| Objective:Drug is a serious social problem in the world today. China has gone through a period of no drug abuse from the 1950 s to the 1970 s. Since the reform and opening up in 1979, the illegal drug trade in China emerged again. As the world’s most populous country, China has witnessed the rapid growth of drug addicts in the past three decades. By the end of 2011, the data of the Ministry of Public Security shows the number of drug addicts officially registered in the country has reached 1.794 million, and the number of heroin addicts has reached 1.156 million(accounting for 64.5%). The Chinese government is increasing the crackdowns on drug crime, but affected by various factors, it did not reduce drug use and drug-related crimes, and the species of drug abuse become diverse, especially in small cities and rural areas. Meanwhile,it is estimated that every registered drug user imply 2-4 drug addicts, so we can assume that if including the unregistered drug users, the number of drug users will be more.Drug users have become high-risk behavior groups infected and spread by a variety of infectious diseases including AIDS, hepatitis, tuberculosis, sexually transmitted diseases. Therefore, mastering the base of IDUs helps control the number of HIV-infected persons, providing a scientific basis for the development and implementation of AIDS control strategies.At present, the estimation methods of AIDS cardinality in domestic and foreign high-risk groups are mainly two types of direct and indirect methods. The direct methods, such as screening method, enumeration method, population survey method, the indirect methods, such as the nomination method, multiplier method, network size superposition method, CMR method(Capture-Mark-Recapture Method), divisor method and Delphi method. Most methods of them can not do statistical inference or are not suitable for investigating sensitive issues. Because of that the log-linear model pf CMR method can be based on existing overlapping incomplete database, allowing correlation between the sample, improving sampling representativeness, and doing statistical inference, we use it to estimate the population size of drug users.This article describes two sources and three sources CMR methods under simple random sampling and their statistical formulas. For the first time,we use CMR method of three sources being related to each other under simple random sampling to investigate and estimate the cardinal number of DUs in the city of Xichang in 2014, providing the basic data for the control of sexually transmitted diseases and the prevalence of AIDS in Xichang. This article completed the investigation and estimation of the cardinal number of DUs in Xichang in the study of the National Natural Science Foundation(ID: 81273188) carried out by our team for health administrative departments to provide a scientific basis for developing AIDS prevention,controlling strategies and measures. In addition, we use SAS programming to evaluate the reliability and validity of three sources CMR method and its formulas under simple random sampling by Monte Carlo simulation, to provide an effective and reliable statistical method for survey and estimation of population at high risk of AIDS.Methods:According to mathematical statistical theories and methods, namely, the classical sampling theory, the nature of the variance, maximum likelihood estimation, the log-linear model, Bartlett criterion, orthogonal projection, interval estimation, on the basis of previous studies, this paper respectively describes the calculated formulas of the estimation of the overall cardinality and its variance in two sources and three sources CMR method under random sampling. In April to July 2014, three sources CMR method and its formulas under simple random sampling of this study were adopted in investigating and estimating the cardinal number of DUs in Xichang for instance(recycled 1007 questionnaires). In addition, regarding the calculation of the actual survey results of DUs in Xichang in 2014 as whole parameters to establish simulated population, for three relevant sources CMR method under simple random sample between the period of six months, we respectively used SAS programming to simulate and investigate 100 samples(sample size for each sample is close to 1007 cases), then we calculated the corresponding statistics according to the formulas of three relevant sources CMR method in the first part of this paper under simple random sampling. As a result, we respectively obtained the estimations and 95% confidence intervals of 100 overall cardinal number. Finally, according to the basic concepts of reliability and validity, we evaluated the reliability and validity of the survey methodology and its statistical formulas studied in this paper.Results:1. In April to July 2014,we use three relevant sources CMR method under simple random sampling to investigate DUs in Xichang whether they were active in drug rehabilitation centers, communities, methadone clinics in Xichang, whether received AIDS preventive intervention services, whether used drugs over the past six months and so on. We gave out a total of 1007 questionnaires, all of them were returned and qualified. The cardinal number of DUs in the city of Xichang is estimated to reach 5264 between the period of six months, the asymptotic standard deviation is 157 persons, and 95% confidence interval of the overall base is from 4956 to 5572 persons.2. Among 1007 drug users in the survey, in the past six months, only 242 cases(24.03%) had received preventive intervention services of free condoms; 835 cases(82.92%) had received education and behavioral intervention about AIDS; 537 cases(53.33%) had received HIV antibody testing.3. For three relevant sources CMR method under simple random sampling applied in DUs in Xichang between a period of six months, we simulate results of investigation and analysis of 100 samples by Monte Carlo simulation: among 100 95% confidence intervals of simulated overall base, there are 96 including the simulated overall base.Conclusions:1. Three sources CMR survey method and statistical formulas under simple random sampling of this study practically applied in estimation of massing radix of DUs in Xichang achieved good results, providing a new scientific theory and method for mastering the basic data for the preventions and controls of AIDS in the city of Xichang, and for carrying out the study about estimating the cardinal number of population at high risk of HIV in the rest areas of our country.2. The cardinal number of DUs in Xichang investigated and estimated in this article is 5264, and the 95% confidence interval of the whole base is from 4956 to 5572, pointing out a lot of drug addicts. The ratio of receiving free condoms among DUs in Xichang is low(24.03%). The scale of receiving education and behavioral intervention about AIDS is 82.92%, and it should be further improved in the future. The proportion of having received HIV antibody testing is low(53.33%). The proportion of needle exchange behavior is low(6.76%). These data suggest that the relevant health departments should strengthen the monitoring and intervention of DUs in Xichang.3. 100 95% confidence intervals of simulated massing radices of 100 samples investigated and estimated by Monte Carlo simulation about DUs in Xichang were almost(96%) including simulated massing radix, illustrating that survey method and its statistical formulas of this paper has good reliability(100 sample radices are close to the same number——simulated massing radix) and good validity(100 sample radices are close to the simulated overall true value——simulated massing radix). Therefore, the survey methodology and its statistical formulas of three sources CMR method under simple random sampling in this study are proved to be scientific, effective, reliable, and have broad prospects of application and significance of promotion. |
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