Question:
A diagnostic researcher is analysing the performance of a screening test. Which expression correctly represents the probability that a person who tests positive truly has the disease?
a) Sensitivity ÷ (1 − specificity)
b) True positives ÷ (true positives + false positives)
c) True negatives ÷ (true negatives + false positives)
d) True negatives ÷ (true negatives + false negatives)
e) True positives ÷ (true positives + false negatives)
Answer:
b) True positives ÷ (true positives + false positives)
Detailed Explanation:
Positive Predictive Value (PPV) answers a clinically practical question:
👉 “If the test is positive, what is the chance the patient actually has the disease?”
Mathematically:
- True Positives (TP): correctly identified diseased patients
- False Positives (FP): healthy individuals incorrectly labeled as diseased
So PPV focuses only on positive test results.
Why others are wrong:
- Sensitivity / (1 − specificity) → Likelihood ratio for a positive test (LR+)
- TN / (TN + FP) → Specificity
- TN / (TN + FN) → Negative predictive value (NPV)
- TP / (TP + FN) → Sensitivity
High-Yield Concept:
- PPV depends heavily on disease prevalence
- Higher prevalence → higher PPV
- Lower prevalence → more false positives → lower PPV
Cheat Sheet for Exam
| Measure | Formula | Meaning |
|---|---|---|
| Sensitivity | TP / (TP + FN) | Detect disease if present |
| Specificity | TN / (TN + FP) | Exclude disease if absent |
| PPV | TP / (TP + FP) | Chance disease if test positive |
| NPV | TN / (TN + FN) | Chance no disease if test negative |
| LR+ | Sens / (1 − Spec) | Rule IN disease |
| LR− | (1 − Sens) / Spec | Rule OUT disease |
🔑 Memory trick:
- PPV → “Positive test → Positive disease”
- NPV → “Negative test → No disease”
Flash Cards
Flashcard 1
Q: What does PPV represent?
A: Probability that a person with a positive test truly has the disease.
Flashcard 2
Q: Formula of PPV?
A: TP / (TP + FP)
Flashcard 3
Q: Does PPV depend on prevalence?
A: Yes, strongly dependent.
Flashcard 4
Q: What happens to PPV when prevalence increases?
A: PPV increases.
Flashcard 5
Q: Which metric is independent of prevalence?
A: Likelihood ratios.
Challenging MCQs
MCQ 1
A screening test yields many false positives in a low-prevalence population. Which parameter will be most affected?
a) Sensitivity
b) Specificity
c) Positive predictive value
d) Likelihood ratio positive
Answer: c
Explanation: PPV falls in low prevalence due to increased proportion of false positives.
MCQ 2
Which of the following is FALSE regarding PPV?
a) It increases with disease prevalence
b) It reflects post-test probability
c) It depends on specificity
d) It is independent of prevalence
Answer: d
Explanation: PPV is highly prevalence dependent.
MCQ 3
A test has high sensitivity but low PPV. What is the most likely reason?
a) High disease prevalence
b) Low disease prevalence
c) High specificity
d) Low false negatives
Answer: b
Explanation: Low prevalence → many false positives → low PPV.
MCQ 4
Which parameter answers: “If test is positive, how likely disease is present?”
a) Sensitivity
b) Specificity
c) PPV
d) NPV
Answer: c
Explanation: This is the exact definition of PPV.
MCQ 5
Which formula corresponds to sensitivity?
a) TP / (TP + FP)
b) TN / (TN + FP)
c) TP / (TP + FN)
d) TN / (TN + FN)
Answer: c
Explanation: Sensitivity = ability to detect disease → TP / (TP + FN).
MCQ 6 (Advanced)
Two populations undergo the same test. Population A has higher PPV than B. Which is most likely?
a) Population A has lower prevalence
b) Population A has higher prevalence
c) Test sensitivity is lower in A
d) Test specificity is irrelevant
Answer: b
Explanation: Higher prevalence → higher PPV.
Summary for Quick Exam Revision
Positive predictive value (PPV) is defined as the probability that a person with a positive test result actually has the disease and is calculated using the formula TP divided by TP plus FP. It focuses exclusively on individuals who test positive and distinguishes true positives from false positives. PPV is highly dependent on disease prevalence; as prevalence increases, PPV rises, and as prevalence decreases, PPV falls due to a higher proportion of false positives. It differs from sensitivity and specificity, which are intrinsic test characteristics, whereas PPV reflects real-world clinical usefulness. Sensitivity measures the ability to detect disease (TP/(TP+FN)), while specificity measures the ability to exclude disease (TN/(TN+FP)). Negative predictive value (NPV) reflects the probability of not having disease when the test is negative. Likelihood ratios are independent of prevalence and are useful for diagnostic reasoning. In clinical practice, PPV is crucial when interpreting positive results, especially in screening scenarios where prevalence significantly alters diagnostic confidence.