1932

Abstract

Applications of estimating population sizes range from estimating human or ecological population size within regions or countries to estimating the hidden number of civilian casualties in war. Total enumeration via a census is typically infeasible. However, a series of partial enumerations of a population is often possible, leading to capture-recapture methods, which have been extensively used in ecology to estimate the size of wildlife populations with an associated measure of uncertainty and are most effectively applied when there are multiple capture occasions. Capture-recapture ideology can be more widely applied to multiple data sources by the linkage of individuals across multiple lists, often referred to as multiple systems estimation (MSE). The MSE approach is preferred when estimating capture-shy or hard-to-reach populations, including those who are caught up in the criminal justice system, trafficked, or civilian casualties of war. Motivated by the public policy applications of MSE, each briefly introduced, we discuss practical problems with methodological implications. They include period definition; case definition; scenarios when an observed count is not a true count of the population of interest but an upper bound due to mismatched definitions; exact or probabilistic matching of cases across lists; demographic or other information about the case that influences capture propensities; permissions to access lists; list creation by research teams or interested parties; referrals (if presence on list results, almost surely, in presence on list ); different mathematical models leading to widely different estimated population sizes; uncertainty in estimation; computational efficiency; external validation; hypothesis generation; and additional independent external information. Returning to our motivational applications, we focus finally on whether the uncertainty that qualified their estimates was sufficiently narrow to orient public policy.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-statistics-031017-100641
2018-03-07
2024-04-19
Loading full text...

Full text loading...

/deliver/fulltext/statistics/5/1/annurev-statistics-031017-100641.html?itemId=/content/journals/10.1146/annurev-statistics-031017-100641&mimeType=html&fmt=ahah

Literature Cited

  1. Advis. Counc. Misuse Drugs. 2000. Reducing Drug-Related Deaths London: Stationery Off.
  2. Baillargeon S, Rivest LP. 2007. : Loglinear models for capture-recapture in . J. Stat. Softw. 19:51–31 [Google Scholar]
  3. Ball P, Asher J, Sulmont D, Manrique D. 2003. How Many Peruvians Have Died? An Estimate of the Total Number of Victims Killed or Disappeared in the Armed Internal Conflict Between 1980 and 2000 Washington, DC: Am. Assoc. Adv. Sci.
  4. Besbeas P, Borysiewicz RS, Morgan BJT. 2009. Completing the ecological jigsaw. Modeling Demographic Processes in Marked Populations DL Thomson, EG Cooch, MJ Conroy 513–39 New York: Springer [Google Scholar]
  5. Bird SM. 2008. Fatal accident inquiries into 97 deaths over five years in Scottish prison custody: long elapsed times and recommendations. Howard J. Crim. Just. 47:343–70 [Google Scholar]
  6. Bird SM, Fairweather CB. 2009. IEDs and military fatalities in Iraq and Afghanistan. J. R. United Serv. Inst. 154:30–38 [Google Scholar]
  7. Bird SM, Hutchinson SJ. 2003. Male drugs-related deaths in the fortnight after release from prison: Scotland, 1996–1999. Addiction 98:185–90 [Google Scholar]
  8. Bird SM, Leigh Brown AL. 2001. Criminalisation of HIV transmission: implications for public health in Scotland. BMJ 323:1174–77 [Google Scholar]
  9. Bird SM, McAuley A, Munro A, Hutchinson SJ, Taylor A. 2017. Prison-based prescriptions aid Scotland's National Naloxone Programme. Lancet 389:1005–6 [Google Scholar]
  10. Borchers DL, Distiller G, Foster R, Harmsen B, Milazzo L. 2014. Continuous-time spatially explicit capture-recapture models, with an application to a jaguar camera-trap survey. Methods Ecol. Evol. 5:656–65 [Google Scholar]
