals. When they are manipulatedby adjustment for distance of move, population concentrations, and so forth, weagain leave the realm of factual description to engage in tests of consistency withpostulated models.
3. Given a population sample characterized by residence at two points in time,the primary frame of reference for analysiscould be either place of origin (first residence) or place of destination; the remarks in items 1 and 2 would then holdwithout change. Or, alternatively, theinformation on origin and destination considered jointly can define a universe of"moves." Moves between i and j, andvice-versa, can be summed and represented by a single figure (gross migration).Since moves have direction, their additionas vector quantities would cancel outmoves in opposite directions (net migration). Counts of both gross and net migration describe population redistribution,although neither retains all the information contained in the separate figures forM ij and M ji. Difficulties arise when theabsolute numbers are converted to rates,since the simple additive properties of theabsolute numbers no longer hold withoutrestriction. In the probability approachto rate construction, we are confronted bytwo populations at risk to two differentevents. M,j and M j, are generated, respectively, by Pi and P j, and there is noobvious way in which the specific information contained in Mij/Pi and Mij/Pj canbe combined into one summary figure.The step of rate computation has relatedeach individual stream of migration to itssource in a manner analogous to describing the flow of a river in relation to itswatershed characteristics.
The device of relating migration to PiP j
was introduced to define a rate combininginformation on M ij and M j i • This line ofattack, however, required the assumption(implied by the universe of messages described by ter Heide) that volume of migration is directly proportional to thepopulations in the areas of origin and destination. For this a price has been paid,one not always recognized by the proponents. The ratio M ii ± Mji/PiPj is nota descriptive estimator determined solelyby the data, since an analytical model hasbeen incorporated at the outset. Rather,it constitutes a test of the hypothesis thatmigration is a random variable proportionate to population. As Tolley has remarked, "The resulting ratios should notdiffer significantly from the overall migration rate in the universe under study, ifthe null hypothesis is true."!
The use of P ,Pi is essentially equivalentto the computation of expected numbersof moves for cells in a contingency tableand closely resembles the familiar x2-testfor independence of row and column effects, in which expected numbers arecalculated as (A)(B)/N, where A, B, andN are the observed values for the corresponding column, row, and total table.
This may not be immediately obvious,but the point can be elaborated as follows.Table 1 is a schematic representation of apopulation distributed by place of residence at two points in time (t l and t2).While not essential for the discussion thatfollows, it may be noted that such a tablewould conceal information on intermediate moves (return moves from j to icanceling out moves from i to j) and thuscould report on net migration only. Also,the table would normally cover only individuals surviving to t2 ; allowance for migration associated with terminal illnesscould be introduced by substituting residence at time of death for residence at t2
a G. S. Tolley, "Migration Research in Relation to Agricultural Policy," in The Farmer andMi(J1'ation in the United States (API Series No.3 [Raleigh: North Carolina State College ofAgriculture and Engineering, 1961]), pp. 14-23.
Concept, Measurement, and Datain Migration Analysis 257
and, in principle, population registerscould produce such information. Onewould not often be misled by assuming themigration experience of survivors to approximate that of the initial cohorts oflike age and sex.
Given these qualifications, the stable(non-migrant) population is contained inthe diagonal cells of the table
and a count of all moves is obtained bysummation of observed numbers over theremaining cells:
The number of moves can be related tothe total population ('2P i = '2Pj) to compute an over-all migration rate for theuniverse under study
consistent with vital statistics practiceembodied in equation (2). The model"volume of migration is directly proportional to the populations in the areas oforigin and destination" determines anexpected number of moves correspondingto each observed number (Mij) calculatedas follows:
E(Mi j ) = ~Mijir<i
In this equation, P ,Pi can be recognizedas a proportionality factor introduced inthe context of a specific model, one consequence of which is that the expected numbers for moves in opposite directions (mirror-image cells on opposite sides of thediagonal) are equal, E(Mii ) = E(Mi i ) .
The ratio of observed to expected movesfor each cell-Mii/E(Mii)-tests, in linewith Tolley's remarks, the correspondenceof observation with model.
