(Stratified) Three-Stage Sampling Design With RRT Mothod And Its Application On Sensitive Questions Survey

Objective:Sensitive issues survey is usually difficult to be implemented since most respondents, to protect their privacy, are unwilling to give the honest answer, or even refused to give response directly. In this situation, the quality of the survey can not be ensured and the results are often bias. To increase truthful respondent participation, Warner (1965) proposed the first Randomized Response Technique (RRT) for binary sensitive characteristics, which allows respondents to respond to sensitive issues (such as criminal behavior or sexuality) while maintaining confidentiality.A series of modified RRT models are proposed by statistician based on Warner model in recent several decades. Currently, RRT researches are mainly foucus on dichotomous sensitive questions and quantitative sensitive questions, while RRT methods for multichotomous sensitive questions are seldom reported-And most sensitive issues sampling survey are limited to simple random sampling(SRS), formulae for SRS are misused in the situation of large scale complicated survey such as stratified multiple stage sampling survey. In recent years, our research team consistently focused on all kinds of RRT modal application in complex sampling method for large scale survey such as cluster sampling, three-stage sampling, stratified sampling, stratified cluster sampling, stratified three-stage sampling, etc, and developed a large numbers of formulae and methods for estimating population parameters as well as corresponding population variance. By now there is no report for three-stage sampling and stratified three-stage sampling survey with RRT model in sensitive questions investigation. In this paper, we are intend to develop the formulae for calculating estimators of population proportion and corresponding population variance for binary sensitive questions and multichotomous sensitive questions, population mean and corresponding population variance for quantitative sensitive questions in three-stage sampling and stratified three-stage sampling servey. Also we built sampling simulation models with SAS programs based on Monte Carlo method, and simulated (stratified) three-stage sampling with6different RRT models to evaluate the validity and reliability of the methods. All our deduced formulae were successfully applied in a project to investigate sensitive features of MSM in Beijing, which provided scientific basis for helth authority to make regional policies and decisions to effectively control HIV/AIDS among MSM.Method: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. three-stage sampling and stratified three-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. RRT randomized devices and questionnaires with the sensitive questions were designed. A survey with several RRT model and stratified stratified three-stage sampling was employed to investigate sensitive features of MSM in Beijing from August to December in2010. Based on the deduced statistical formulae, the point estinators for population proportion or population means with corresponding95%confidence interval are calculated.3. Based on the investigation results of sensitive features of MSM in Beijing and Menta Carlo method, we built simulating population with SAS program, including16districts, with15sites in each district, and283MSM subjects in each site, totally67750subjects. Then we simulated the stratified three-stage sampling process and the application of6RRT models(e.g. Warner RRT model, Simmons RRT model, the improved RRT model, multiple choice questions with single response RRT model, Additive constant model and Multiplicative RRT model) for different kinds of sensitive questions on this simulated population. Each time we selected3district randomly, each of them with5sampled site, and for each site, we sampled60%MSM subjects for investigation, so totally about2533subjects were selected for each three stage sampling. And we repeated this process for100times with different seeds. Each time, we calculated sample statistics and get95%confidence interval(CI) of population proportion or population mean based on the deduced formulae. If almost all the100CIs include the population proportion or population mean, then we get the conclusion that the method is of high validity. At the same time, since the100sample statistics are all close to the same population parameter, we can get the conclusion that the method is of high reliability.Results:1. This paper designs9randomized response model with three stages, stratified three-stage sampling methods for combination of18kinds of survey methods. For each survey method, formulae for estimators of overall proportion, population mean and population variance are deduced based on classic sampling theories, total possibility formulae and properties of mean and variance.2. Three kinds of RRT models were applied in the stratified three-stage sampling survey for investigating sensitive features of MSM in Beijing, with following results: The average age for first time of the male male behaviour is21.96years old among MSM in