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.