Generalized linear models and Capture-Recapture Method in a closed population: strengths and weaknesses

Authors

  • Giuseppe Rossi CNR, Consiglio Nazionale delle Ricerche - Pisa
  • Pasquale Pepe CNR, Consiglio Nazionale delle Ricerche - Pisa
  • Olivia Curzio CNR, Consiglio Nazionale delle Ricerche - Pisa
  • Marco Marchi Università degli Studi di Firenze

DOI:

https://doi.org/10.6092/issn.1973-2201/3593

Abstract

Capture-recapture methods are used by epidemiologists in order to estimate the size of hidden populations using incomplete and overlapping lists of cases. These models can be both continuous and discrete time and the particular population we want to obtain a quantitative evaluation can be assumed to be closed or open. Here we specifically consider discrete-time models for closed population. The problem was treated using Generalized Linear Models as they allow to treat simultaneously both forms of dependence between sources than observed heterogeneity due to covariates effects. Specifically, we analyzed the strengths and weaknesses of Multinomial Conditional Logistic Model and presented a comparison with a correspondent Bayesian approach. The estimates obtained on simulated and real data appear to be enough reliable.

References

D.D. ABENI, G. BRANCATO, C.A. PERUCCI (1994), Capture-recapture to estimate the size of the population with human immunodeficiency virus type 1 infection, “Epidemiology”, 5, pp. 410-414.

J.M. ALHO (1990), Logistic regression in capture-recapture models, “Biometrics”, 46, pp. 623-635.

G. BAKER STUART (1994), The multinomial-Poisson transformation, “The Statistician”, 43, pp. 495-504.

F. BARTOLUCCI, A. FORCINA (2006). A class of latent marginal models for capture-recapture data with continuous covariates, “Journal of the American Statistical Association”, 101, pp. 786-794.

D. BOHNING, B. SUPPAWATTANABODEE, W. KUSOLVISITKUL, C..VIWATWONGKASEM (2004), Estimating the number of drug users in Bangkok 2001: A Capture-Recapture Approach Using Repeated Entries in one list, “European Journal of Epidemiology”, 19, pp. 1075-1083.

M.T. BRUGAL, A. DOMINGO-SALVANY, A. MAGUIRE, J.A. CAYLA, J.R. VILLALBI, R. HARTNOLL (1999), A small area analysis estimating the prevalence of addiction to opioids in Barcelona, “Journal of Epidemiology & Community Health”, 53, 488-494.

K. P. BURNHAM, D. R. ANDERSON (2004), Multimodel Inference. Understanding AIC e BIC in Model Selection, “Sociological Methods and Research”, 33, pp. 261-304.

M.C. BUSTER, G.H. VAN BRUSSEL, W. VAN DEN BRINK (2001), Estimating the number of opiate users in Amsterdam by capture-recapture: the importance of case definition, “European Journal of Epidemiology”, 17, pp. 935-942.

A. CHAO (2001), An overview of closed Capture-Recapture Models, “Journal of Agricultural, Biological, and Environmental Statistics”, 6, pp. 158-175.

Z. CHEN, L. KUO (2001), A note on the estimation of the multinomial Logit Model with Random effects, “The American Statistician”, 55, pp. 89-95.

R.M. CORMACK (1989), Log-linear Models for Capture-Recapture, “Biometrics”, 45, pp. 395-413.

A. DAVIES, R. CORMACK, AND A. RICHARDSON (1999). Estimation of injecting drug users in the City of Edinburgh, Scotland, and the number infected with human immunodeficiency virus, “International Journal of Epidemiology”, 28, pp. 117-121.

S. FIENBERG (1972), The multiple recapture census for closed populations and incomplete 2k contingency tables, “Biometrika”, 59, pp. 591-603.

M. FRISCHER, M. BLOOR, A. FINLAY, D. GOLDBERG, S. GREEN, S. HAW, N. MCKEGANEY, S. PLATT (1991), A new method of estimating prevalence of injecting drug use in an urban population: results from a Scottish city, “International Journal of Epidemiology”, 20, pp. 997-1000.

M. FRISCHER, M. HICKMAN, L. KRAUS, F. MARIANI, L. WIESSING (2001), A comparison of different meth ods for estimating the prevalence of problematic drug misure in Great Britain, “Addiction”, 96, pp. 1465-1476.

A. E. GELFAND AND S. K. GHOSH (1998), Model choice: A minimum posterior predictive loss approach, “Biometrika”, 85, pp. 1-11.

I. GEMMELL, T. MILLAR, G. HAY (2004), Capture-recapture estimates of problem drug use and the use of simulation based confidence intervals in a stratified analysis, “Journal of Epidemiology & Community Health”, 58, pp. 758-765.

S.K. GHOSH, J.L. NORRIS (2004), Bayesian Capture-Recapture Analysis and Model Selection Allowing for Heterogeneity and Behavioral Effects, NCSU Institute of Statistics, Mimeo Series 2562, pp. 1-27.

G. HAY, N. MCKEGANEY (1996), Estimating the prevalence of drug misure in Dundee, Scotland: an application of capture-recapture methods, “Journal of Epidemiology & Community Health”, 50, pp. 469-472.

