| Objective:If a question in a sampling survey is sensitive or highly personal, it is likely to lead either to refusals or to untruthful answers by using the traditional method of direct interview because of the respondent's concern about revealing their privacy, which makes it difficult to acquire the real character of the population. By ingenious use of a randomizing device, Warner (1965) showed that it is possible to estimate the proportion without the respondents revealing their personal status with respect to the sensitive questions and thus introduced a new method for the sensitive questions survey—randomized response technique(RRT). Over the past few decades, a number of modifications of Warner's method as well as several other new methods have been emerged in the literature of randomized response. But, before our research project, most of the RR procedures available in the literature are developed and studied with the restriction that the sample is selected by simple random sampling. In the applications of RRT on sensitive questions, the formulas for simple random sampling are abused when the sample is selected by stratified sampling, cluster sampling or other relatively complicated sampling methods. What's more, the study on assessing the reliability and validity of the investigation on sensitive questions with RRT is seldom reported. In this regard, we select three RRT methods of Additive model, Multiplicative model, and Unrelated model, and aim to explore the feasibility of the methods to investigate quantitative sensitive issues with the sample selected by two-stage cluster sampling, and to estimate the population character of MSM of Beijing city. Meanwhile, the reliability of the methods is assessed by the application example as well as simulative sampling by computer.Method: Total probability formula and the theory of RRT was employed to deduce the formula for the estimator of the population proportion and its variance when the three RRT methods are applied to investigate quantitative sensitive issues with the sample selected by two-stage cluster sampling. In the following survey, from August to October, 2010, 30 chambers of MSM from 6 districts of Beijing city are randomly selected by two-stage cluster sampling, and all the 1523 MSMs from these chambers are surveyed by Additive model of RRT. Monte-Carlo simulative survey is performed to evaluate the reliability of the methods above.Results: In the condition of two-stage cluster sampling and three RRT models above-mentioned, the formulas to calculate the estimator of population's parameter and its variance are conducted. And the results of the three RRT models are consistent on the whole. The results of our application sample are: in Beijing city, the average age when MSM had sex with a man is 20.24; the average of sexual partners of MSM per month is 2.09; and the average of sexual behavior between men is 4.72 for every MSM of Beijing city per month. The difference between Monte-Carlo simulative survey and application sample is not significant in statistical test (P>0.1).Conclusion: With the RRT models and the formulas we deduced, we provide the method for the first time to calculate the estimator of the population parameter and its variance in quantitative sensitive issue survey under the situation of relatively complicated sampling method such as two-stage cluster sampling. The survey about MSM of Beijing city by two-stage cluster sampling and RRT Additive model is performed successfully and the result of Monte-Carlo simulative survey show that our survey methods and formulas are reliable. RRT has an extensive application in sensitive issue investigation on a large scale. |
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