Estimating the size of hidden populations from register data

BMC Medical Research Methodology

Peter Wennberg¹  Anders Ledberg¹ 

[1] Centre for Social Research on Alcohol and Drugs, SoRAD, Stockholm University, SE-10691 Stockholm, Sweden

关键词: Mortality;    Heroin;    Opiates;    Truncated Poisson;    Capture-recapture;    Hidden population;    Prevalence;   

Others  :  866349
DOI  :  10.1186/1471-2288-14-58

 received in 2014-01-14, accepted in 2014-04-15,  发布年份 2014

【 摘 要 】

Background

Prevalence estimates of drug use, or of its consequences, are considered important in many contexts and may have substantial influence over public policy. However, it is rarely possible to simply count the relevant individuals, in particular when the defining characteristics might be illegal, as in the drug use case. Consequently methods are needed to estimate the size of such partly ‘hidden’ populations, and many such methods have been developed and used within epidemiology including studies of alcohol and drug use. Here we introduce a method appropriate for estimating the size of human populations given a single source of data, for example entries in a health-care registry.

Methods

The setup is the following: during a fixed time-period, e.g. a year, individuals belonging to the target population have a non-zero probability of being “registered”. Each individual might be registered multiple times and the time-points of the registrations are recorded. Assuming that the population is closed and that the probability of being registered at least once is constant, we derive a family of maximum likelihood (ML) estimators of total population size. We study the ML estimator using Monte Carlo simulations and delimit the range of cases where it is useful. In particular we investigate the effect of making the population heterogeneous with respect to probability of being registered.

Results

The new estimator is asymptotically unbiased and we show that high precision estimates can be obtained for samples covering as little as 25% of the total population size. However, if the total population size is small (say in the order of 500) a larger fraction needs to be sampled to achieve reliable estimates. Further we show that the estimator give reliable estimates even when individuals differ in the probability of being registered. We also compare the ML estimator to an estimator known as Chao’s estimator and show that the latter can have a substantial bias when applied to epidemiological data.

Conclusions

The population size estimator suggested herein complements existing methods and is less sensitive to certain types of dependencies typical in epidemiological data.

【 授权许可】

   
2014 Ledberg and Wennberg; licensee BioMed Central Ltd.

【 图 表 】

【 参考文献 】

• [1]UNO: Tungt Narkotikamissbruk: en Totalundersökning 1979 [Heavy Drug Abuse: A Complete Population Stud 1979]. Stockholm: Socialdepartementet; 1980.
• [2]Olsson B, Adamsson Warhen C, Byqvist S: Det Tunga Narkotikabrukets Omfattning i Sverige 1998. Stockholm: CAN; 2001.
• [3]European Monitoring Centre for Drugs and Drug Addiction: Annual Report 2012. The State of the Drug Problem in Europe. Luxembourg: Publications Office of the European Union; 2012.
• [4]Hook E: Capture recapture methods in epidemiology: methods and limitations. Epidemiol Rev 1995, 17(2):243-264.
• [5]Yip P, Bruno G, Tajima N, Seber G, Buckland S, Cormack R, Unwin N, Chang Y, Fienberg S, Junker B, LaPorte R, Libman I, McCarty D: Capture-recapture and multiple-record systems estimation II applications in human-diseases. Am J Epidemiol 1995, 142(10):1059-1068.
• [6]Chao A, Tsay P, Lin S, Shau W, Chao D: The applications of capture-recapture models to epidemiological data. Stat Med 2001, 20(20):3123-3157.
• [7]Frischer M, Leyland A, Cormack R, Goldberg D, Bloor M, Green S, Taylor A, Covell R, McKeganey N, Platt S: Estimating the population prevalence of injection-drug use and infection with human-immunodeficiency-virus among injection-drug users in Glasgow, Scotland. Am J Epidemiol 1993, 138(3):170-181.
• [8]Domingo-Salvany A, Hartnoll R, Maguire A, Brugal M, Albertin P, Cayla J, Casabona J, Suelves J: Analytical considerations in the use of capture-recapture to estimate prevalence: case studies of the estimation of opiate use in the metropolitan area og Barcelona, Spain. Am J Epidemiol 1998, 148(8):732-740.
• [9]Chao A: Estimating the population-size for capture recapture data with unequal catchability. Biometrics 1987, 43(4):783-791.
• [10]Zelterman D: Robust estimation in truncated discrete-distributions with application to capture recapture experiments. J Stat Plan Infer 1988, 18(2):225-237.
• [11]Hay G, Smit F: Estimating the number of drug injectors from needle exchange data. Addict Res Theory 2003, 11(4):235-243.
• [12]Bohning D, Suppawattanabodee B, Kusolvisitkul W, Viwatwongkasem C: Estimating the number of drug users in Bangkok 2001 : a capture-recapture approach using repeated entries in one list. Eur J Epidemiol 2004, 19(12):1075-1083.
• [13]Cormack R: Problems with using capture-recapture in epidemiology: an example of a measles epidemic. J Clin Epidemiol 1999, 52(10):909-914.
• [14]Hayne D: Two methods for estimating population from trapping records. J Mammal 1949, 30(4):399-411.
• [15]Moran P: A mathematical theory of animal trapping. Biometrika 1951, 38(3–4):307-311.
• [16]Zippin C: An evaluation of the removal method of estimating animal populations. Biometrics 1956, 12(2):163-189.
• [17]Chao A: Nonparametric estimation of the number of classes in a population. Scand J Statist 1984, 11:265-270.
• [18]Seber G, Whale J: The removal method for two and three samples. Biometrics 1970, 26(3):393-400.
• [19]Feller W: An Introduction to Probability Theory and Its Applications. Stockholm: Wiley; 1968.