The ratio of observed to expected numbers is termed, in other subject-matter applications, "standardized ratio." By multiplying the migration rate for the totalstudy population by the appropriatestandardized ratio, a schedule of rates formoves from i to i. adjusted for size ofplaces of origin and of destination, can beobtained. The underlying argument andprocedures follow precisely the wellknown "indirect method" for age adjustment of death rates."
The close dependency of standardizedratios and derivative rates on the postulated model deserves reiteration. A crucialfeature of this model-that M ii and Mi ,
should be approximately equal on the
eSpiegelman, op. cit.
Table i.-DISTRIBUTION OF POPULATION BY PLACE OF
RESIDENCE AT tl AND t,
Residence at t2
Residence at tl
PI P2
P3
.... Pn
"i .............. MIl M2 1
M3 l
Mnl....
P2" ............ M1 2M
2 2M
32M
n 2....I'
M1 3
M23 M
33M~-l •••••••••••••• n3....
P M M2n M3n I Mn ••..•••••••...
In .... nn
258 DEMOGRAPHY
average-can be tested empirically. Failure of observed data to support this thesiswould gravely compromise the case forretention and use of PiP;-type rates, sincethis would imply, among other things,that moves do not vary in a predictable,uniform manner with population size ofplace of destination. Under these circumstances, the question to be posed wouldbe, "Why should migration rates be adjusted inversely to population size atplace of destination?"
The measure of velocity or rate of flowof the migration stream proposed byBogue'? retains the PiPj concept, as canbe seen from a trivial rearrangement ofhis formula:
V=Mij+Mji·pt·l00,PiP j
The new element introduced is P t, thetotal population in the universe underinvestigation. This adjustment transformsthe absolute size of all eligible places ofdestination into relative terms and thusfacilitates direct comparison of resultsfrom investigations carried out in studyuniverses of different size. In commonwith all ratios invoking the P'P, concept,velocity retains the assumption that migration is proportionate to population inareas of destination and thus can be characterized as a test of a specific hypothesisrather than as a descriptive estimator fora set of data. Its use in the manner proposed by Bogue, as a dependent variableamenable to multivariate analysis, cannotbe recommended without reservations,since the values of the dependent variableare influenced by both observation andmodel. Before proceeding, one must askwhat connection this implicit model mayhave with the questions posed for investigation by multivariate analysis.
FUTURE WORK
An assessment of rates of the PiP;variety should consider their potential
10 D. J. Bogue, "Internal Migration," in TheStudy of Population: An Inventory and Appraisaled. P. M. Hauser and O. D. Duncan (Chicago:University of Chicago Press, 1959).
for extension to more complex observational situations made possible by sophisticated study designs and by computercapabilities for data processing. The outlook in this regard would not appearpromising. The PiP; concept was developed to handle the comparison ofpopulations distributed as of two pointsin time, the source from which most of thedata on migration have been assembled.What happens when information for threeor more points in time becomes available?On the assumption that successive movesare random variables proportionate topopulation, the three-dimensional analogue of PiP; would be PiP;Pk • This modelis unattractive since the underlying hypothesis seems so far removed from thefacts. Work with residence histories hasdemonstrated that the antecedent historyof moves between t l and t2 will be correlated with later events, so that it wouldbe unwise to ignore information from theinterval h to t2 in analyzing data for thesucceeding interval." Eldridge," in herrecent analysis of data based on status asof three points in time (date of birth,1955, and 1960), found it necessary anddesirable to analyze the moves between1955 and 1960 with control for previoushistory of migration. Moreover, presentation of rates based on PiP;Pk would nothave been helpful in a discussion of whatshe has termed "primary," "secondary,"and "return" migration and which sheelected to relate to the several populations at risk (the approach of eq. [2]).These considerations make it unnecessaryto dwell on other complications inherent inPiP;Pk-type rates, including the need fordefinitions to handle data on moves between t1 and t2 accompanied by no changebetween t2 and ts, and vice-versa.
