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Diagnostic test statistics flashcards

12 high-yield MRCP Part 1 cards from the Intellect Medicos Basic sciences & statistics course. Try to answer each question before you open it — then study them properly with spaced repetition, which brings each card back just before you would forget it.

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1. Sensitivity = ______; specificity = TN / (TN + FP).

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   TP / (TP + FN)

   Why? Sensitivity is the proportion of people WITH the disease who test positive; specificity is the proportion WITHOUT the disease who test negative.

2. Sensitivity = TP / (TP + FN); specificity = ______.

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   TN / (TN + FP)

   Why? Sensitivity is the proportion of people WITH the disease who test positive; specificity is the proportion WITHOUT the disease who test negative.

3. Positive predictive value = ______; negative predictive value = TN / (TN + FN).

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   TP / (TP + FP)

   Why? Predictive values answer the patient's question: given my result, how likely is it that I do (or do not) have the disease?

4. Positive predictive value = TP / (TP + FP); negative predictive value = ______.

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   TN / (TN + FN)

   Why? Predictive values answer the patient's question: given my result, how likely is it that I do (or do not) have the disease?

5. Positive likelihood ratio = ______; negative likelihood ratio = (1 − sensitivity) / specificity.

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   sensitivity / (1 − specificity)

   Why? Likelihood ratios compare how likely a given result is in someone with the disease versus someone without it, and do not change with prevalence.

6. Positive likelihood ratio = sensitivity / (1 − specificity); negative likelihood ratio = ______.

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   (1 − sensitivity) / specificity

   Why? Likelihood ratios compare how likely a given result is in someone with the disease versus someone without it, and do not change with prevalence.

7. 100 patients are tested: 40 have the disease. The test is positive in 30 of those with disease and in 10 of the 60 without. Calculate the sensitivity and specificity.

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   Sensitivity = 30/40 = 75%. Specificity = 50/60 ≈ 83%.

   Why? Draw the 2x2 table: TP 30, FN 10, FP 10, TN 50.

8. Which test characteristics change when the prevalence of the disease changes?

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   The predictive values: PPV rises and NPV falls as prevalence rises. Sensitivity, specificity and likelihood ratios do not change.

   Why? In a low-prevalence population most positives are false positives, so the same test has a lower PPV.

9. A patient's pre-test probability of disease is 40%. The test has a positive likelihood ratio of 4.5 and comes back positive. What is the post-test probability?

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   Pre-test odds = 0.4/0.6 ≈ 0.67; post-test odds = 0.67 × 4.5 = 3; post-test probability = 3/(1 + 3) = 75%.

   Why? Convert probability to odds, multiply by the likelihood ratio, then convert back: probability = odds/(1 + odds).

10. A screening test with 90% sensitivity and 90% specificity is used in 1,000 people. The prevalence of the disease is 1%. What is the positive predictive value?

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    About 8%: TP = 9 and FP = 99, so PPV = 9/108 ≈ 8.3%.

    Why? 10 people have the disease (9 test positive); 990 do not, and 10% of them (99) test falsely positive. In low-prevalence settings most positive results are false positives.

11. A test has a sensitivity of 80% and a specificity of 90%. Calculate the positive and negative likelihood ratios.

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    LR+ = 0.8/(1 − 0.9) = 8. LR− = (1 − 0.8)/0.9 ≈ 0.22.

    Why? An LR+ above 10 or an LR− below 0.1 causes a large shift in probability; values close to 1 barely change it.

12. A patient's pre-test probability of disease is 50%. A test with a negative likelihood ratio of 0.2 comes back negative. What is the post-test probability?

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    Pre-test odds = 0.5/0.5 = 1; post-test odds = 1 × 0.2 = 0.2; post-test probability = 0.2/1.2 ≈ 17%.

    Why? Probability → odds: p/(1 − p). Multiply by the LR. Odds → probability: odds/(1 + odds).