  11. Borchers DL, Efford MG. 2008. Spatially explicit maximum likelihood methods for capture-recapture studies. Biometrics 64:377–85 [Google Scholar]
  12. Borchers DL, Fewster R. 2016. Spatial capture-recapture models. Stat. Sci. 31:219–32 [Google Scholar]
  13. Brooks SP, King R, Morgan BJT. 2004. A Bayesian approach to combining animal abundance and demographic data. Animal Biodivers. Conserv. 27:515–29 [Google Scholar]
  14. Chapman DG. 1951. Some Properties of the Hypergeometric Distribution with Applications to Zoological Sample Censuses Berkeley: Univ. Calif. Press
  15. Cormack RM. 1964. Estimates of survival from the sighting of marked animals. Biometrika 51:429–38 [Google Scholar]
  16. Coull B, Agresti A. 1999. The use of mixed logit models to reflect heterogeneity in capture-recapture studies. Biometrics 55:294–301 [Google Scholar]
  17. Darroch JN. 1958. The multiple recapture census. I. Estimation of a closed population. Biometrika 45:343–59 [Google Scholar]
  18. Durban JW, Elston DA. 2005. Mark: recapture with occasion and individual effects: abundance estimation through Bayesian model selection in a fixed dimensional parameter space. J. Agric. Biol. Environ. Stat. 10:291–305 [Google Scholar]
  19. Efford MG. 2004. Density estimation in live-trapping studies. Oikos 106:598–610 [Google Scholar]
  20. Fienberg SE. 1972. The multiple recapture census for closed populations and incomplete 2k contingency tables. Biometrika 59:591–603Provides the foundation of log-linear models applied to contingency table data. [Google Scholar]
  21. Fienberg S, Johnson M, Junker B. 1999. Classical multilevel and Bayesian approaches to population size estimation using multiple lists. J. R. Stat. Soc. A 163:383–405 [Google Scholar]
  22. Fisher N, Turner SW, Pugh R, Taylor C. 1994. Estimated numbers of homeless and homeless mentally ill people in north east Westminster by using capture-recapture analysis. BMJ 308:27–30Uses multiple systems estimation for additional hidden population (the homeless). [Google Scholar]
  23. Forster JJ, Gill RC, Overstall AM. 2012. Reversible jump methods for generalised linear models and generalised linear mixed models. Stat. Comput. 22:107–20 [Google Scholar]
  24. Gao L, Dimitropoulou P, Robertson JR, McTaggart S, Bennie M, Bird SM. 2016. Risk-factors for methadone-specific deaths in Scotland's methadone-prescription clients between 2009 and 2013. Drug Alcohol. Depend. 167:214–23 [Google Scholar]
  25. Gimenez O, Choquet R. 2010. Incorporating individual heterogeneity in studies on marked animals using numerical integration: capture-recapture mixed models. Ecology 91:951–57 [Google Scholar]
  26. Goodman LA. 1974. Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika 61:215–31 [Google Scholar]
  27. Gore SM, Bird AG, Burns SM, Goldberg DJ, Ross AJ, Macgregor J. 1995. Drug injection and HIV prevalence in inmates of Glenochil prison. BMJ 310:293–96 [Google Scholar]
  28. Goudie IBJ, Goudie M. 2007. Who captures the marks for the Petersen estimator?. J. R. Stat. Soc. A 170:825–39 [Google Scholar]
  29. Grigg DB. 1980. Population Growth and Agrarian Change: An Historical Perspective Cambridge, UK: Cambridge Univ. Press
  30. Hald A. 1990. A History of Probability and Statistics and Their Applications Before 1750 New York: Wiley
  31. Harron K, Goldstein H, Dibben C. 2016. Methodological Developments in Data Linkage Chichester, UK: Wiley
  32. Hay G, Gannon M, Casey J, McKeganey N. 2009. Estimating the national and local prevalence of problem drug misuse in Scotland Executive Rep., Univ. Glasgow. http://www.scotpho.org.uk/downloads/drugs/Prevalence_Report_%202006.pdf
  33. Health Protection Scotland. 2017. The Needle Exchange Surveillance Initiative: Prevalence of blood-borne viruses and injecting risk behaviours among people who inject drugs attending injecting equipment provision services in Scotland, 2008–09 to 2015–16 Rep., Health Protection Scotland, Glasgow, Scotl.