G. HAY (2000), Capture-recapture estimates of drug misure in urban and non-urban settings in the north east of Scotland, “Addiction”, 95, pp. 1795-1803.

W.D. HALL, J.E. ROSS, M.T. LYNSKEY, M.G. LAW, L.J. DEGENHARDT (2000), How many dependent heroin users are there in Australia? “The Medical Journal of Australia”, 173, pp. 528-531.

M. HICKMAN, S. COX, J HARVEY, S. HOWES, M. FARRELL, M. FRISCHER, G. STIMSON, C. TAYLOR, K. TILLING (1999), Estimating the prevalence of problem drug use in inner London: a discussion of three capture-recapture studies, “Addiction”, 94, pp. 1653-1662.

M. HICKMAN, V. HIGGINS, V. HOPE, M. BELLIS, K. TILLING, A. WALKER (2004), Injecting drug use in Brighton, Liverpool, and London: best estimates of prevalence and coverage of public health indicators, “Journal of Epidemiology & Community Health”, 58, pp. 766-771.

V.D. HOPE, M. HICKMAN, K. TILLING (2005). Capturing crack cocaine use: estimating the prevalence of crack cocaine use in London using capture-recapture with covariates. “Addiction”, 11, pp. 1701-1708.

R. M. HUGGINS (1989), On the statistical analysis of capture experiments, “Biometrika”, 76, pp. 133-140.

W. H. HWANG AND R. M. HUGGINS (2005), An examination of the effect of heterogeneity on the estimation of population size using capture-recapture data, “Biometrika”, 92, pp. 229-233.

INTERNATIONAL WORKING GROUP FOR DISEASE MONITORING AND FORECASTING (1995a), Capturerecapture and multiple record systems estimation 1: history and theoretical development. “American Journal of Epidemiology”, 142, pp. 1047-1058.

INTERNATIONAL WORKING GROUP FOR DISEASE MONITORING AND FORECASTING (1995b), Capturerecapture and multiple record systems estimation 2: applications, “American Journal of Epidemiology”, 142, pp. 1059-1068.

J. NORRIS AND K. POLLOCK (1996), Including model uncertainty in estimating variances in multiple capture studies,” Environmental and Ecological Statistics”, 3, pp. 235-244.

L. PLATT, M. HICKMAN, T. RHODES, L. MIKHAILOVA, V. KARAVASHKIN, A. VLASOV, K. TILLING, V. HOPE,

M. KHUTORKSOY, A. RENTON (2004), The prevalence of injecting drug use in a Russian city: implications for harm reduction and coverage, “Addiction”, 99, pp. 1430-1438.

S. PLEDGER (2000), Unified maximum likelihood estimates for closed capture-recapture models using mixtures, “Biometrics”, 56, 443-450.

K. H.POLLOCK, J. E. HINES,AND J. D. NICHOLS (1984), The use of auxiliary variables in capturerecapture and removal experiments, “Biometrics”, 40, pp. 329-340.

K. H. POLLOCK (2002), The use of auxiliary variables in capture-recapture modeling: an overview, “Journal of Applied Statistics”, 29, 85-102.

J. RAZZAK, AND S. LUBY (1998), Estimating deaths and injuries due to road traffic accidents in Karachi, Pakistan, through the capture-recapture method, “International Journal of Epidemiology”, 27, pp. 866-870.

M. JOHN ROBERTS JR, DEVON D. BREWER (2006), Estimating the prevalence of male clients of prostitute women in Vancouver with a simple capture-recapture method, “Journal of the Royal Statistical Society: Series A”, 169, pp. 745-756.

C. SCHWARZ, AND G. SEBER (1999), A review of estimating animal abundance III, “Statistical Science”, 14, pp. 427-456.

D. SPIEGELHALTER, A. THOMAS, N. BEST AND D. LUNN (2001), WinBUGS User Manual version 1.4, MRC Biostatistics Unit, Cambridge, UK. http://www.mrc-bsu.cam.ac.uk/bugs

K. TILLING, J. STERNE (1999), Capture-recapture models including covariate effects, “American Journal of Epidemiology”, 49, pp. 392-400.

K. TILLING, J. STERNE (2001), Estimation of the incidence of stroke using a capture-recapture model including covariates, “International Journal of Epidemiology”, 30, pp. 1351-1359.

E. ZWANE, P. VAN DER HEIJDEN (2003), Implementing the parametric bootstrap in capture-recapture models with continuous covariates, “Statistics and Probability Letters”, 65, pp. 121-125.

E. ZWANE, P. VAN DER HEIJDEN (2005), Population estimation using the multiple system estimator in the presence of continuous covariates, “Statistical Modelling”, 5, pp. 39-52.

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Published

2010-09-30

How to Cite

Rossi, G., Pepe, P., Curzio, O., & Marchi, M. (2010). Generalized linear models and Capture-Recapture Method in a closed population: strengths and weaknesses. Statistica, 70(3), 371–390. https://doi.org/10.6092/issn.1973-2201/3593

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