The use of capture-recapture methods in public health.

To make policy on disease control and toput it into practice, public health officialsneed to know the size and compositionof target populations. Incidence and pre-valence estimates provide the foundationfor the design and evaluation of essentialhealth programmes. Compulsory reportingto registers is the broadest approach toobtainingtheseestimates,butitisexpensiveand the goal of complete enumeration israrely achieved. Births and deaths, inindustrialized countries at least, are welldocumented, but rates of HIV infectionmuch less so. Health surveys, on the otherhand — whether periodic or ad hoc, cross-sectional or longitudinal — identify casesfrom a random or nationally representativesample. Inferences about the whole popu-lationarethendrawnbyextrapolation.Bothapproaches have their limits in practice.Fortunately, a third alternative — acapture–recapture census — may providemore reliable estimates. The technique wasfirstusedin1662toestimatethepopulationof London, but it was not until 150 yearslater that Laplace laid out its mathematicalfoundations. In 1896, Petersen used theapproachtoestimate theharvestablestocksof Danish fish populations, and in 1930Lincoln used it to estimate waterfowlabundance in US flyways. In wildlifeapplications, the method is often called theLincoln–Petersen estimator; in demogra-phy, it is known as dual-system estimation.Its continued refinement over the last 75years has been stimulated mostly, but notexclusively,bytheneedsofwildliferesearchand management (1).In the original form of this method,a sample of individuals from a targetpopulation is captured, marked andreleased, and a second sample captured atsome later time. The number of individualsobserved in each sample, as well as thenumber observed in both, is noted. Thereare four critical assumptions implicit inthe statistical analysis: the populationis closed, individuals captured on bothoccasions can be matched, capture in thesecond sample is independent of capture inthe first, and the probabilities of capturearehomogeneousacrossindividuals.Undertheseconditions,thedatamakeitpossibletoestimate the probability of being capturedand the size of the population. Log-linearmodelsprovideaconvenientrepresentationof this basic census and its extension tomultiple capture–recapture occasions.By analogy, the kth list in a set of Kindependent lists of members of a targetpopulationmaybethoughtofasidentifyingindividuals ‘‘captured’’ on the kthoccasion. If individuals can be matched, acount of the number that appear on onlyone list, on two lists and so on up tothe number on all K lists can be compiled.These are the data needed for a capture–recapture analysis. In health applications,lists can be obtained with little addedcost from many sources such as hospitals,doctors,laboratories,insurers,socialserviceagencies, religious institutions, and schools.Theearliestmodernapplicationofthismethod in demography appears to havebeen to estimate vital rates in India in 1949(2); its earliest use in epidemiology was toestimate the number of hospital patientsusing methicillin in 1966 (3). Capture–recapture methods have been used toestimatepopulationsizeinawidevarietyofhealth applications including, for example,infantsbornwithbirthdefects,womenwithpreclinical cancer, persons with severeand persistent mental illness, drug abusers,and persons with sexually transmittedinfections. Such methods have also beenusedtoevaluatethedegreeofascertainmentof various disease monitoring systems.Yip et al. document epidemiologicalapplications and include an extensivebibliography (4).The study on the annual incidence ofacute flaccid paralysis reported in this issueoftheBulletinbyWhitfield&Kelly(pp.846–851) puts the method to good use. Theirestimate is based on a statistical analysis ofdata from two lists: routine surveillance,and hospital records. In addition, thestudy documents the ascertainment short-comings of the surveillance system.In recent years, related new methodshave been developed, stimulated in part byproblems involving human rather thanwildlife populations. For example, ‘‘singlesample methods’’ in the spirit of thecapture–recaptureapproachhaveappeared.The plant-capture method was used toestimate the number of street-dwellinghomeless people in southern Manhattan aspart of the 1990 US decennial census. Inlieu of a first capture, study participantswhose behaviour and appearance are indis-tinguishable from the target population aredistributed or ‘‘planted’’ throughout sitesoccupiedbythetargetpopulation(5).Usingdata on time since last service, a one-weeksample survey was used to estimate thenumber of individuals served annually bya large mental health services system (6). Arecently developed method relaxes therequirement that individuals can be exactlymatched from capture to capture. Instead,the likelihood of a match based on demo-graphic variables is used.Capture–recapture techniques are of-ten much less expensive and may be moreinformativethanclassicapproachestocase-finding. Public health officials face limitedbudgets in both the developing and theindustrializedworld.Thoseinterestedinthesize of difficult-to-identify populations willundoubtedly find estimation proceduresbased on these methods appealing.