论文标题
贝叶斯更新和顺序测试：克服筛选测试的推论限制
Bayesian Updating and Sequential Testing: Overcoming Inferential Limitations of Screening Tests
论文作者
论文摘要
贝叶斯定理赋予筛查测试准确性的固有局限性，这是疾病患病率的函数。我们在先前的工作中表明，测试系统可以忍受大量的患病率下降，直到某个定义明确的点被称为$ PERTICES $ $ $ threshold $，低于阳性筛选测试的可靠性会急剧下降。在此，我们建立了一个数学模型，以确定顺序测试是否克服了上述贝叶斯的局限性，从而提高了筛选测试的可靠性。我们表明，对于接近$ k $的$ρ$所需的积极预测值，所需的正测试迭代$ n_i $的数量是： 美元 其中$ n_i $ =实现$ρ$所需的测试迭代次数，所需的积极预测值，a =敏感性，b =特异性，$ ϕ $ =疾病普遍存在和$ k $ =常数。根据上述推导，我们为获得50、75、95、95和99 $ \％$获得$ρ（ϕ）$所需的测试迭代次数提供了参考表，这是各种敏感性，特异性和疾病普遍性的函数的函数。
Bayes' Theorem confers inherent limitations on the accuracy of screening tests as a function of disease prevalence. We have shown in previous work that a testing system can tolerate significant drops in prevalence, up until a certain well-defined point known as the $prevalence$ $threshold$, below which the reliability of a positive screening test drops precipitously. Herein, we establish a mathematical model to determine whether sequential testing overcomes the aforementioned Bayesian limitations and thus improves the reliability of screening tests. We show that for a desired positive predictive value of $ρ$ that approaches $k$, the number of positive test iterations $n_i$ needed is: $ n_i =\lim_{ρ\to k}\left\lceil\frac{ln\left[\frac{ρ(ϕ-1)}{ϕ(ρ-1)}\right]}{ln\left[\frac{a}{1-b}\right]}\right\rceil$ where $n_i$ = number of testing iterations necessary to achieve $ρ$, the desired positive predictive value, a = sensitivity, b = specificity, $ϕ$ = disease prevalence and $k$ = constant. Based on the aforementioned derivation, we provide reference tables for the number of test iterations needed to obtain a $ρ(ϕ)$ of 50, 75, 95 and 99$\%$ as a function of various levels of sensitivity, specificity and disease prevalence.
