Parameterization of Continuous Covariates in the Poisson Capture-Recapture Log Linear Model for Closed Populations
Keywords:Capture-recapture, Closed population, Continuous covariates, Poisson log-linear model, Multinomial conditional logit model
The capture-recapture method is widely used by epidemiologists to estimate the size of hidden populations using incomplete and overlapping lists of subjects. Closed populations, heterogeneity of inclusion probabilities and dependence between lists are taken into consideration in this work. The main objective is to propose a new parameterization for the Poisson log linear odel (LLM) to treat continuous covariates in their original measurement scale. The analytic estimate of the confidence bounds of the hidden population is also provided. Proposed model was applied to simulated and real capture-recapture data and compared with the multinomial conditional logit model (MCLM). The proposed model is very similar to the MCLM in dealing with continuous covariates and the analytic confidence interval performs better than the bootstrap estimate in case of small sample size.
D. ABENI, G. BRANCATO, C. PERUCCI (1994). Capture-recapture to estimate the size of the population with human immunodeficiency virus type 1 infection. Epidemiology, 5, pp. 410–414.
J. ALHO (2000). Unified maximum likelihood estimates for closed capture-recapture models using mixtures. Biometrics, 56, pp. 443–450.
S. BAKER (1994). The multinomial-Poisson transformation. The Statistician, 43, no. 4, 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.
M. BRUGAL, A. DOMINGO-SALVANY, A. MAGUIRE, J. CAYLA, R. H. J.R. VILLALBI (1999). A small area analysis estimating the prevalence of addiction to opioids in Barcelona 1993. Journal of Epidemiology and Community Health 1999, 53, pp. 488–494.
M. BRUGAL, A. DOMINGO-SALVANY, E. D. D. QUIJANO, L. TORRALBA (2004). Prevalence of problematic cocaine consumption in a city of Southern Europe, using capture-recapture with a single list. Journal of Urban Health, 81, pp. 416–427.
M. BUSTER, G. V. BRUSSEL, W. V. D. 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, no. 2, pp. 158–175.
Z. CHEN, K. LYNN (2001). A note on the estimation of the multinomial logit model with random effects. The American Statistician, 55, no. 2, pp. 89–95.
C. COMISKEY, J. BARRY (2001). A capture-recapture study of the prevalence and implications of opiate use in Dublin. European Journal of Public Health, 11, pp. 198–200.
R. CORMACK (1989). Log-linear models for capture-recapture. Biometrics, 45, no. 2, pp. 395–413.
S. FIENBERG (2002). The multiple recapture census for closed populations and incomplete 2k contingency tables. Journal of Applied Statistics, 29, pp. 85–102.
M. FRISCHER, M. HICKMANN, L. KRAUS, F. MARIANI, L.WIESSING (2001). A comparison of different methods for estimating the prevalence of problematic drug measure in Great Britain. Addiction, 96, pp. 1465–1476.
I. GEMMELL, T. MILLAR, G. HAY (2004). Capture-recapture estimates of problematic drug use and the use of simulation based confidence intervals in a stratified analysis. Journal of Epidemiology and Community Health, 58, pp. 758–765.
J. HARDIN, J. HILBE (2001). Generalized Linear Models and Extensions. Stata Press, Texas, USA.
G. HAY (2000). Capture-recapture estimates of drug measure in urban and non-urban settings in the north east of Scotland. Addiction, 95, pp. 1795–1803.
M.HICKMANN, V.HIGGINS, V.HOPE, K. T. M. BELLIS, A.WALKER (2004). Injecting drug use in Brighton, Liverpool, and London: best estimates of prevalence and coverage of public health indicators. Journal of Epidemiology and Community Health, 58, pp. 766–771.
V. HOPE, M. HICKMANN, 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. HUGGINS (1989). On the statistical analysis of capture experiments. Biometrika, 76, pp. 133–140.
W. HWANG, R. 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). Capture-recapture and multiple-record estimation I: History and theoretical development. American Journal of Epidemiology, 142, no. 10, pp. 1047–1058.
INTERNATIONAL WORKING GROUP FOR DISEASE MONITORING AND FORECASTING (1995b). Capture-recapture and multiple-record estimation II: Applications in human diseases. American Journal of Epidemiology, 142, no. 10, pp. 1059–1068.
J. LANGE, R. L. PORTE, E. TALBOTT, Y. CHANG (2003). Capture-recapture method: the gold standard for incidence and prevalence. Journal of the New Zealand Medical Association, 20, p. 116.
J. NORRIS, K. POLLOCK (1996). Including model uncertainty in estimating variances in multiple capture studies. Environmental and Ecological Statistics, 3, pp. 235–244.
L. PLATT, M. HICKMANN, 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.
K. POLLOCK (2002). The use of auxiliary variables in capture-recapture modelling: An overview. Journal of Applied Statistics, 29, pp. 85–102.
K. POLLOCK, J. HINES, J. NICHOLS (1984). The use of auxiliary variables in capturerecapture andremoval experiments. Biometrics, 40, pp. 329–340.
J. RAZZAK, 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.
J. ROBERTS, 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, no. 4, pp. 182–204.
G. ROSSI, P. PEPE, O. CURZIO, M. MARCHI (2010). Generalized linear models and capture-recapture method in a closed population: Strengths and weaknesses. Statistica, 70, no. 3, pp. 371–390.
C. SCHWARZ, G. SEBER (1999). A review of estimating animal abundance III. Statistical Science, 14, pp. 427–456.
C. SEKAR, W. DEMING (1949). On a method of estimating birth and death rates and the extent of registration. Journal of the American Statistical Association, 44, pp. 101–115.
K. TILLING, J. STERNE (1999). Capture-recapture models including covariate effects. American Journal of Epidemiology, 149, no. 4, pp. 392–400.
K. TILLING, J. STERNE, C.WOLFE (2001). Estimation of the incidence of stroke using a capture-recapture model including covariates. International Journal of Epidemiology,
, no. 6, pp. 1351–1359.
E. ZWANE, P. V. D. HEIJDEN (2005). Population estimation using the multiple system estimator in the presence of continuous covariates. Statistical Modeling, 5, no. 1, pp.39–52.