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Using Bayes' Theorem, we derive generalized equations to determine thepositive and negative predictive value of screening tests undertakensequentially. Where a is the sensitivity, b is the specificity, $\phi$ is thepre-test probability, the combined positive predictive value, $\rho(\phi)$, of$n$ serial positive tests, is described by:  $\rho(\phi) =\frac{\phi\displaystyle\prod_{i=1}^{n}a_n}{\phi\displaystyle\prod_{i=1}^{n}a_n+(1-\phi)\displaystyle\prod_{i=1}^{n}(1-b_n)}$  If the positive serial iteration is interrupted at term position $n_i-k$ by aconflicting negative result, then the resulting negative predictive value isgiven by:  $\psi(\phi) =\frac{[(1-\phi)b_{n-}]\displaystyle\prod_{i=b_{1+}}^{b_{(n-1)+}}(1-b_{n+})}{[\phi(1-a_{n-})]\displaystyle\prod_{i=a_{1+}}^{a_{(n-1)+}}a_{n+}+[(1-\phi)b_{n-}]\displaystyle\prod_{i=b_{1+}}^{b_{(n-1)+}}(1-b_{n+})}$  Finally, if the negative serial iteration is interrupted at term position$n_i-k$ by a conflicting positive result, then the resulting positivepredictive value is given by: $\lambda(\phi)= \frac{\phia_{n+}\displaystyle\prod_{i=a_{1-}}^{a_{(n-1)-}}(1-a_{n-})}{\phia_{n+}\displaystyle\prod_{i=a_{1-}}^{a_{(n-1)-}}(1-a_{n-})+[(1-\phi)(1-b_{n+})]\displaystyle\prod_{i=b_{1-}}^{b_{(n-1)-}}b_{n-}}$  The aforementioned equations provide a measure of the predictive value indifferent possible scenarios in which serial testing is undertaken. Theirclinical utility is best observed in conditions with low pre-test probabilitywhere single tests are insufficient to achieve clinically significantpredictive values and likewise, in clinical scenarios with a high pre-testprobability where confirmation of disease status is critical.

Derivation of Generalized Equations for the Predictive Value of Sequential Screening Tests