论文标题
衍生的一般方程式用于顺序筛选测试的预测值
Derivation of Generalized Equations for the Predictive Value of Sequential Screening Tests
论文作者
论文摘要
使用贝叶斯定理，我们得出了广义方程，以顺序确定筛选测试的正和负预测值。如果a是敏感性，则b是特异性，$ ϕ $是预测试概率，合并的正预测值$ρ（ϕ）$，$ n $序列阳性测试，由以下方式描述。 $ρ（ϕ）= \ frac {ϕ \ displaystyle \ prod_ {i = 1}^{n} a_n} {ϕ \ displayStyle \ prod_ {i = 1}^{n}^{n} a_n = a_n+（1- ϕ） 如果正式位置$ n_i-k $中断正序列迭代，则由矛盾的负面结果，则由此产生的负预测值由以下方式给出： $ψ（ϕ）= \ frac {[（1- ϕ）b_ {n - }] \ displayStyle \ prod_ {i = b_ {1+}}}^{b _ {（n-1）+}}（1-b_ {n+}）} rod_ {i = a_ {1+}}^{a _ {（n-1）+}} a_ {n+}+[（1- ϕ）b_ {n-}] \ displayStyle \ prod_ {i = b_ = b_ {1+}}}}^{b _ {b _ {n-1）} =} 最后，如果负相互矛盾的积极结果在期限位置$ n_i-k $中断负序列迭代，则结果的正预测值由以下方式给出：$λ（ϕ）= \ frac {ϕa_ {n+} \ displaystyle \ prod_ {i = a_ {1-}}}^{a _ {（n-1） - }}}}（1-a_ {n-}}} _ {1 - }}^{a _ {（n-1） - }}}（1-a_ {n-}）+[（1- ϕ）（1-b_ {n+}）] \ displayStyStyle \ prod_ {i = b_ = b_ {1-}}}}}^{b _ {b _ {n-1）} 在进行串行测试的不同可能情况下，上述方程式提供了预测价值的度量。在预测试概率较低的情况下，最好观察到它们的临床实用性，而单个测试不足以实现临床上显着的预测值，而同样，在临床情况下，在具有较高测试概率的临床情况下，确认疾病状况至关重要。
Using Bayes' Theorem, we derive generalized equations to determine the positive and negative predictive value of screening tests undertaken sequentially. Where a is the sensitivity, b is the specificity, $ϕ$ is the pre-test probability, the combined positive predictive value, $ρ(ϕ)$, of $n$ serial positive tests, is described by: $ρ(ϕ) = \frac{ϕ\displaystyle\prod_{i=1}^{n}a_n}{ϕ\displaystyle\prod_{i=1}^{n}a_n+(1-ϕ)\displaystyle\prod_{i=1}^{n}(1-b_n)}$ If the positive serial iteration is interrupted at term position $n_i-k$ by a conflicting negative result, then the resulting negative predictive value is given by: $ψ(ϕ) = \frac{[(1-ϕ)b_{n-}]\displaystyle\prod_{i=b_{1+}}^{b_{(n-1)+}}(1-b_{n+})}{[ϕ(1-a_{n-})]\displaystyle\prod_{i=a_{1+}}^{a_{(n-1)+}}a_{n+}+[(1-ϕ)b_{n-}]\displaystyle\prod_{i=b_{1+}}^{b_{(n-1)+}}(1-b_{n+})}$ Finally, if the negative serial iteration is interrupted at term position $n_i-k$ by a conflicting positive result, then the resulting positive predictive value is given by: $λ(ϕ)= \frac{ϕa_{n+}\displaystyle\prod_{i=a_{1-}}^{a_{(n-1)-}}(1-a_{n-})}{ϕa_{n+}\displaystyle\prod_{i=a_{1-}}^{a_{(n-1)-}}(1-a_{n-})+[(1-ϕ)(1-b_{n+})]\displaystyle\prod_{i=b_{1-}}^{b_{(n-1)-}}b_{n-}}$ The aforementioned equations provide a measure of the predictive value in different possible scenarios in which serial testing is undertaken. Their clinical utility is best observed in conditions with low pre-test probability where single tests are insufficient to achieve clinically significant predictive values and likewise, in clinical scenarios with a high pre-test probability where confirmation of disease status is critical.
