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

arXiv: https://arxiv.org/abs/2007.13046 · HTML: https://mlsanity.com/paper/2007.13046/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [A Priori Determination of the Pretest Probability](https://mlsanity.com/paper/2401.04086/) (2024)

## Abstract (arXiv)

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) = fracφdisplaystyleprodi=1nanφdisplaystyleprodi=1nan+(1-φ)displaystyleprodi=1n(1-bn) If the positive serial iteration is interrupted at term position ni-k by a conflicting negative result, then the resulting negative predictive value is given by: psi(φ) = frac[(1-φ)bn-]displaystyleprod_i=b1+^b(n-1)+(1-bn+)[φ(1-an-)]displaystyleprod_i=a1+^a(n-1)+an++[(1-φ)bn-]displaystyleprod_i=b1+^b(n-1)+(1-bn+) Finally, if the negative serial iteration is interrupted at term position ni-k by a conflicting positive result, then the resulting positive predictive value is given by: λ(φ)= fracφ an+displaystyleprod_i=a1-^a(n-1)-(1-an-)φ an+displaystyleprod_i=a1-^a(n-1)-(1-an-)+[(1-φ)(1-bn+)]displaystyleprod_i=b1-^b(n-1)-bn- 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.