敏感问题二阶段抽样调查的统计方法及应用
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摘要
目的:调查敏感问题时,被调查者往往会拒绝回答或者提供虚假答案。为了获得敏感问题的真实答案,也为了保护被调查者的隐私,l965年沃纳(Warner)首先创立了一个二项属性特征的敏感性问题的随机化回答模型,它提供了对诸如考试作弊、漏税、吸毒等敏感性问题进行调查的一种方法,被命名为沃纳模型。1967年由西蒙斯(Simmons)对沃纳模型进行了改进,形成了西蒙斯模型。后来,逐渐形成了专门调查敏感性问题的随机化应答技术( Randomized Response Technique,RRT)。
在本项目组研究之前,国内外对敏感问题抽样调查的统计方法研究,主要局限于简单随机抽样,实际应用也主要局限于小范围特殊人群小样本的简单随机抽样调查,或将分层简单随机抽样、(分层)整群抽样、(分层)多阶段抽样调查资料误用简单随机抽样调查有关公式来统计分析。鉴于此,本文选定了二分类敏感问题Warner随机应答模型、Simmons随机应答模型、双无关问题模型、改进的随机应答模型,多分类敏感问题随机应答模型以及数量特征敏感问题单无关联问题模型、加法模型、乘法模型,对这八种RRT模型与二阶段抽样方法组合的8种调查方法及其统计公式进行探讨,为属性特征敏感问题和数量特征敏感问题的大规模的复杂抽样调查提供科学的调查方法及有效、可靠的统计公式。
方法:在本文研究中,根据Cochran的经典抽样理论、全概率公式、方差的性质等概率论与数理统计学基本理论方法,以及二项选择敏感问题Warner模型、Simmons模型、双无关问题模型和改进的RRT模型,多项选择敏感问题单一样本随机应答模型,数量特征敏感问题单无关联问题模型、加法模型、乘法模型八种RRT模型的理论方法,设计出八种RRT模型的二阶段抽样的调查方法,推导出其敏感问题总体比例、总体均值的估计量及其方差、估计方差的计算公式。于2010年8月至2010年10月,采用二阶段抽样方法,在北京市随机抽取9个区县,分别从被抽中9区县内随机抽取部分男男性行为者,共620人,成功运用三种RRT模型对其二项选择、多项选择、数量特征的敏感问题进行了调查分析。对本文研究的调查方法及其统计公式:在全国范围内挑选30名相关学科的专家,进行了表面效度和内容效度的专家咨询评价;经寻求合适的准则效标变量,对敏感问题二项选择Simmons随机应答模型、多项选择敏感问题单一样本随机应答模型、数量特征敏感问题加法模型下二阶段抽样的调查方法及其统计公式进行了准则效度评价。
结果:
一、本研究中将抽样技术理论和随机应答技术的理论相结合,推导出二阶段抽样方法下八种RRT模型调查敏感问题时总体比例的估计量及其方差计算公式。
二、运用本文研究的二阶段抽样条件下3种RRT模型的调查方法及其统计公式,调查估计出北京市男男性行为人群10个敏感问题结果如下:
1.肛交中安全套的使用比例为78.65%;
2.最近1个月中肛交从不全程使用安全套、有时全程使用安全套、每次全程使用安全套、没有肛交的发生比例分别是7.2055%、28.8687%、55.9630%、7.9627%;
3.最近一年男男商业性性行为中平均每次收费<200元、200～399元、400～599元、600元以上、无男男商业性性行为的比例分别是3.2988%、4.9569%、2.6000%、5.8566%、87.8276%。
4.最近一年HIV检测结果为阳性、阴性、检查过但不知道结果、结果不确定、没有检查过的比例分别是8.0272%、72.4350%、8.2792%、5.2110%、6.0476。
5.最近一年中到正规医疗机构进行性病检查结果为有性病、无性病、检查过但不知道结果、结果不确定、没有检查过的比例分别是15.1704%、67.9019%、4.1940%、5.4319%、7.3017%。
6.男男性性行为(达到射精高潮时)的方式为肛交、口交、其它性行为方式的比例分别是64.6453%,18.7388%,16.6159%。
7.男男性行为中安全套有破损、无破损、没有使用安全套的比例分别是12.4620%,67.7727%,19.7653%。
8.首次男男性行为的平均年龄为21.9747岁。
9.每人每月男男性行为不同性伴的平均人数为3人。
10.月平均男男性行为的次数为4.8次。
三、进行表面效度和内容效度评价,专家咨询结果优良比例达100%;对三种RRT模型下二阶段抽样的调查方法及其统计公式实际调查计算的5项指标,分别与相应效度准则变量的差别作假设检验,P值分别为0.73125、0.62605、0.5164、0.59147、0.3262,差异均无统计学意义。表面效度、内容效度、准则效度评价结果,效度均较高。
结论:本文研究的敏感问题RRT模型下二阶段抽样的调查方法及其统计公式科学、可靠、有效,具有广泛的应用前景。北京市男男性行为人群存在无固定性伴、肛交为主要性行为方式、全程使用安全套比例低、安全套破损比例高等艾滋病、性病高危性行为,应引起政府、卫生部门的高度重视。
Objective: When it comes to sensitive problem, respondents often refuse to answer or providing false answer. In order to obtain the real answers of sensitive problem and protect the privacy of respondents, randomized-response models proposed by Warner(1965) and Greenberg(1969) presumed that two yes/no questions were provided for each respondent and that a randomization device was used to determine which question would be answered.
