贝叶斯分组检测回归与无形状稀释曲线
Bayesian Group Testing Regression with a Shape-Free Dilution Curve
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中文总结 AI 辅助
提出BADGER模型，用无形状稀释曲线和Dirichlet先验建模分组检测灵敏度，通过精确Gibbs采样推断，并用贝叶斯因子衡量稀释证据，模拟和实际数据验证有效。
中文摘要 AI 辅助
分组检测通过合并样本来降低筛查成本，但将阳性样本与阴性样本混合会降低检测灵敏度，因此合并检测的灵敏度取决于其中阳性样本的数量。分组检测的回归模型通过固定稀释效应依赖关系的一参数形状的子模型来适应这一稀释效应。我们提出了BADGER（分组检测回归中稀释的贝叶斯分析），这是一种包含无形状稀释曲线的回归模型。合并灵敏度被建模为非递减函数，由具有Dirichlet先验的非负增量表示，从而使参数子模型成为特例。通过适当的增广，BADGER的每个全条件分布都具有闭式形式，推断通过精确的Gibbs采样器进行。稀释的证据通过从后验抽样计算得到的贝叶斯因子来衡量。我们通过不同稀释形状、患病率和合并规模的模拟研究验证了BADGER模型。我们进一步将该方法应用于一项全国健康调查中的戊型肝炎血清学数据。
英文摘要
Group testing pools specimens to cut the cost of screening, but pooling positive specimens with negative ones lowers assay sensitivity, so that the sensitivity of a pooled test depends on how many of its members are positive. Regression models for group testing accommodate this dilution effect through submodels that fix a one-parameter shape for that dependence. We propose BADGER (Bayesian Analysis of Dilution in Group tEsting Regression), a regression model incorporating a shape-free dilution curve. The pooled sensitivity is modeled as a nondecreasing function represented by nonnegative increments with a Dirichlet prior, so that the parametric submodels become special cases. By an appropriate augmentation, every full conditional of BADGER is in closed form and inference is carried out by an exact Gibbs sampler. The evidence for dilution is measured by a Bayes factor computed from the posterior draws. We validate the BADGER model through simulation studies across different dilution shapes, prevalences and pool sizes. We further illustrate the method on hepatitis E serology from a national health survey.
