| Objective:Acquired immunodeficiency syndrome(AIDS)is a serious global public health issue,which is a kind of infectious disease caused by human immunodeficiency virus(HIV)and sometimes fatal.Some populations are more vulnerable to HIV infection due to their increased behavioral risk factors,e.g.,unsafe sex behavior,multiple partnerships,injection of drugs,etc.These are the high risk populations of HIV/ADIS.The size of high risk populations of HIV/AIDS is one of the core variables in AIDS epidemiological research,as well as the basis of the objective analysis and full understanding of the current HIV epidemic and its trend.Meanwhile,it can provide scientific justifications for HIV related policy making,resource allocation,as well as the planning and implementation of the programs targeting HIV prevention and control.Capture-mark-recapture(CMR)methods are extensively applied in HIV/AIDS research due to its scientific rationale,easy implementation and low cost induced.So far in the research of the sizes of HIV high risk populations,the applications of CMR are mostly based on simple random sampling techniques and/or two-source CMR methods.Complex sampling techniques,like Multi-stage sampling and stratified sampling,aiming to reducing sampling error or implementation complexity,are often necessary in actual research programs.Compared with two-source CMR methods,multiple sources sampling data are more representative and generate more reliable results.Research on the sizes of HIV/AIDS high risk populations using multiple sources CMR methods with complex sampling techniques has not been reported in the literature.Our study aimed to employ three-source CMR methods with complex sampling techniques,i.e.,two-stage sampling,stratified two-stage sampling,three-stage sampling and stratified three-stage sampling,to estimate the sizes of HIV/AIDS high risk populations,and to deduce the formulae of the point estimate and variance of the population size,as well as its variance estimate.Two case studies were conducted to estimate the sizes of HIV/AIDS high risk populations using the survey methods and statistical formulae derived from our study of the three-source CMR methods with complex sampling techniques.These two case studies are:the 2013 Beijing men who have sex with men(MSM)population size study and the 2015 Guangxi female sex workers(FSW)population size study.Meanwhile,the validity and reliability of the three-source CMR methods using complex(i.e.,two-stage,stratified two-stage,three-stage,stratified three-stage)sampling techniques were also evaluated.The purpose of our study is to provide scientific survey methodology,statistical formulae and evaluation approaches on validity and reliability of the estimation of the sizes of HIV/AIDS high risk populations.The results from the case studies can provide related health authorities and policy-makers with valuable data and information for strategizing HIV/AIDS prevention and control policies and optimal allocation of the resources for curbing the HIV/AIDS epidemic.Methods:According to the classical sampling theory and the theory and methodology of mathematical statistics including maximum likelihood estimation,log-linear modeling,orthogonal projection,the nature of variance,interval estimation,etc.,we designed the survey methods for the three-source CMR methods with complex sampling(i.e.,two-stage,stratified two-stage,three-stage,stratified three-stage)techniques,and deduced the formulae of the point estimate and variance of the population size,as well as its variance estimate for the respective CMR methods,based on previous research on the survey methods and statistical formulae of the three-source CMR methods with simple random sampling.Subsequently,we applied the survey methods and statistical formulae of the resultant three-source CMR method with two-stage random sampling technique to the estimation of the size of the Beijing MSM population from September to December of 2013.Likewise,the survey methods and statistical formulae of the resultant three-source CMR with stratified three-stage random sampling was applied to the estimation of the size of the Guangxi FSW from August to October of 2015.Based on the respective results of the statistics from the investigations of the Beijing MSM population size in 2013 and the Guangxi FSW population size in 2015,the simulated populations were constructed using the above-mentioned statistics from the actual investigation cases as the simulated population parameters,through the Monte Carlo simulation with SAS programming.One hundred random samples were simulated for each investigation period for the three-source CMR method in question with the complex sampling techniques and the estimates of the sizes for the MSM or FSW populations,the respective standard deviations and 95%confidence intervals of the population sizes were obtained using the formulae with pair-wise between-source correlation of the three-source CMR methods