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Solve this question for neet pg from psm
NPV = 80/100 = 80%
The question asks for the Negative Predictive Value (NPV) of the CA-125 test.
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Let me reconstruct the 2x2 table from the given data:
Setting Up the 2x2 Table
The question states:
- Cohort of 100 tested positive by CA-125, of which 60/100 were true positive
- 100 tested negative by CA-125, of which 80/100 were true negative
| Disease + | Disease - | Total | |
|---|---|---|---|
| Test + | 60 (TP) | 40 (FP) | 100 |
| Test - | 20 (FN) | 80 (TN) | 100 |
| Total | 80 | 120 | 200 |
Formula for NPV
$$NPV = \frac{TN}{TN + FN} = \frac{80}{80 + 20} = \frac{80}{100} = \mathbf{80%}$$
Key Concept (PSM)
Negative Predictive Value (NPV) answers: "Of all the people who tested NEGATIVE, what proportion truly do NOT have the disease?"
- NPV depends heavily on disease prevalence - higher prevalence lowers NPV
- Compare with Specificity = TN/(TN+FP) = 80/120 = 66.7% (a fixed property of the test)
- NPV tells us how reassured we can be when a test is negative
Answer: NPV = 80/100 = 80%
Quick memory tip for NEET PG:
- PPV = TP / (TP + FP) - looks at the positive test column
- NPV = TN / (TN + FN) - looks at the negative test column
Solve using formula
NPV Using Direct Formula
$$\boxed{NPV = \frac{TN}{TN + FN}}$$
Identifying Values from the Question
The question gives:
- 60/100 were true positive → TP = 60, so out of 100 test-positives → FP = 40
- 80/100 were true negative → TN = 80, so out of 100 test-negatives → FN = 20
Plugging into Formula
$$NPV = \frac{TN}{TN + FN}$$
$$NPV = \frac{80}{80 + 20}$$
$$NPV = \frac{80}{100}$$
$$\boxed{NPV = 0.80 = \textbf{80%}}$$
What Each Number Means
| Symbol | Meaning | Value |
|---|---|---|
| TN | Truly disease-free among test-negatives | 80 |
| FN | Actually diseased but tested negative | 20 |
| TN + FN | Total who tested negative | 100 |
So out of 100 people who tested negative, 80 truly don't have ovarian cancer - that's your NPV = 80%.
Sensitivity and specificity formula
Sensitivity & Specificity Formulas
The 2x2 Table (Master This First)
| Disease + | Disease - | |
|---|---|---|
| Test + | TP | FP |
| Test - | FN | TN |
Sensitivity
$$\boxed{Sensitivity = \frac{TP}{TP + FN}}$$
- Denominator = all truly diseased people (entire top row of disease column)
- Answers: "Of all sick people, how many did the test correctly identify?"
- Also called: True Positive Rate
- High sensitivity = few false negatives → good for ruling OUT disease
- Mnemonic: SnNout (Sensitive test, Negative result = rules Out disease)
Specificity
$$\boxed{Specificity = \frac{TN}{TN + FP}}$$
- Denominator = all truly healthy people (entire bottom row of disease column)
- Answers: "Of all healthy people, how many did the test correctly identify?"
- Also called: True Negative Rate
- High specificity = few false positives → good for ruling IN disease
- Mnemonic: SpPin (Specific test, Positive result = rules In disease)
All 4 Formulas Together (NEET PG Must Know)
| Parameter | Formula | Denominator |
|---|---|---|
| Sensitivity | TP / (TP + FN) | All diseased |
| Specificity | TN / (TN + FP) | All healthy |
| PPV | TP / (TP + FP) | All test positive |
| NPV | TN / (TN + FN) | All test negative |
Quick Memory Trick
Sensitivity & Specificity - look DOWN the disease columns PPV & NPV - look ACROSS the test rows
- Sensitivity + False Negative Rate = 1
- Specificity + False Positive Rate = 1
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