It provides a method of sensitive question survey, such as cheating in the exam, tax loophole, drugs, and so on. The randomized-response technique (RRT) can be an effective survey method to find such estimates because individual anonymity is preserved. Then it gradually formed a special investigation of sensitive problem, which was randomized response technology.
Before the study, researches of randomized response technique (RRT) for dichotomous and multichotomous sensitive questions were developed and studied with the restriction that the sample was selected through simple random sampling. In the applications of RRT, respondents were restricted to a small population coming from simple random sampling or the formulae for simple random sampling were abused when the sample was selected by stratified sampling, cluster sampling or other relatively complicated sampling methods.
In this regard,we select eight RRT models, e.g. Warner model ,Simmons model, double irrelevant problem model and the improved RRT model, to explore the 8 methods to investigate sensitive issues with the sample selected by two-stage sampling. In this way, we can provide scientific and effective methods and formulas on sensitive questions under the condition of two-stage sampling from large population.
Method: Two-stage sampling techniques, Cochran’s classic sampling theories, total probability formulae, properties of the variance were applied to eight RRT models. In addition, reliability and validity were used to evaluate the statistical methods. Formulae were deduced for the estimator of the population proportion and its estimated variance for eight RRT model used for sensitive questions survey in two-stage sampling. There were 620 person which were drawn from a sample of MSM in Beijing in 2010. And it was successfully applied three RRT model to obtain their sensitive characters. Face validity and content validity of methods and formula of this study was evaluated by 30 selected nationwide experts in related disciplines. After seeking appropriate criterion variable, we evaluated the criteriaon validity of methods and formula about three RRT models in two-stage sampling.
Result:
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 for eight RRT model used for sensitive questions survey in two-stage sampling.
2. The investigation methods and the statistical formula of three RRT model were applied to obtain the results of ten sensitive questions of MSM(men who have sex with men ) in Beijing. The results of ten sensitive questions are as follows:
2.1 The proportion of anal sex with condoms was 78.65%.
2.2 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, was 7.2055%, 28.8687%, 55.9630% and 7.9627% respectively last month.
2.3 The proportion of average charge of commercial sex of MSM, which was classified into less than 200 RMB, 200 to 399 RMB, 400 to 599 RMB, more than 600 RMB and no commercial sex, was 3.2988%, 4.9569%, 2.6000%, 5.8566% and 87.8276% respectively last year.
2.4 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, was 8.0272%, 72.4350%, 8.2792%, 5.2110% and 6.0476 respectively last year .
2.5 The results of STD test were classified into five types, which were positive, negative, checked but not know the results, a uncertain results and not checked. The proportion of five results was 15.1704%、67.9019%、4.1940%、5.4319% and 7.3017% respectively last year.
2.6 The proportion of way(up to ejaculation orgasm) of sexual behavior, which was anal sex, oral sex and other sexual behavior for MSM, were 64.6453%, 18.7388% and 16.6159% respectively.
2.7 The proportion of Condom breakage, which was classified into broken, no damage and not use of condom for MSM, was 12.4620%, 67.7727, and 19.7653 respectively.
2.8 The average age of MSM was 21.9747 years in the first time.
2.9 The average number of different sexual partners of MSM was 3 person every month for per person .
2.10 It was 4.8 times of the number of MSM on average monthly.
3. Thirty experts all over the country evaluated the face validity and content validity of the survey methods, the rate of“excellent”and“good”was 100%. Comparing the results p got by the three sensitive questions RRT models with the valid criterion p0, there are no statistically significant difference between p and p0. So we can draw the conclusion that our survey methods and corresponding formulae are scientific, reliable and valid.