  34. Hutchinson SJ. 2004. Modelling the hepatitis C virus disease burden among injecting drug users in Scotland PhD Thesis, Univ Glasgow:
  35. Hutchinson SJ, Bird SM, Goldberg DJ. 2005. Modeling the current and future disease burden of hepatitis C among injecting drug users in Scotland. Hepatology 42:711–23 [Google Scholar]
  36. Hutchinson SJ, Goldberg DJ, Gore SM, Cameron S, McGregor J. et al. 1998. Hepatitis B outbreak at Glenochil Prison during January to June 1993. Epidemiol. Infect. 121:185–91 [Google Scholar]
  37. ISD Scotl. (Inf. Serv. Div. Scotl.). 2016. Estimating the national and local prevalence of problem drug use in Scotland 2012/13 Publ. Rep., ISD Scotl. https://isdscotland.scot.nhs.uk/Health-Topics/Drugs-and-Alcohol-Misuse/Publications/2014-10-28/2014-10-28-Drug-Prevalence-Report.pdf?33819216490
  38. Jolly GM. 1965. Explicit estimates from capture-recapture data with both death and immigration-stochastic model. Biometrika 52:225–47 [Google Scholar]
  39. Jones HE, Hickman M, Welton NJ, De Angelis D, Harris RJ, Ades AE. 2014. Recapture or precapture? Fallibility of standard capture-recapture methods in the presence of referrals between sources. Am. J. Epidemiol. 179:1383–93Identification and impact of referrals within multiple systems estimation. [Google Scholar]
  40. King R. 2014. Statistical ecology. Annu. Rev. Stat. Appl. 1:401–26 [Google Scholar]
  41. King R, Bird SM, Brooks SP, Hutchinson SJ, Hay G. 2005. Prior information in behavioral capture-recapture methods: demographic influences on drug injectors' propensity to be listed in data sources and their drug-related mortality. Am. J. Epidemiol. 162:694–703 [Google Scholar]
  42. King R, Bird SM, Hay G, Hutchinson SJ. 2009.a Estimating current injectors in Scotland and their drug-related death rate by sex, region and age-group via Bayesian capture-recapture methods. Stat. Methods Med. Res. 18:341–59 [Google Scholar]
  43. King R, Bird SM, Overstall A, Hay G, Hutchinson SJ. 2013. Injecting drug users in Scotland, 2006: listing, number, demography, and opiate-related death-rates. Addict. Res. Theory 21:235–46 [Google Scholar]
  44. King R, Bird SM, Overstall A, Hay G, Hutchinson SJ. 2014. Estimating prevalence of injecting drug users and associated heroin-related death-rates in England by using regional data and incorporating prior information. J. R. Stat. Soc. A 177:209–36Validation of gender and age-group interaction for people who inject drugs. [Google Scholar]
  45. King R, Brooks SP. 2001.a On the Bayesian analysis of population size. Biometrika 88:317–36Describes a Bayesian table analysis model-averaging approach for hierarchical log-linear models. [Google Scholar]
  46. King R, Brooks SP. 2001.b Prior induction in log-linear models for general contingency. Ann. Stats. 29:715–47 [Google Scholar]
  47. King R, Brooks SP. 2008. On the Bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty. Biometrics 64:816–24 [Google Scholar]
  48. King R, McClintock B, Kidney D, Borchers DL. 2016. Capture-recapture abundance estimation using a semi-complete data likelihood approach. Ann. Appl. Stat. 10:264–85 [Google Scholar]
  49. King R, Morgan BJT, Gimenez O, Brooks SP. 2009.b Bayesian Analysis for Population Ecology Boca Raton, FL: CRC Press
  50. Knuiman MW, Speed TP. 1988. Incorporating prior information into the analysis of contingency tables. Biometrics 44:1061–71 [Google Scholar]