A related approach to data for three ormore points in time would be consideration of each interval separately. If oneconcedes for the moment that ratios in the
11 K. E. Tauber, L. Chiazze, and W. Haenszel,Migration in the United States: An Analysis ofResidence Histories (Public Health ReportsMonograph [in pressj),
12 Eldridge, op. cit.
Concept, Measurement, and Data in Migration Analysis 259
form (M ii ± Mii/PiPj ) can be defined ina manner which permits extension andapplication of the multiplication rule forcombining two probabilities, the dimensional units for the results would betimet/population', the denominator taking the form of P iPlPk. The computational problems might be overcome, but aformidable question of interpretation ofvalues with meaning only in relation to aspecific model would remain. Their interpretation would become so specializedthat the effort is best abandoned if analternative is at hand.
An obvious solution would be to divorce estimation of population parametersfrom tests of hypotheses. For three ormore points in time, the probability of adefined change in residence status overany combination of intervals can be estimated by multiplication of the intervalspecific probabilities, if each has beencalculated in accordance with equation(2). A table of rates specific for time anddirection of move will contain all the information on migration in the sense that,given the population distribution at t.,one could reconstruct from the probability matrix the population distributionsat all subsequent dates (given survivaldata input).
The computation and presentation oftransitional probabilities in great detailfor small subdivisions of the United Stateswould be impractical even with largecomputers. Analytical work must be imaginative and creative, and a major problem for any investigator would be toidentify the major components necessaryto describe and understand the forces atwork. This would require discriminationin definition of moves and in selection ofkey combinations of transitional probabilities. Study hypotheses can be an important tool in shaping analytical decisions, but one must also remain attentiveto what the data have to say. Within thisdescriptive framework, the option ofchecking facts against model predictionsat any step in the process is retained.
While no one can foresee the preciseformat that presentation of results of
large-scale, longitudinal studies of migration might take in the future, the use ofmultiple decrement tables, a device wellknown to actuaries, should be explored.Multiple decrement tables are well-suitedfor reporting on dependent probabilities,"and migration represents a classical competitive risk situation in that the probability of moving from i to j seems conditioned by and dependent on alternativesavailable. The probability of a specificmove (Mii/Pi) would change if the imposition or removal of barriers (immigration restrictions, etc.) added or eliminated potential destinations and wouldremain independent and unchanged onlyif removal of alternate destinations led todecisions not to move or if addition of newdestinations attracted individuals whowould not have migrated otherwise. Theconcept of "intervening opportunities"formulated by Stouffer" can be viewed asone attempt to measure and evaluate theinterplay of competitive risks.
OTHER APPROACHES TO
MEASURE MIGRATION
To this point, the comments have dealton rather narrow, technical grounds withthe relative merits of the P,- and PiP,type rates. If the Gordian knot were cutand the model "moves are distributed as arandom population variable," which underlies the PiPj concept, abandoned,other analytical options, such as thosedisplayed in the literature on communicable diseases and the mathematical theory of epidemics, would become available.In a sense, migration can be thought of asa contagious process-a psychic infection-since the departure of an individualfrom a community, if he retains links withthose remaining behind, would influencethe probability of subsequent departures.The connection between migration andepidemics is not too farfetched, and we
13 J. L. Anderson and J. B. Dow, ActuarialStatistics (Cambridge: Cambridge UniversityPress, 1952), Vol. II.
14 S. A. Stouffer, "Intervening Opportunities:A Theory Relating to Mobility and Distance,"American Sociological Review, V (1940), 845-67.
260 DEMOGRAPHY
may note that this idea occurred in 1911to Brownlee in his paper "The Mathematical Theory of Random Migration andEpidemic Distribution."15
The course of communicable diseaseepidemics within a community can becharted by noting the time intervals between cases and geographical spread overtime. Another tool is the "secondary attack" rate, which measures the risk ofsubsequent cases developing among individuals intimately exposed to a knowncase (members of the same household,same classroom). Stochastic and deterministic models have been applied tosuch data to correlate theory and observation. These methods employ whatare known as "contagious distributions;"the null hypothesis of independence isdiscarded and attention directed insteadto the estimation of conditional probabilities, which are introduced as parameters in mathematical models to testthe observed configurations and clustersagainst theoretical predictions."
