Worked Example
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- Relationships among terms
| Condition (as determined by "Gold standard") |
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| Condition Positive | Condition Negative | |||
| Test Outcome |
Test Outcome Positive |
True Positive | False Positive (Type I error) |
Positive predictive value = Σ True Positive Σ Test Outcome Positive |
| Test Outcome Negative |
False Negative (Type II error) |
True Negative | Negative predictive value = Σ True Negative Σ Test Outcome Negative |
|
| Sensitivity = Σ True Positive Σ Condition Positive |
Specificity = Σ True Negative Σ Condition Negative |
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- A worked example
- A diagnostic test with sensitivity 67% and specificity 91% is applied to 2030 people to look for a disorder with a population prevalence of 1.48%
| Patients with bowel cancer (as confirmed on endoscopy) |
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| Condition Positive | Condition Negative | |||
| Fecal Occult Blood Screen Test Outcome |
Test Outcome Positive |
True Positive (TP) = 20 |
False Positive (FP) = 180 |
Positive predictive value
= TP / (TP + FP) = 20 / (20 + 180) = 10% |
| Test Outcome Negative |
False Negative (FN) = 10 |
True Negative (TN) = 1820 |
Negative predictive value
= TN / (FN + TN) = 1820 / (10 + 1820) ≈ 99.5% |
|
| Sensitivity
= TP / (TP + FN) = 20 / (20 + 10) ≈ 67% |
Specificity
= TN / (FP + TN) = 1820 / (180 + 1820) = 91% |
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Related calculations
- False positive rate (α) = type I error = 1 − specificity = FP / (FP + TN) = 180 / (180 + 1820) = 9%
- False negative rate (β) = type II error = 1 − sensitivity = FN / (TP + FN) = 10 / (20 + 10) = 33%
- Power = sensitivity = 1 − β
- Likelihood ratio positive = sensitivity / (1 − specificity) = 66.67% / (1 − 91%) = 7.4
- Likelihood ratio negative = (1 − sensitivity) / specificity = (1 − 66.67%) / 91% = 0.37
Hence with large numbers of false positives and few false negatives, a positive screen test is in itself poor at confirming the disorder (PPV = 10%) and further investigations must be undertaken; it did, however, correctly identify 66.7% of all cases (the sensitivity). However as a screening test, a negative result is very good at reassuring that a patient does not have the disorder (NPV = 99.5%) and at this initial screen correctly identifies 91% of those who do not have cancer (the specificity).
Read more about this topic: Sensitivity And Specificity
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