  51. Lader D. 2016. Drug misuse: findings from the 2015 to 2016 CSEW Stat. Bull. 07/16, Home Off U.K:. , 2nd ed..
  52. Laska EM, Meisner M. 1993. A plant-capture method for estimating the size of a population from a single sample. Biometrics 49:209–20 [Google Scholar]
  53. Lee A. 2002. Effect of list errors on the estimation of population size. Biometrics 58:185–91 [Google Scholar]
  54. Lincoln FC. 1930. Calculating waterfowl abundance on the basis of banding returns Circ. No. 118, USDA Washington, DC:
  55. Madigan D, York JC. 1997. Bayesian methods for estimation of the size of a closed population. Biometrika 84:19–31 [Google Scholar]
  56. Manly BFJ, McDonald TL, Amstrup SC. 2005. Introduction to the Handbook. Handbook of Capture-Recapture Analysis SC Amstrup, TL McDonald, BFJ Manly 1–21 New Jersey: Princeton Univ. Press [Google Scholar]
  57. McCrea R, Morgan B. 2014. Analysis of Capture-Recapture Data Boca Raton, FL: Chapman and Hall/CRC
  58. Merrall ELC, Bird SM, Hutchinson SJ. 2012. Mortality of those who attended drug services in Scotland 1996–2006: record linkage study. Int. J. Drug Policy 23:24–32 [Google Scholar]
  59. Merrall ELC, Kariminia A, Binswanger IA, Hobbs M, Farrell M. et al. 2010. Meta-analysis of drug-related deaths soon after release from prison. Addiction 105:1545–54 [Google Scholar]
  60. Millar T, McAuley A. 2017. EMCDDA assessment of drug-induced death data and contextual information in selected countries Tech. Rep., EMCDDA Lisbon:
  61. Natl. Rec. Scotl. 2016. Drug-related deaths in Scotland in 2015 https://www.nrscotland.gov.uk/files//statistics/drug-related-deaths/15/drugs-related-deaths-2015.pdf
  62. Otis DL, Burnham KP, White GC, Anderson DR. 1978. Statistical inference from capture data on closed animal populations. Wildl. Monogr. 62:3–135 [Google Scholar]
  63. Overstall AM, King R. 2014.a A default prior distribution for contingency tables with dependent factor levels. Stat. Methodol. 16:90–99 [Google Scholar]
  64. Overstall AM, King R. 2014.b conting: an R package for Bayesian analysis of complete and incomplete contingency tables. J. Stat. Softw. 58:1–27Provides an R package for conducting Bayesian analysis of hierarchical log-linear models in the presence of model uncertainty. [Google Scholar]
  65. Overstall A, King R, Bird SM, Hay G, Hutchinson SJ. 2014. Incomplete contingency tables with censored cells with application to estimating the number of people who inject drugs in Scotland. Stat. Med. 33:1564–79 [Google Scholar]
  66. Petersen CGJ. 1896. The yearly immigration of young plaice into the Limfjord from the German Sea. Rep. Danish Biol. Stat. (1895) 6:5–84Lays the formal foundation of multiple systems estimation. [Google Scholar]
  67. Pierce M, Bird SM, Hickman M, Marsden J, Dunn G. et al. 2016. Impact of treatment for opioid dependence on fatal drug-related poisoning: a national cohort study in England. Addiction 111:298–308 [Google Scholar]
  68. Pierce M, Bird SM, Hickman M, Millar T. 2015. National record-linkage study of mortality for a large cohort of opioid users ascertained by drug treatment or criminal justice sources in England, 2005–2009. Drug Alcohol Depend 146:17–23 [Google Scholar]
  69. Pierce M, Millar T, Robertson JR, Bird SM. 2017. Ageing opioid users' increased risk of methadone-specific death in the UK: irrespective of gender Tech. Rep., MRC Biostat. Unit. https://www.mrc-bsu.cam.ac.uk/wp-content/uploads/2014/02/SMB2017_1.pdf
  70. Pledger S. 2000. Unified maximum likelihood estimates for closed capture-recapture models using mixtures. Biometrics 56:434–42 [Google Scholar]
  71. Prevost TC, Presanis AM, Taylor A, Goldberg DJ, Hutchinson SJ, de Angelis D. 2015. Estimating the number of people with hepatitis C virus who have ever injected drugs and have yet to be diagnosed: an evidence synthesis approach for Scotland. Addiction 110:1287–300 [Google Scholar]