Adaptation of some of these ideasmight prove to be a fruitful exercise,although one must guard against a rigidmechanical translation of techniques andstrive to develop concepts meaningfulfor migration data. Attention might begiven to what constitutes a suitable indexof familial aggregation of migration (Isthe nuclear or extended family an appropriate study unit?). Inquiry into thepossible presence and spacing of waves ofsecondary migration might also provideinsights into the dynamics of migration.These studies would require observationson the population at risk to migration inthe area of origin and could not be implemented solely by data collected at thepoint of destination.
15 J. Brownlee, "The Mathematical Theory ofRandom Migration and Epidemic Distribution,"Proceedings of the Rcryal Society of Edinburgh,XXXI (1911), 262-88.
16 N. T. J. Bailey, The Matherrwtical Theory ofEpidemics (New York: Hafner Publishing Oo.,1957).
DISCUSSION
Reliance on rates of the FiP j varietymay not be an isolated event but rathersymptomatic of a more general outlookand frame of reference shared by manystudents of migration. As one primarilyconcerned with vital statistics and epidemiology and as a recent intruder in themore specialized domain of migrationdemography, I have been impressed bythe differences in history and traditionembodied in the respective literatures.
Work on migration and population redistribution appears to have been stronglyinfluenced by the early successesof Ravenstein in formulating "laws of migration.i"?Subsequent papers have placed a premium on the development and testing ofnew hypotheses rather than on descriptions of facts and their collation. In thisclimate, the use of those rates which introduced assumptions keyed to a particular model and represented implicittests of hypotheses could become theprevailing practice. The fact that mostdata on migration and population distribution have been obtained from secondary sources, censuses, and populationregisters not under the direct control ofthe investigator may have been a contributing factor. One wonders whetheringenuity in the construction of theorieshas not outrun the capacity for collectionof relevant observations.
This is in contrast to the history of vitalstatistics. While Graunt" more than twocenturies before Ravenstein, had madeseveral important generalizations fromthe study of "bills of mortality" in London, his successors continued to concentrate on descriptions of the forces ofmortality and natality by means of ratesbased on populations at risk. While
17 E. G. Ravenstein, "The Laws of Migration,"Journal of the Royal Statistics Society, XLVIII(1885), 167-235; E. G. Ravenstein, "The Lawsof Migration," Journal of the Royal StatisticsSociety, LII (1889), 241-305.
18 J. Graunt, Natural and Political Observations Made upon the Bills of Mortality, 1882, ed.W. F. Wilcox (Baltimore: The Johns HopkinsPress, 1939).
Concept, Measurement, and Data in Migration Analysis 261
generalizations concerning the nature ofthe curves for age-specific mortality andother relationships among age- and disease-specific rates were later deduced,there was no strong tendency to developtheories solely within the framework ofdata provided by birth and death registration. A lively concern with descriptivedata was natural for investigators whowere in the main responsible for registration of vital statistics or who needed thedata to direct or plan public health programs.
However, this cannot be the completeanswer. Inquiries into the epidemiologyof specific diseases called for correlationand synthesis of vital statistics data withinformation from many other sourcesclinical observations, autopsy findings,animal experiments, and so forth. Theserequirements fostered a tradition of "shoeleather" epidemiology (the practice ofobserving and recording at first-hand) andgave vital statisticians and epidemiologists an intimate knowledge and commandof their data sources. These specialistshave traditionally paid careful attention
to problems of nosology and classification,and to assessments of the accuracy andcompleteness of data reported, includingthe nature of diagnostic evidence underlying medical certifications of death.
While the importance of models as atool for building a systematic, coherentbody of knowledge in any discipline is notin question, repeated calls by Kirk andothers" for new theoretical insights inmigration studies may have been overdone. Should the emphasis in migrationnow be placed on the design of studies tocollect data not available from census andother administrative sources and to exploit new opportunities that are nowarising as by-products of human population study centers and long-term followup of cohorts in order to investigate therole of factors in chronic diseases?"
19 D. Kirk, "Some Reflections on AmericanDemography in the Nineteen Sixties" (President's address to the American Population Association, May 1960).
10 W. Haenszel and R. W. Miller, Role ofHuman Population Study Centers in Studie« ofCancer Etiology (Public Health Reports 77 [1962]),pp.713-18.