Beijing, with the standard error of0.144; The average number of sexual parterner for each month is2.80, with the standard error of0.096; The average times of the male male behavior for each month is4.85, with the standard error of0.559; The proportion of condom usage in latest anal sex is77.80%, with the standard error of1.88%; The proportion of condom usage in anal sex during last month is:Never use (6.46%), Sometimes use(31.78%), Always use(51.81%), No anal sex(9.96%), with corresponding standard error of0.77%,0.71%,0.95%,0.44%, respectively; The proportion of average cost per time for commercial male male sexul behavior is:<200Yuan(5.65%),200-399Yuan(4.86%),400-599Yuan(2.67%),>600Yuan(6.48%), No commercial sexual behavior(80.34%), with corresponding standard error of0.70%,0.49%,0.57%,0.76%,2.20%, respectively; The proportion for different kinds of HIV virus detection result is:Positive(6.31%), Negative(78.67%), Uncertain(2.89%), Not receive HIV virus detection(6.45%), with corresponding standard error of0.42%,1.96%,0.28%,0.45%, respectively. The proportion for different kinds of STD detection result in recent one year is:Positive(16.79%), Negative(67.02%), Uncertain(6.25%), Not receive STD detection(5.23%), with corresponding standard error of0.66%,1.98%,0.46%,0.33%, respectively; The type of mam mam sexual behavior consist of:Anal sex(65.83%) and Oral sex(18.70%), with standard error of0.930%and0.658%, respectively; The proportion of occurrence of condom broken is5.50%, with standard error of0.57%.3. The simulation results for6kinds of RRT model applied in simulated stratified three-stage sampling survey are as follows:3.1For Simmons model applied for dichotomous sensitive questions investigation,99CIs for population proportion out of100include the real population proportion of binary sensitive feature, which shows high validity and rellability of the sampling survey method and the formulae we deduced for Simmons model.3.2For Warner model applied for dichotomous sensitive questions investigation,96CIs for population proportion out of100include the real population proportion of binary sensitive feature, which shows high validity and reliability of the sampling survey method and the formulae we deduced for Warner model.3.3For improved model applied for dichotomous sensitive questions investigation,97CIs for population proportion out of100include the real population proportion of binary sensitive feature, which shows high validity and reliability of the sampling survey method and the formulae we deduced for the improved RRT model. 3.4For single sample model applied for multichotomous sensitive questions investigation, There are individually96,99, and97CIs for population proportion out of100include the real population proportion for each category, which shows high validity and reliability of the sampling survey method and the formulae we deduced for single response RRT model.3.5For addtive model applied for quantitative sensitive questions investigation, all the100CIs for population mean include the real population mean of quantitative sensitive feature, which shows high validity and reliability of the sampling survey method and the formulae we deduced for additive RRT model.3.6For multiplication model applied for quantitative sensitive questions investigation, all the100CIs for population mean include the real population mean of quantitative sensitive feature, which shows high validity and reliability of the sampling survey method and the formulae we deduced for multiplicative RRT model.Conclusion:1. In this paper, we deduced statistical formulas for estamationg population proportion, population meam and corresponding population variance for eighteen survey methods combined of nine RRT models and two sampling methods. The deduced formulae were successfully applied in a Beijing CDC project to investigate sensitive features of Men who have sex with men (MSM), who are the high risk group of AIDS and STD. The results calculated based on our fomulas provided scientific basis for helth authority to make regional policies and decisions to effectively control HIV/AIDS among MSM.2. The MSM investigation showed that MSM did not have fixed sexual partners and had anal sex as the main way of sexual behavior. The proportion of MSM ever using condoms during homosexual behaviour was quite low, while the proportions of commercial sex behaviors, the proportion of never testing for HIV or STD, and the proportion of condoms breakage were relatively high. The government and health authorities should pay more attention to these less optimistic situation and make every efforts to seek for appropriate solutions for it.3. The simulation results for12methods combined with6RRT models and2sampling methods of three-stage sampling and stratified three-stage sampling shows that almost all95%CIs for population parameters calculated with our formulas include the real population proportion or real population mean in a large scale simulating investigation based on Monte Carlo method, indicating that all the survey methods and their statistical formulae are effective and reliable, and have a broad perspective in application.