| Objective: With the rapid development of economy and prosperous culture, our attitude towards sex has been liberated since 21 st century. The amount of homosexual is rising, especially men who have sex with men(MSM). They are an important bridge crowd of Human Immunodeficiency Virus(HIV) transmission and infection. As a second high risk group of Acquired Immune Deficiency Syndrome(AIDS) after female sex workers, the estimated population size of MSM is an important base to comprehensively analyse and grasp their situation, which is also as a core variable to analyse and predict the epidemic trends of AIDS. The methods of cardinality estimation at home and abroad are divided into two categories: direct and indirect methods. Direct methods such as Census Method, Enumeration Methods, Population Survey Methods and indirect methods such as Nomination Methods, Network Scale-Up Methods, Divisor Methods, Multiplier Methods, Capture-Mark-Recapture Methods(CMR), Delphi Method. Most of the methods can not do statistical inference or not fit sensitive groups. CMR log-linear model was applied to estimate the population size of MSM in Beijing, because of its suitability in incomplete database, allowing dependence among samples, improving sample representativeness and its ability for statistical inference. In this paper, two sources, three sources CMR and their statistical formulae under simple random sampling were presented based on previous study. Cardinality estimation formulae of three sources CMR under stratified random sampling were deduced by us and were first used to survey MSM in Beijing in 2013.In addition, Monte Carlo simulation using SAS programming languages was adopted to evaluate the reliability and validity of three sources CMR under stratified random sampling. Our study offered supports for following study on cardinality survey of female sex workers(FSW) in 2015, for cardinality estimations of other AIDS high risk groups which were contents of national natural science funds(No.81273188) and for theory basis of HIV/AIDS prevention and control measures.Methods: According to classical sampling theory, variance, maximum likelihood estimation, log-linear model, Bartlett criterion, orthogonal projection, and interval estimation statistical theory, we presented two sources, three sources CMR and their statistical formulae under simple random sampling based on previous study. We also deduced statistical formulae of cardinality estimation and its variance using three sources CMR under stratified random sampling. 1774 copies of questionnaires in a survey were recovered among MSM in Beijing from September to December of 2013. Three sources CMR under stratified random sampling were applied to estimate population size of MSM in Beijing. Besides that, Monte Carlo simulation using SAS programming languages was applied to assess the validity and reliability of our survey methods and statistical formulae. The actual survey results of MSM in Beijing in 2013 were used to establish simulated parameters. We simulated three sources CMR under stratified random sampling to get 100 samples of MSM in Beijing every different capture interval. And then, according to statistical formulae of three sources CMR under stratified random sampling we have deduced, cardinality and its standard deviation, 95% confidence intervals(CI) of MSM can be acquired.Results:1. Based on previous studies, we presented the methods and statistical formulae of two sources, three sources CMR under simple random sampling on cardinality estimation. We had also deduced the statistical formulae of three sources CMR under stratified random sampling.2. Dependent three sources CMR under stratified random sampling was applied to survey MSM in Beijing from September to December of 2013. The contents of survey were if MSM had been in MSM venues, HIV Voluntary Counseling & Testing(VCT) clinics, MSM websites in Beijing last week. We recovered 1774 copies of questionnaires and 1763 copies qualified. Cardinality estimation of MSM in Beijing was 80399 and its asymptotic standard deviation was 4630, 95%CI was(71325, 89474).3. Dependent three sources CMR under stratified random sampling was applied to survey MSM in Beijing from September to December of 2013. The contents of survey were if MSM had been in MSM venues, HIV VCT clinics, MSM websites in Beijing last month. We recovered 1774 copies of questionnaires and 1766 copies qualified. Cardinality estimation of MSM in Beijing was 79481 and its asymptotic standard deviation was 4575, 95%CI was(70514, 88448).4. Dependent three sources CMR under stratified random sampling was applied to survey MSM in Beijing from September to December of 2013. The contents of survey were if MSM had been in MSM venues, HIV VCT clinics, MSM websites in Beijing last half a year. We recovered 1774 copies of questionnaires and 1766 copies qualified. Cardinality estimation of MSM in Beijing was 76790 and its asymptotic standard deviation was 4442, 95%CI was(68083, 85497).5. The results of 100 simulated samples using Monte Carlo on three sources CMR which were applied to MSM in Beijing last week were: 98 analog overall bases were included in 95%CI of overall estimated cardinalities.6. The results of 100 simulated samples using Monte Carlo on three sources CMR which were applied to MSM in Beijing last month were: 96 analog overall bases were included in 95%CI of overall estimated cardinalities.7. The results of 100 simulated samples using Monte Carlo on three sources CMR which were applied to MSM in Beijing last half a year were: 99 analog overall bases were included in 95%CI of overall estimated cardinalities.Conclusions:1. Three sources CMR under stratified random sampling and its formulae that applied to survey of MSM in Beijing in this paper have achieved good application effect. It provided the basis to investigate cardinalities of other AIDS high risk groups in Beijing or nationwide, such as female sex workers(FSW), persons who inject drugs(PWID).2. We investigated the cardinality of MSM in Beijing with three sources CMR under stratified random sampling from September to December of 2013 and acquired periods were a week, a month and half a year. The results of cardinalities were 80399, 79481, 76790 respectively, which were about 1.1%~1.15% of men at the same age. MSM whose cardinality should be more than the number our study presented are of high sensibility. It is clear that MSM is an important component of AIDS high risk groups. Surveillance and health education should be strengthened by health sector, and also more health-related behavioral interventions should be taken.3. The results of Monte Carlo simulation on MSM in Beijing at different acquired periods stated that almost all the simulated overall cardinalities of 100 samples were included in the 95%CI of overall cardinalities. Survey method and its formulae in our study are of great science, reliability and validity. The method in our study has broad application prospects in epidemiological research. |
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