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Positive predictive value

The positive predictive value, or precision rate, is the proportion of patients with positive test results who are correctly diagnosed. It is considered the physician's gold standard, as it reflects the probability that a positive test reflects the underlying condition being tested for.

## Worked example

Relationships among terms
 Condition (as determined by "Gold standard") True False Test outcome Positive True Positive False Positive (Type I error, P-value) → Positive predictive value Negative False Negative (Type II error) True Negative → Negative predictive value ↓ Sensitivity ↓ Specificity
A worked example
the Fecal occult blood (FOB) screen test is used in 203 people to look for bowel cancer:
 Patients with bowel cancer (as confirmed on endoscopy) True False ? FOB test Positive TP = 2 FP = 18 = TP / (TP + FP) = 2 / (2 + 18) = 2 / 20 ≡ 10% Negative FN = 1 TN = 182 = TN / (TN + FN) 182 / (1 + 182) = 182 / 183 ≡ 99.5% ↓ = TP / (TP + FN) = 2 / (2 + 1) = 2 / 3 ≡ 66.67% ↓ = TN / (FP + TN) = 182 / (18 + 182) = 182 / 200 ≡ 91%

Related calculations

• False positive rate (α) = FP / (FP + TN) = 18 / (18 + 182) = 9% = 1 - specificity
• False negative rate (β) = FN / (TP + FN) = 1 / (2 + 1) = 33% = 1 - sensitivity
• Power = 1 − β

## Definition

The Positive Predictive Value can be defined as

or, alternatively,

Where prevalence is the probability that the disease exists in the population. The positive predictive value is also known as the statistical power in statistics and probability of detection, PD , in engineering.

## Problems with positive predictive value

Predictive values are often used in medical research to evaluate the usefulness of a diagnostic test. Hence the PPV is used to indicate the probability that in case of a positive test, that the patient really has the specified disease. However there may be more than one cause for a disease and any single potential cause may not always result in the overt disease seen in a patient.

An example is the microbiological throat swab used in patients with a sore throat. Usually publications stating PPV of a throat swab are reporting on the probability that this bacteria is present in the throat, rather than that the patient is ill from the bacteria found. If presence of this bacteria always resulted in a sore throat, then the PPV would be very useful. However the bacteria may colonise individuals in a harmless way and never result in infection or disease. Sore throats occurring in these individuals is caused by other agents such as a virus. In this situation the gold standard used in the evaluation study represents only the presence of a bacteria (that might be harmless) but not a causal bacterial sore throat illness. It can be proven that this problem will affect positive predictive value far more than negative predictive value. To evaluate diagnostic tests where the gold standard looks only at potential causes of disease, one may use an extension of the predictive value termed the Etiologic Predictive Value.

## References

• Altman DG, Bland JM (9 Jul 1994). "Diagnostic Tests 2 - Predictive Values". British Medical Journal 309 (6947): 102.
• Gunnarsson RK, Lanke J. The predictive value of microbiologic diagnostic tests if asymptomatic carriers are present. Statist. Med. 2002; 21:1773-1785

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