Conclusion:The methods and corresponding formulas on sensitive questions survey with the sample selected by two-stage sampling were feasible. The AIDS and STD high-risk behaviors of MSM in Beijing, such as no fixed sexual partners, anal sex, the low proportion of full use of condoms and high proportion of condoms breakage, should aroused the great concerns of our government and health sector.
在本项目组研究之前,国内外对敏感问题抽样调查的统计方法研究,主要局限于简单随机抽样,实际应用也主要局限于小范围特殊人群小样本的简单随机抽样调查,或将分层简单随机抽样、(分层)整群抽样、(分层)多阶段抽样调查资料误用简单随机抽样调查有关公式来统计分析。鉴于此,本文选定了二分类敏感问题Warner随机应答模型、Simmons随机应答模型、双无关问题模型、改进的随机应答模型,多分类敏感问题随机应答模型以及数量特征敏感问题单无关联问题模型、加法模型、乘法模型,对这八种RRT模型与二阶段抽样方法组合的8种调查方法及其统计公式进行探讨,为属性特征敏感问题和数量特征敏感问题的大规模的复杂抽样调查提供科学的调查方法及有效、可靠的统计公式。
方法:在本文研究中,根据Cochran的经典抽样理论、全概率公式、方差的性质等概率论与数理统计学基本理论方法,以及二项选择敏感问题Warner模型、Simmons模型、双无关问题模型和改进的RRT模型,多项选择敏感问题单一样本随机应答模型,数量特征敏感问题单无关联问题模型、加法模型、乘法模型八种RRT模型的理论方法,设计出八种RRT模型的二阶段抽样的调查方法,推导出其敏感问题总体比例、总体均值的估计量及其方差、估计方差的计算公式。于2010年8月至2010年10月,采用二阶段抽样方法,在北京市随机抽取9个区县,分别从被抽中9区县内随机抽取部分男男性行为者,共620人,成功运用三种RRT模型对其二项选择、多项选择、数量特征的敏感问题进行了调查分析。对本文研究的调查方法及其统计公式:在全国范围内挑选30名相关学科的专家,进行了表面效度和内容效度的专家咨询评价;经寻求合适的准则效标变量,对敏感问题二项选择Simmons随机应答模型、多项选择敏感问题单一样本随机应答模型、数量特征敏感问题加法模型下二阶段抽样的调查方法及其统计公式进行了准则效度评价。
结果:
一、本研究中将抽样技术理论和随机应答技术的理论相结合,推导出二阶段抽样方法下八种RRT模型调查敏感问题时总体比例的估计量及其方差计算公式。
二、运用本文研究的二阶段抽样条件下3种RRT模型的调查方法及其统计公式,调查估计出北京市男男性行为人群10个敏感问题结果如下:
1.肛交中安全套的使用比例为78.65%;
2.最近1个月中肛交从不全程使用安全套、有时全程使用安全套、每次全程使用安全套、没有肛交的发生比例分别是7.2055%、28.8687%、55.9630%、7.9627%;
3.最近一年男男商业性性行为中平均每次收费<200元、200～399元、400～599元、600元以上、无男男商业性性行为的比例分别是3.2988%、4.9569%、2.6000%、5.8566%、87.8276%。
4.最近一年HIV检测结果为阳性、阴性、检查过但不知道结果、结果不确定、没有检查过的比例分别是8.0272%、72.4350%、8.2792%、5.2110%、6.0476。
5.最近一年中到正规医疗机构进行性病检查结果为有性病、无性病、检查过但不知道结果、结果不确定、没有检查过的比例分别是15.1704%、67.9019%、4.1940%、5.4319%、7.3017%。
6.男男性性行为(达到射精高潮时)的方式为肛交、口交、其它性行为方式的比例分别是64.6453%,18.7388%,16.6159%。
7.男男性行为中安全套有破损、无破损、没有使用安全套的比例分别是12.4620%,67.7727%,19.7653%。
8.首次男男性行为的平均年龄为21.9747岁。
9.每人每月男男性行为不同性伴的平均人数为3人。
10.月平均男男性行为的次数为4.8次。
三、进行表面效度和内容效度评价,专家咨询结果优良比例达100%;对三种RRT模型下二阶段抽样的调查方法及其统计公式实际调查计算的5项指标,分别与相应效度准则变量的差别作假设检验,P值分别为0.73125、0.62605、0.5164、0.59147、0.3262,差异均无统计学意义。表面效度、内容效度、准则效度评价结果,效度均较高。
结论:本文研究的敏感问题RRT模型下二阶段抽样的调查方法及其统计公式科学、可靠、有效,具有广泛的应用前景。北京市男男性行为人群存在无固定性伴、肛交为主要性行为方式、全程使用安全套比例低、安全套破损比例高等艾滋病、性病高危性行为,应引起政府、卫生部门的高度重视。
Objective: When it comes to sensitive problem, respondents often refuse to answer or providing false answer. In order to obtain the real answers of sensitive problem and protect the privacy of respondents, randomized-response models proposed by Warner(1965) and Greenberg(1969) presumed that two yes/no questions were provided for each respondent and that a randomization device was used to determine which question would be answered.
