| Objective:Sensitive issues are difficult to be surveyed due to highly private confidentiality or inconvenience in public statement. Direct questions are often asked in traditional survey methods. So no response bias or deliberately lying bias will be produced. In order to improve the correct response rate of sensitive problems, statisticians developed a series of Randomized Response Technique (RRT) models for sensitive question survey.At present, researchers at home and abroad lay emphasis on dichotomous sensitive questions and quantitative sensitive questions, while multichotomous sensitive questions are less widely noticed. Sample investigation in sensitive topics is 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 in complex sampling survey methods for sensitive issues have been implemented in the formulas about simple random sampling. Sampling survey is an important method. Estimation of sample size is an important link of the sampling design that is the key factor of sampling survey. Estimations of sample size for sensitive questions Randomized Response models based on multistage sampling survey are seldom reported. Therefore, in the present study, eighteen survey methods were selected, which were comprised of varied permutations and combinations of nine RRT models and two sampling methods. On the existing basis of formulae for sensitive characteristics related statistic, optimum sample size formulae for estimating the population proportion and the population mean of sensitive problems were deduced. Two premises should be satisfied simultaneously:limitation of sampling error to minimize investigation costs and limitation of investigation costs to minimize sampling error. Complex sample methods for large scale survey are provided with sample size estimate formulae. 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 stage of two stage sampling and each stratum of stratified 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.Methods:1. Eighteen survey methods were comprised of varied permutations and combinations of nine RRT models (e.g. Warner RRT model, Simmons RRT model, Greenberg 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, Additive constant model and Multiplicative RRT model) and two sampling methods (e.g. two-stage sampling and stratified two-stage sampling). Cochran’s classic sampling theories, total possibility formulae and properties of mean and variance were applied to deducing formulae for the estimators of population proportion and population mean and population variance.2. Methods of deducing the minimum value and the Cauchy-Schwarz inequality were applied to deduce the formulae for the optimum sample sizes for two-stage and stratified two-stage sampling, in order to minimize the cost for specified values of the sampling errors and to minimize the sampling errors for specified cost.3. RRT randomized devices and questionnaires with the sensitive questions were designed. Two-stage sampling and stratified two-stage sampling were employed to investigate behavioral features of MSM in Beijing from August to October in2010. According to the statistical formulae, the survey data were preliminarily analyzed so as to estimate related statistics value from sample size formulae.4. For a total of ten sensitive issues through the investigation based on Simmons model, multiple choice questions with single response model and additive constant model under two-stage and stratified two-stage sampling, optimum sample sizes were obtained with the limitation of the sampling errors for the minimum of cost and were obtained with the limitation of cost on the minimum of sampling errors. All these were depending on the related statistic value from preliminary survey data and sample size formulae deduced in the present study.Results:1. This paper designs18survey methods of9randomized response models with two stages and stratified two-stage sampling methods. For the18kinds of survey methods, the pupulation proportion and population mean of sensitive issues and variance estimation formulas were given.2. In9randomized response model combined with2complicated sampling methods, when defining the size of the sampling error and let survey cost minimized and limiting the size of the sampling error of survey and let cost minimum, we try to estimate the population proportion, population mean, and each stage optimal sample size.3. This article surveyed on sensitive questions of the Beijing MSM group under3randomized response models with two-stage sampling and stratified two-stage sampling. The results of the following preliminary survey under two-stage sampling:The first time MSM crowd MSM average age is21.9years old in Beijing, The standard error is0.1792years old; The number of MSM monthly per capita different partners is2.79, The standard error is0.0860people; The time of per capita monthly MSM is4.8, and the standard error is0.1587times; The last male condom use behavior during anal sex ratio is77.63%, and the standard error is1.82%; ratios of never full use of condoms, sometimes the full use of condoms, each full use of condoms, and no anal sex last month are respectively6.07%,29.16%,55.60%,8.86%, The standard errors are respectively0.93%,1.30%,1.84%,1.10%; the average expense of male commercial sex behavior is respectively<200yuan,200～399yuan,400～599yuan,600yuan respectively2.60%,3.18%,0.88%,5.99%, The standard errors are respectively0.57%,1.05%,0.35%,0.65%; In the recent year, the proportions of positive result of HIV virus detection, the uncertain results and not being checked are4.89%,1.31%and4.22%respectively and the corresponding standard errors are1.05%,0.54%,1.26%respectively; In the recent year, STD testing results, ratios of no disease, no STD checked are respectively14.58%,77.49%,7.38%, the standard error is respectively1.70%,2.37%,1.45%; ratios of anal intercourse, oral sex are respectively69.23%,15.57%, the standard error are2.21%,1.79%; condom use have broken the proportion is3.53%, the standard error is0.92%.4. The team are expected to be launched during2013National Natural Science Fund Project "Statistical methods and applications in survey of base number of high-risk groups with sensitive issues"(No.81273188) study in the Beijing city the size of male homosexual population and sensitive characteristics of two-stage and stratified two-stage sampling survey, according to the formulas and the results of the survey, calculation each layer of each phase in sample size estimation value.4.1Two stage sampling:in the first stage we need to extract13districts (n1=13), and in the second stage, we need to draw129MSM people (n2=129) from each district.4.2Stratified two-stage sampling:in the first layer (15-29layer), we need to extract8districts (n11=8), and we need to draw121MSM people from each district (n21=121); in the second layer (30-49layer), we need to extract8districts (n12=8), and we need to drawl13MSM people from each district (n22=113). Conclusion:1. In this paper, we deduced Formulas or two-stage sampling and dichotomous sensitive questions on two-stage sampling. And corresponding survey methods and formulas of three RRT models were successfully designed and applied in the pre-survey of the Men who have sex with men (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 have a broad perspective in application.2. The initial investigation showed that MSM did not have fixed sexual partners and had anal sex as the main sexual behavior. The proportion of MSM ever using condoms during homosexual behaviour was low, while the proportions of commercial sex behaviors and never testing for HIV or other STD and condoms breakage were high. The government and health departments should pay more attention to these little optimistic situations and seeking for appropriate measures.3. Formulae for optimum sample size were deduced to provide sensitive survey with scientific methods. Optimum sample size for each stage and stratum were obtained from formal survey of MSM in Beijing asked ten sensitive questions by six survey methods (that is, combination of three RRT models and two sampling methods), which had a broad prospect of application and popularized significance. |
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