AM  Vol.4 No.9 , September 2013
Mixture Models for Estimating the Number of Drug Users in Thailand 2005-2007
Abstract: It is difficult to measure the sizes of illegal drug user populations directly by using the survey method because of many “hidden drug addicts” and the difficulty of receiving a true response. Systematic and routine information on treatment episodes of drug users is adopted to estimate the population size in this study. Mixture models of zero-truncated Poisson distributions using the nonparametric maximum likelihood estimators (NPMLE) by means of capture-recapture repeated count data were used to project the number of drug users. The method was applied to surveillance data of drug users identified by treatment episodes in over 1140 health treatment centers in Thailand from the Bureau of Health Service System Development, Ministry of Public Health. We presented how this mixture model could be utilized to construct the unobserved frequency of drug users with no treatment episode and further estimated the total population size of drug users in the country from 2005 to 2007. The result of simulation was confirmed that mixture model is suitable when population is large. By means of mixture models, the estimations for the number of drug users were fitted with excellent goodness-of-fit values and we were also compared to the conventional Chao estimates. The NPMLE for the total number of drug users in Thailand 2005, 2006, and 2007 were 184,045 (95% CI: 181,297-86,793), 230,665 (95% CI: 226,611-234,719), 299,670 (95% CI: 294,217-305,123), respectively, also 125,265 (95% CI: 123,092-127,142), 166,287 (95% CI: 163,222-169,352), 228,898 (95% CI: 224,766 - 233,030) for the number of methamphetamine (Yaba) users, and 11,559 (95% CI: 10,234-12,884), 11,333 (95% CI: 9276-13,390), 8953 (95% CI: 7878-10,028) for the number of heroin users, respectively. The numbers of marijuana, kratom-plant, opium, and inhalant users were underestimated because their symptoms were mild and not severe enough to remedy in health treatment centers which led to the smaller size of the total number of drug users. The well-estimated sizes of heroin and methamphetamine addicts are high reliable because they are based on clearly evident count with a severe addiction problem to health treatment centers. The estimation by means of mixture models can be recommended to monitor drug demand trend and drug health service routinely; it is easy to calculate via the available programs MIXTP based on request.
Cite this paper: C. Viwatwongkasem, P. Satitvipawee, S. Jareinpituk and P. Soontornpipit, "Mixture Models for Estimating the Number of Drug Users in Thailand 2005-2007," Applied Mathematics, Vol. 4 No. 9, 2013, pp. 1242-1250. doi: 10.4236/am.2013.49168.

[1]   E. B. Hook and R. R. Regal, “Capture-Recapture Methods in Epidemiology: Methods and Limitations,” Epidemiologic Reviews, Vol. 17, No. 2, 1995, pp. 243-264.

[2]   T. D. Mastro, D. Kitayaporn, B. G. Weniger, et al., “Estimating the Number of HIV-Infected Injection Drug Users in Bangkok: A Capture-Recapture Method,” American Journal of Public Health, Vol. 84, No. 7, 1994, pp. 1094-1099. doi:10.2105/AJPH.84.7.1094

[3]   B. Suppawattanabodee, “Estimating the Number of Drug Users in Bangkok: A Capture-Recapture Method,” Master of Sciences Thesis, Mahidol University, Bangkok, 2003.

[4]   D. Bohning, B. Suppawattanabodee, W. Kusolvisitkul, and C. Viwatwongkasem, “Estimating the Number of Drug Users in Bangkok 2001: A Capture-Recapture Ap proach Using Repeated Entries in One List,” European Journal of Epidemiology, Vol. 19, No. 12, 2004, pp. 1075-1083. doi:10.1007/s10654-004-3006-8

[5]   C. Viwatwongkasem, R. Kuhnert and P. Satitvipawee, “A Comparison of Population Size Estimators under the Truncated Count Model with and without Allowance for Contaminations,” Biometrical Journal, Vol. 50, No. 6, 2008, pp. 1006-1021. doi:10.1002/bimj.200810484

[6]   D. Bohning, “Computer-Assisted Analysis of Mixtures and Applications. Meta-Analysis, Disease Mapping and Others,” Chapman & Hall/CRC, Boca Raton, 2000.

[7]   B. G. Lindsay, “The Geometry of Mixture Likelihoods Part I: A General Theory,” Annals of statistics, Vol. 11, No. 3, 1983, pp. 783-792. doi:10.1214/aos/1176346245

[8]   G. McLachlan and D. Peel, “Finite Mixture Models,” Wiley, New York, 2000. doi:10.1002/0471721182

[9]   D. Bohning and D. Schon, “Nonparametric Maximum Likelihood Estimation of Population Size Based on the Counting Distribution,” Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 54, No. 4, 2005, pp. 721-737. doi:10.1111/j.1467-9876.2005.05324.x

[10]   D. Bohning and R. Kuhnert, “Equivalence of Truncated Count Mixture Distributions and Mixture of Truncated Count Distributions,” Biometrics, Vol. 62, No. 4, 2006, pp. 1207-1215. doi:10.1111/j.1541-0420.2006.00565.x

[11]   N. Punyacharoensin and C. Viwatwongkasem, “Trends in Three Decades of HIV/AIDS Epidemic in Thailand by Nonparametric Backcalculation Method,” AIDS, Vol. 23, No. 9, 2009, pp. 1143-1152. doi:10.1097/QAD.0b013e32832baa1c

[12]   N. M. Laird, “Nonparametric Maximum Likelihood Estimation of a Mixing Distribution,” Journal of the Ame rican Statistical Association, Vol. 73, No. 364, 1978, pp. 805-811. doi:10.1080/01621459.1978

[13]   A. Chao, “Estimating the Population Size for Capture Recapture Data with Unequal Catchability,” Biometrics, Vol. 43, No. 4, 1987, pp. 783-791. doi:10.2307/2531532

[14]   Office of the Narcotics Control Board (ONCB), “Thailand Narcotics Annual Report,” Aroon Printing Co., Ltd., Bangkok, 2006.

[15]   Office of the Narcotics Control Board (ONCB), Academic Network Organization Board on Substance Abuse, “Estimation of the Number of Drug Addicts in Thailand 2007,” Union Ultra Violet Co., Ltd., Bangkok, 2007.

[16]   R. Kuhnert, V. J. Del Rio Vilas, J. Gallagher and D. Bohning, “A Bagging-Based Correction for the Mixture Model Estimator of Population Size,” Biometrical Journal, Vol. 50, No. 6, 2008, pp. 993-1005. doi:10.1002/bimj.200810485

[17]   N. Wannasirikul, “A Comparison of Truncated Poisson Estimators of Population Size under Model Contamina tions,” Master of Sciences Thesis, Mahidol University, Bangkok, 2005.

[18]   D. Zelterman, “Robust Estimation in Truncated Discrete Distributions with Application to Capture-Recapture Ex periments,” Journal of Statistical Planning and Inference, Vol. 18, No. 2, 1988, pp. 225-237. doi:10.1016/0378-3758(88)90007-9

[19]   A. Chao, “Estimating Population Size for Sparse Data in Capture-Recapture Experiments,” Biometrics, Vol. 45, No. 2, 1989, pp. 427-438. doi:10.2307/2531487

[20]   R. M. Cormack, “Interval Estimation for Mark-Recapture Studies of Closed Populations,” Biometrics, Vol. 48, No. 2, 1992, pp. 567-576. doi:10.2307/2532310