中文摘要：

目的研究二项选择敏感问题RRT模型下两阶段抽样调查样本量的估计公式，探讨敏感问题复杂抽样调查设计的统计方法。方法使用二项选择敏感问题西蒙斯模型，根据概率论和数理统计学的理论方法，在给出二项选择敏感问题两阶段抽样样本比例及其方差计算公式的基础上；使用哥西不等式、求条件极小值点等方法，从数学上推导二项选择敏感问题西蒙斯模型下两阶段抽样调查各阶段抽样的最优样本量的计算公式；通过对北京MSM人群预调查获取相关统计量的数值，进而估计北京MSM人群敏感问题RRT模型下两阶段抽样调查各阶段的最优样本量。结果当限定抽样误差而使调查费用最小时需要抽取13个区县，当限定调查费用而使抽样误差最小时需要抽取9个区县；从每个被抽中的区县中需要抽取的MSM人数平均为51人。结论本文研究的二项选择敏感问题RRT模型下两阶段抽样调查样本量的估计公式及相关统计方法具有创新理论意义和很好的实际应用价值。

英文摘要：

Objective To investigate the two-stage sampling method and determine the sample size for dichotomous sensitive question survey. Methods By using statistical theories and methods, the population proportion of dichotomous sensitive question under Simmons model and its variance were estimated; Cauchy-Schwarz inequality and the minimum method were used to deduce the sample size determination formulae for two-stage sampling survey of dichotomous sensitive questions; the survey method and relevant formulae were applied to the two-stage sampling survey of condom use in sex behavior among MSM（ men who have sex with men） in Beijing. Re- sults Based on the pre-survey data of MSM in Beijing,51 MSM should be extracted in each selected county. If the sampling error is to be limited, 13 counties should be extracted to make the survey cost minimum in the first stage of sampling. On the contrary ,9 counties should be extracted to minimize the sampling error in the first stage of sampling if the survey cost is to be limited. Condusion The survey meth- od and sample size determination formulae are useful in the two-stage sampling survey of dichotomous sensitive questions. An optimum sample size can be calculated by using the deduced formulae to reduce the cost and the sampling error of the survey.