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10 - 使用Gibbs采样器进行两次测试估计真实患病率

这个分析使用了贝叶斯 方法和 吉布斯采样器 to estimate the true animal-level prevalence of infection based on testing of individual (not pooled) samples using two (2) tests with imperfect sensitivities and/or specificities. The analysis requires prior estimates of true prevalence and sensitivity and specificity for both tests as Beta概率分布. 输出是后验概率分布 流行,敏感和特异性。 分析假设这两项测试是独立的,以疾病状态为条件。见约瑟夫等人。(1995年) 了解更多详情.

此分析所需的输入是:

The number of samples tested must be a positive integer and the number of positive samples must be an integer >=0 and <= the number of samples tested. Alpha and beta parameters for prevalence, sensitivities and specificities must be >0 and upper and lower confidence limits must be >0 and <1. Starting values for the numbers of truly infected individuals in each cell of the 2x2 table must be integers >= zero and <= the number of results in that cell. The number of iterations and the number discarded must both be positive integers (>0) and the number discarded must be less than the number of iterations.

对于该分析,可以在下表中描述使用两个测试的测试结果:

测试2:
测试1:       +ve       -ve   
+ve: a b
-ve: c d

where a, b, c & d are the observed number of sample results in each cell. A proportion of these samples in each cell will be from truly infected animals, depending on true prevalence and test sensitivities and specificities. The 吉布斯采样器 is used to estimate the true number of infected animals represented in each of the cells ( Y1, Y2, Y3 & Y4) 因此产生后验概率分布 for true prevalence, and test sensitivities and specificities that best fit the data and the prior distributions provided.

Prior estimates of the true prevalence and test sensitivity and specificity may be based on expert knowledge or on previous data. These estimates are specified as Beta概率分布, 带参数阿尔法和 公测. Beta probability distributions are commonly used to express uncertainty about a proportion based on a random sample of individuals. In this situation, if x individuals are positive for a characteristic out of n examined, then the alpha and beta parameters can be calculated as alpha = x + 1 and beta = n - x + 1. Alternatively, alpha and beta can be calculated using the Beta分发实用程序, provided estimates of the mode and 5% or 95% confidence limits are available from expert opinion.

Gibbs采样器的输出是后验概率分布:

  • 动物水平的流行;
  • 两种测试的测试灵敏度;
  • 测试两种测试的特异性;
  • 消极预测值 两个测试;和
  • 真正受感染的人数 ( Y1, Y2, Y3 & Y4) 在2x2表的每个单元格中描述对比测试结果.

这些分布由他们描述:

Because the Gibbs sampler estimates prevalence iteratively, based on the data and the prior distributions, it may take a number of 迭代 for the model to converge on the true value. Therefore, a specified number of initial iterations must be 丢弃 (not used for estimation) to allow the model to converge on the true values. This number must be sufficient to allow convergence, and should be at least 2000 - 5000. It is also important to carry out an adequate number of iterations to support inference from the results. Suggested minimum values for the total number of iterations and the number to be discarded are provided, but can be varied if desired.

此分析可能需要几分钟才能完成,具体取决于所需的迭代次数.


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内容
1 介绍
2 概观
3 贝叶斯与Frequentist方法
4 固定泳池大小和完美测试
5 固定的游泳池大小和已知的Se&Sp
6 固定的游泳池大小和不确定的Se&Sp
7 可变池大小和完美测试
8 使用Gibbs采样器汇集流行率
9 使用一次测试确实流行
10 使用Gibbs采样器进行两次测试估计真实患病率
11 估计先前Beta分布的参数
12 样本大小,完美的游泳池大小和完美的测试
13 固定池的样本大小和已知的测试灵敏度和特异性
14 固定池大小的样本大小和不确定的测试灵敏度和特异性
15 模拟固定池大小的采样
16 模拟可变池大小的采样
17 重要假设
18 汇总流行率估计有偏见!