Stratified Two-stage Cluster Sampling Design With RRT Method And It’s Application On Qualitative Sensitive Questions Survey

Objective:Before our research project, most researchers at home and abroad of sensitive topics especially about HIV high risk group were always limited to simple random sampling. What is more, research subjects with sensitive characteristics are narrowly chosen by a simple random design. In large scale survey, the data which are obtained by convenience sampling,internet survey,Respondent-Driven Sampling(RDS), complex sampling survey methods for sensitive issues have been implemented in the formulas about simple random sampling, and the sample size was also ignored. The actual survey of AIDS high risk groups requires complex sampling methods.Estimation of sample size is an important link of the sampling design that is the key factor of sampling survey. Therefore, in the present study, six RRT models under stratified two-stage cluster sampling were selected. On the existing basis of formulae for sensitive characteristics related statistic, optimum sample size formulae for estimating the population proportion of sensitive problems were deduced. Pre-investigation into sensitive behavioral features of men having sex with men (MSM) in Beijing not only gave STD/AIDS preliminary data in order to comprehend popular trend of STD/AIDS but also estimate values from related statistic formulae of sample size. Sample size for each stratum and each stage of stratified two-stage cluster sampling derived from calculation formulae in this paper would be the basis for scientifically estimating sensitive features of MSM in Beijing. This would also allow regional policy maker to prevent and control HIV/AIDS among MSM effectively.Method:Six survey methods were comprised of varied permutations and combinations of six RRT models (Warner RRT model, Simmons RRT model, The improved RRT model, Multiple choice questions with single response RRT model, Multiple choice questions with indirect response RRT model, Unrelated question RRT model) and stratified two-stage cluster sampling. Cochran’s classic sampling theories, total possibility formulae and variance were applied to deducing formulae for the estimators of population proportion and its population variance. Methods of deducing the minimum value and the Cauchy-Schwarz inequality were applied to deduce the formulae for the optimum sample sizes for stratified two-stage cluster sampling, in order to minimize the cost for specified values of the sampling errors and to minimize the sampling errors for specified cost.During July to September2013, Simmons RRT model and Multiple choice questions with single response RRT model were employed to investigate behavioral features of MSM in Beijing. According to the statistical formulae, the survey data were preliminarily analyzed so as to estimate related statistics value from sample size formulae.Results:1.Sampling technology theory was combined with the theory of RRT in this study, and formulae were deduced for the estimator of the population proportion and its estimated variance for4RRT models(Warner RRT model, The improved RRT model, Multiple choice questions with single response RRT model, Multiple choice questions with indirect response RRT model) used for sensitive questions survey in stratified two-stage cluster sampling.2. When defining the size of the sampling error of survey cost minimized and limit to the size of the sampling error of survey cost minimum.6RRT models with stratified two-stage cluster sampling method were used to derive an estimated sensitivity characteristics of the overall proportion of population, each stratum and each stage optimal sample size calculation formula.3. The investigation methods and the statistical formula of two RRT models were applied to obtain the results of seven sensitive questions of MSM in Beijing. The following preliminary survey results:The proportion of anal sex with condoms of MSM in Beijing were84.6963%. The proportion of condoms usage in the whole anal sex, which was classified into never used, sometimes used, every time used and no anal sex in Beijing were10.0277%、27.5991%、51.1208%、14.9054%, respectively. The proportion of average charge of commercial sex of MSM, which was classified into less than200RMB,200to399RMB,400to599RMB, more than600RMB and no commercial sex in Beijing were7.9024%、6.3025%、8.7941%、7.9456%、78.6419%, respectively. The proportion of results of HIV test of MSM, which were classified into positive, negative, checked but not know the results, a uncertain results and not checked in the last year in Beijing were5.8356%、79.0336%、6.8098%、7.1772%、8.8146%, respectively. The proportion of results of STD test of MSM, which were classified into positive, negative, checked but not know the results, a uncertain results and not checked in the last year in Beijing were10.0833%、74.9760%、7.8417%、6.6617%、8.1743%, respectively. The proportion of way(up to ejaculation orgasm) of sexual behavior, which was anal sex, oral sex and other sexual behavior for MSM in Beijing were70.2608%、19.1676%、17.0062%, respectively. The proportion of condom breakage, no breakage, no condom use of MSM in Beijing were11.9626%、77.0380%、18.8211%, respectively.4. The team are expected to be launched during2014National Natural Science Fund Project (ID:81273188) study in the Beijing city the size of male homosexual population and sensitive characteristics of stratified two-stage cluster sampling survey, according to this formula and the results of the survey, calculation each stratum and each stage in sample size estimation value. Stratified two-stage cluster sampling:the first layer (15-29stratum) need to extract the district number n11is10, average each district needs to pump the cluster number n21is18; the second stratum (30-49stratum) need to extract the district number n12is4, average each district needs to pump the cluster number n22is12.Conclusion:1. This paper shows mathematically that for the four kinds of survey methods designed in this paper, the overall proportion of sensitive issues and variance estimation formule were deduced. When defining the size of the sampling error of survey cost minimized and limit to the size of the sampling error of survey cost minimum,Formulae for optimum sample size were deduced to provide sensitive survey with scientific methods. It showed that survey methods and their statistical formulae have innovation significance and the theoretical value.2. Simmons RRT model and Multiple choice questions with single response RRT model with stratified two-stage cluster sampling were successfully applied in preliminary survey of MSM who are the high risk group of AIDS and Venereal diseases in Beijing of China. Survey methods and their statistical formulae were effective and reliable, and has a broad perspectives in application.3. The survey showed that MSM had anal sex as the main sexual behavior,they were high-risk population for STD/AIDS in Beijing, token anal intercourse as their primary sexual behavior, with low proportion of condom use in the whole process of intercourse, high proportion of positive HIV or STDs results, high proportion of condom breakage. This should be paid more attention to by health sector.The government and health departments should pay more attention to these little optimistic situations and seeking for appropriate measures.4. The sample size estimation value of male homosexual population according to the preliminary survey data of MSM in Beijing is12492, it is more than the sample size (1480people) in pre-study. This paper describes the sampling error in preliminary investigation is too large, it is necessary to carry out further investigation.