# Screening tests in Series and Parallel

### A. Parallel testing

2 screening tests are applied simultaneously:

1. Disease positives: Test positive in either of the two tests (If one test is negative, still the other test can prove positive)
2. Disease negatives: Test negative in both the tests (If one test is negative, the other test must also be negative)

So, this test will have:

1. Less false negatives (increased sensitivity and increased negative predictive value or NPV)
2. More false positives (decreased sensitivity and decreased positive predictive value or PPV)

### B. Series testing

After the 1st screening test is conducted, those who test positive are onyl tested with the 2nd screening test:

1. Disease positives: Those who test positive in both the tests (If 1st test is positive, he must test positive in 2nd test as well)
2. Disease negatives: Those who test negative in either of the tests

So, this test will have:

1. Less false positives: Increased specificity and PPV
2. More false negatives: Decreased sensitivity and NPV

#### Formulae for combined specificity and sensitivity

A. Parallel testing:

1. Combined specificity = Specificity of test A X Specificity of test B
2. Combined sensitivity = Sensitivity of test A + Sensitivity of test B – [Sensitivity of test A X Sensitivity of test B]

B. Series testing:

1. Combined specificity = Specificity of test A + Specificity of test B – [Specificity of test A X Specificity of test B]
2. Combined sensitivity = Sensitivity of test A X Sensitivity of test B

Mnemonic:

Remember:

1. Sensitivity is True Positive rate
2. Specificity is True Negative rate

In probability testing, AND = multiplication and OR = Addition

`Example: Probability of getting head in coin and/or 1 in dice`

In parallel testing:

1. Negative (A and B) = Specificity A X Specificity B

2. Positive (A or B) = Sensitivity A + Sensitivity B – [Sensitivity A X Sensitivity B]

In series testing:

1. Negative (A or B) = Specificity A + Specificity B – [Specificity A X Specificity B]

2. Positive (A and B) = Sensitivity A X Sensitivity B

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