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PPV/NPV, Likelihood ratio, Sensitivity/Specificity

03 Jun 2025 • 1 min read

PPV/NPV

Given a positive test result, what is the probability that the patient actually has the disease?
\(PPV = \frac{\text{true positives (TP)}}{\text{TP} + \text{false positives (FP)}}\)
\(NPV = \frac{\text{true negative (TN)}}{\text{TN} + \text{false negatives(FN)}}\)

\(\text{Positive likelyhood ratio} = \frac{\text{true positives (TP)}}{\text{false positives (FP)}}\)
- A positive likelihood ratio of greater than one conveys that a positive result is more likely to be a true positive rather than a false positive
\(\text{Negativelikelyhood ratio} = \frac{\text{false negative (FN)}}{\text{true negative (TN)}}\)
- A negative likelihood ratio of greater than one conveys that a negative result means that they may not have the disease

High Sensitivity -> Low False Negative-> SnOut
- \(\text{Sensitivity}= \frac{\text{TP}}{\text{TP}+\text{FN}}\)
- Also 1-false negatives
- It represents the probability that a patient who genuinely has a disease will test positive for it. A test with high sensitivity is effective at ruling out the disease in those who test negative, as it rarely misses true cases.
  - A test is described as sensitive if it has a high likelihood of correctly identifying those with the disease, and therefore a low likelihood of a false negative (low type 2 error)
High Specificity -> Low False Positive-> SpIn
- \(\text{Specificity }= \frac{\text{TN}}{\text{TN}+\text{FP}}\)
- Also 1-false positives
- Specificity represents the probability that a patient without the disease will have a negative test result. A high specificity indicates a low false-positive rate, meaning the test is reliable in ruling in the presence of the disease when the result is positive.