It provides a method of sensitive question survey, such as cheating in the exam, tax loophole, drugs, and so on. The randomized-response technique (RRT) can be an effective survey method to find such estimates because individual anonymity is preserved. Then it gradually formed a special investigation of sensitive problem, which was randomized response technology.
Before the study, researches of randomized response technique (RRT) for dichotomous and multichotomous sensitive questions were developed and studied with the restriction that the sample was selected through simple random sampling. In the applications of RRT, respondents were restricted to a small population coming from simple random sampling or the formulae for simple random sampling were abused when the sample was selected by stratified sampling, cluster sampling or other relatively complicated sampling methods.
In this regard,we select eight RRT models, e.g. Warner model ,Simmons model, double irrelevant problem model and the improved RRT model, to explore the 8 methods to investigate sensitive issues with the sample selected by two-stage sampling. In this way, we can provide scientific and effective methods and formulas on sensitive questions under the condition of two-stage sampling from large population.
Method: Two-stage sampling techniques, Cochran’s classic sampling theories, total probability formulae, properties of the variance were applied to eight RRT models. In addition, reliability and validity were used to evaluate the statistical methods. Formulae were deduced for the estimator of the population proportion and its estimated variance for eight RRT model used for sensitive questions survey in two-stage sampling. There were 620 person which were drawn from a sample of MSM in Beijing in 2010. And it was successfully applied three RRT model to obtain their sensitive characters. Face validity and content validity of methods and formula of this study was evaluated by 30 selected nationwide experts in related disciplines. After seeking appropriate criterion variable, we evaluated the criteriaon validity of methods and formula about three RRT models in two-stage sampling.
Result:
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 for eight RRT model used for sensitive questions survey in two-stage sampling.
2. The investigation methods and the statistical formula of three RRT model were applied to obtain the results of ten sensitive questions of MSM(men who have sex with men ) in Beijing. The results of ten sensitive questions are as follows:
2.1 The proportion of anal sex with condoms was 78.65%.
2.2 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, was 7.2055%, 28.8687%, 55.9630% and 7.9627% respectively last month.
2.3 The proportion of average charge of commercial sex of MSM, which was classified into less than 200 RMB, 200 to 399 RMB, 400 to 599 RMB, more than 600 RMB and no commercial sex, was 3.2988%, 4.9569%, 2.6000%, 5.8566% and 87.8276% respectively last year.
2.4 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, was 8.0272%, 72.4350%, 8.2792%, 5.2110% and 6.0476 respectively last year .
2.5 The results of STD test were classified into five types, which were positive, negative, checked but not know the results, a uncertain results and not checked. The proportion of five results was 15.1704%、67.9019%、4.1940%、5.4319% and 7.3017% respectively last year.
2.6 The proportion of way(up to ejaculation orgasm) of sexual behavior, which was anal sex, oral sex and other sexual behavior for MSM, were 64.6453%, 18.7388% and 16.6159% respectively.
2.7 The proportion of Condom breakage, which was classified into broken, no damage and not use of condom for MSM, was 12.4620%, 67.7727, and 19.7653 respectively.
2.8 The average age of MSM was 21.9747 years in the first time.
2.9 The average number of different sexual partners of MSM was 3 person every month for per person .
2.10 It was 4.8 times of the number of MSM on average monthly.
3. Thirty experts all over the country evaluated the face validity and content validity of the survey methods, the rate of“excellent”and“good”was 100%. Comparing the results p got by the three sensitive questions RRT models with the valid criterion p0, there are no statistically significant difference between p and p0. So we can draw the conclusion that our survey methods and corresponding formulae are scientific, reliable and valid.
Conclusion:The methods and corresponding formulas on sensitive questions survey with the sample selected by two-stage sampling were feasible. The AIDS and STD high-risk behaviors of MSM in Beijing, such as no fixed sexual partners, anal sex, the low proportion of full use of condoms and high proportion of condoms breakage, should aroused the great concerns of our government and health sector.
引文
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