deduced in current study,as the evaluation of the reliability and validity of the three-source CMR methods with the two-stage,stratified two-stage,three-stage and stratified three-stage random sampling techniques.Results:1.Our study presented for the first time the survey methods for the three-source CMR method with the two-stage,stratified two-stage,three-stage and stratified three-stage random sampling technique,and deduced the statistical formulae of the point estimate and variance of the population size,as well as its variance estimate for this CMR method.2.We applied the three-source CMR method with two-stage random sampling technique to the estimation of the size of the Beijing MSM population through the survey of the MSM sample with Beijing residency or having lived in Beijing for at least six months from 15th September to 31st December,2013.Participants were asked about the status of their presence at the venues dedicated to MSM,the clinics for HIV voluntary counseling&testing(VCT)or the websites for MSM,during the week,the month and six months prior to the survey.From the 16 districts/counties in Beijing,six districts or counties,i.e.,Xicheng,Haidian,Changping,Tongzhou,Huairou and Miyun,were randomly selected as the primary sampling units;1,774 MSM were randomly selected as the secondary sampling units from these six selected districts/counties.The survey resulted in a total of 1,771 valid completed questionnaires for the past week period.The corresponding size of the MSM population in Beijing for this period was estimated to be 94,715,with 9,418 as the asymptotic standard deviation(SD)and 76,256?113,174 as the 95%confidence interval(CI).For the past month period,1,766 valid questionnaires were collected and the resultant estimate of the size of MSM population was 81,720,with 8,291 as the asymptotic SD and 65,470?97,970 as the 95%CI.For the past six months period,1,766 valid questionnaires were collected and the resultant estimate of the size of MSM population was 71,899,with 7,346 as the asymptotic SD and 57,501-86,297 as the 95%CI.3.The three-source CMR method with stratified three-stage random sampling technique was applied to the estimation of the size of the Guangxi FSW population through the survey of the FSW sample from August to October,2015.Participants were asked about the status of receiving the AIDS-related intervention service,testing of sexually transmitted disease(STD)and/or HIV in the certified healthcare facilities,or providing sexual services during the periods of past three and six months prior to the survey.From the 14 prefecture-level cities in Guangxi,three cities,i.e.,Baise,Liuzhou and Yulin,were randomly selected as the primary sampling units;and nine counties/districts were randomly selected as secondary sampling units from these three primary units,with three counties/districts from each selected city.Furthermore,4,267 FSW were randomly selected as the tertiary sampling units from the venues haunted by FSW in the selected nine counties/districts six selected districts/counties.The age of FSW was set as the stratifying factor.According to the distribution of age from the survey data,the median age of this FSW population was 32 years old.Therefore,32 years was set as the cut point of the age strata,with FSW aged 32 years or younger as the first stratum and older than 32 years old as the second stratum.The survey resulted in a total of 4,118 valid completed questionnaires for the past three-month period.The corresponding size of the FSW population in Guangxi for this period was estimated to be 95,662,with 6,922 as the asymptotic SD and 82,094?109,230 as the 95%CL.For the past six month period,4,101 valid questionnaires were collected and the resultant estimate of the size of MSM population was 91,416,with 6,612 as the asymptotic SD and 78,456-104,376 as the 95%CI.4.Based on the three-source CMR method with two-stage random sampling on the survey of the Beijing MSM population for the past week period,the result from the one hundred random samples simulated with the Monte Carlo method was that 99 of the 100 95%CIs of the MSM population size estimate contains the simulated population size.For the past month period,the corresponding result from the one hundred random samples simulated with the Monte Carlo method was that 95 of the 100 95%CIs of the MSM population size estimate contains the simulated population size.For the past six month period,the corresponding result from the one hundred random samples simulated with the Monte Carlo method was that 98 of the 100 95%CIs of the MSM population size estimate contains the simulated population size.5.Based on the three-source CMR method with stratified three-stage random sampling on the survey of the Guangxi FSW population for the past three-month period,the result from the one hundred random samples simulated with the Monte Carlo method was that 96 of the 100 95%CIs of the FSW population size estimate contains the