  72. Reynolds TJ, King R, Harwood J, Frederikesen M, Harris MP, Wanless S. 2009. Integrated data analysis in the presence of emigration and mark loss. J. Agric. Biol. Environ. Stat. 14:411–31 [Google Scholar]
  73. Royle JA, Chandler RB, Sollmann R, Gardner B. 2014. Spatial Capture-Recapture New York: Academic
  74. Sandland RL, Cormack RM. 1984. Statistical inference for Poisson and multinomial models for capture-recapture experiments. Biometrika 71:27–33 [Google Scholar]
  75. Schnabel ZE. 1938. The estimation of total fish populations of a lake. Am. Math. Mon. 45:348–52 [Google Scholar]
  76. Seaman SR, Brettle RP, Gore SM. 1998. Mortality from overdose among injecting drug users recently released from prison: database linkage study. BMJ 316:426–28 [Google Scholar]
  77. Seber GAF. 1965. A note on the multiple-recapture census. Biometrika 52:249–59 [Google Scholar]
  78. Seybolt TB, Aronson JD, Fischhoff B. 2003. Counting Civilian Casualties: An Introduction to Recording and Estimating Non-Military Deaths in Conflict Oxford, UK: Oxford Univ. PressProvides guidance for multiple systems estimation and machine learning for rigorous reproducible matching.
  79. Silverman B. 2014. Modern slavery: an application of multiple systems estimation Rep., Home Off London: https://www.gov.uk/government/publications/modern-slavery-an-application-of-multiple-systems-estimation Governmental report using multiple systems estimation for modern hidden populations (modern-day slavery).
  80. Spiegel PB, Salama P. 2000. War and mortality in Kosovo, 1998–99: an epidemiological testimony. Lancet 355:2204–9Application of multiple systems estimation used by war crimes tribunal to corroborate evidence. [Google Scholar]
  81. Strang J, Hall W, Hickman M, Bird SM. 2010. Impact of supervision of methadone consumption on deaths related to methadone overdose (1993-2008): analyses using OD4 index in England and Scotland. BMJ 341:c4851 [Google Scholar]
  82. Sutherland J, Schwarz CJ. 2005. Multi-list methods using incomplete lists in closed populations. Biometrics 61:134–40 [Google Scholar]
  83. Sutherland J, Schwarz CJ, Rivest LP. 2007. Multilist population estimation with incomplete and partial stratification. Biometrics 63:910–16 [Google Scholar]
  84. Taylor A, Goldberg D, Emslie J, Wrench J, Gruer L. et al. 1995. Outbreak of HIV infection in a Scottish prison. BMJ 310:289–92 [Google Scholar]
  85. Tilling K, Sterne JA. 1999. Capture-recapture models including covariate effects. Am. J. Epidemiol. 149:392–400 [Google Scholar]
  86. White SR, Bird SM, Grieve R. 2014. Review of methodological issues in cost-effectiveness analyses relating to injecting drug users, and case-study illustrations. J. R. Stat. Soc. A 177:625–42 [Google Scholar]
  87. White SR, Bird SM, Merrall ELC, Hutchinson SJ. 2015. Drugs-related death soon after hospital-discharge among drug treatment clients in Scotland: record linkage, validation and investigation of risk-factors. PLOS ONE 10:e0141073 [Google Scholar]
  88. White SR, Muniz-Terrera G, Matthews FE. 2017. Sample size and classification error for Bayesian change-point models with unlabelled sub-groups and incomplete follow-up. Stat. Methods Med. Res. In press. https://doi.org/10.1177/0962280216662298 [Crossref]
  89. Worthington H, McCrea RS, King R, Griffiths RA. 2017. Estimation of population size when capture probability depends on individual states. arXiv1708.00348[stat.AP]
  90. Wright JA, Barker RJ, Schofield MR, Frantz AC, Byrom AE, Gleeson DM. 2009. Incorporating genotyping uncertainty into mark-recapture-type models for estimating abundance using DNA samples. Biometrics 65:833–40 [Google Scholar]
/content/journals/10.1146/annurev-statistics-031017-100641
Loading
/content/journals/10.1146/annurev-statistics-031017-100641
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error