simulated population size.For the past six-month period,the corresponding result from the one hundred random samples simulated with the Monte Carlo method was that 97 of the 100 95%CIs of the MSM population size estimate contains the simulated population size.Conclusions:1.The survey method and statistical formulae for the three-source CMR method with two-stage and stratified three-stage random sampling technique investigated by the current study have produced satisfactory effect in the actual application among Beijing MSM population and Guangxi FSW population,and provided scientific methodology and successful experience for estimating the size of the HIV/AIDS high risk population.2.The size of the MSM population in Beijing in 2013 was estimated to be 81,720(i.e.,1.17%of the total male population of the same age group)for the past month period prior to the survey using the three-source CMR method with two-stage random sampling technique investigated by the current study.The results from our study can provide related health authorities with reliable and valid estimate of the size of the HIV high risk(i.e.,MSM)population in this region,and therefore advocate accurate monitoring of the MSM population.Meanwhile,effective and targeted measures should be taken to precisely control the HIV/AIDS epidemic.Based on the three-source CMR method with two-stage random sampling on the survey of the Beijing MSM population for different survey periods(the past week,the past month and the past six months),almost all the 95%confidence intervals of the population size estimate from the one hundred random samples simulated with the Monte Carlo method contain the simulated population size.This indicates that the three-source CMR method with two-stage random sampling technique investigated by the current study has satisfactory reliability and validity and may be extensively applied in future epidemiological research.3.The size of the FSW population in Guangxi in 2015 was estimated to be 95,662(i.e.,0.42%of the total female population in Guangxi)for the past three-month period prior to the survey using the three-source CMR method with stratified three-stage random sampling technique investigated by the current study.The results from our study can provide related health authorities with reliable and valid estimate of the size of the HIV high risk(i.e.,FSW)population in this region,and therefore advocate accurate monitoring of the FSW population.Meanwhile,effective and targeted measures should be taken to precisely control the HIV/AIDS epidemic in this population.Based on the three-source CMR method with stratified three-stage random sampling on the survey of the Guangxi FSW population for different survey periods(the past three months and the past six months),almost all the 95%confidence intervals of the population size estimate from the one hundred random samples simulated with the Monte Carlo method contain the simulated population size.This indicates that the three-source CMR method with stratified three-stage random sampling technique investigated by the current study has satisfactory reliability and validity and may be extensively applied in future epidemiological research.4.As stratified three-stage random sampling technique implies three-stage sampling within each stratum,the prerequisite for the high reliability and validity of the three-source CMR method with stratified three-stage random sampling technique is that the three-source CMR method with three-stage random sampling technique per se must be suff-iciently reliable and valid.Therefore,we can infer the three-source CMR method with three-stage random sampling technique investigated by the current study also has satisfactory reliability and validity and may be extensively applied in future epidemiological research.5.As in terms of either the deduction of statistical formulae or the sampling techniques,the stratified three-stage sampling technique is an extension of the stratified two-stage sampling technique.The prerequisite for the high reliability and validity of the three-source CMR method with stratified three-stage random sampling technique is that the three-source CMR method with stratified two-stage random sampling technique per se must be sufficiently reliable and valid.Therefore,we can infer the three-source CMR method with stratified two-stage random sampling technique investigated by the current study also has satisfactory reliability and validity and may be extensively applied in future epidemiological research.6.The survey method and statistical formulae for the three-source CMR method with stratified three-stage or three-stage random sampling technique investigated by the current study have produced satisfactory effect in the actual application among Guangxi FSW population,and provided scientific methodology and successful experience for estimating the size of the HIV/AIDS high risk population. |
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