MRCEM Primary Diagnostic Test Calculations—Sensitivity, Specificity and Likelihood Ratios

A diagnostic test can detect most people with a disease yet still produce a surprisingly large number of false-positive results. Understanding why is more useful than memorising four fractions without knowing which patients belong in each denominator.

This guide builds a complete calculation method for MRCEM Primary: organise the data, identify the group in the question, calculate the relevant measure and interpret what the answer means. You will then use likelihood ratios to move from a pre-test probability to a post-test probability, before testing yourself with five original SBAs.

Use it alongside your MRCEM Primary revision plan. Every numerical test below is hypothetical: these are examination exercises, not performance estimates for a named clinical assay.

Exam context: use the syllabus for your sitting

As checked on 31 October 2026, RCEM describes MRCEM Primary as 180 single-best-answer questions in three hours. Its announcement states that the updated Basic Sciences Syllabus becomes the official reference from the 21 April 2027 examination onwards. Evidence-based medicine remains one of the named disciplines. Check the official examination information and syllabus announcement for your sitting; this article does not claim a fixed diagnostic-statistics question allocation.

1. Build the diagnostic 2×2 table

Separate the test result from the reference standard

The index test is the test being evaluated. The reference standard establishes whether the target condition is present for the purposes of the study. A positive index test does not automatically mean disease is present: disagreement between the two classifications creates false positives and false negatives. Cochrane's diagnostic-test overview explains this distinction.

Populate the table and check the totals

Imagine a hypothetical study of 1,000 people. The reference standard identifies disease in 200. The index test is positive in 180 of those 200 and in 80 of the 800 people without disease.

Start with those four facts. Among the people with disease, 200 − 180 = 20 must have a negative test. Among those without disease, 800 − 80 = 720 must have a negative test. Then add the row totals.

Both routes to the grand total must agree: 200 + 800 and 260 + 740 each equal 1,000. This simple check catches transposed figures before they contaminate every later calculation.

2. Sensitivity, specificity and predictive values

Choose the denominator before calculating

Ask which group the question starts with. Sensitivity and specificity start with disease status. Predictive values start with the test result. The word “positive” alone does not identify the formula: both sensitivity and positive predictive value involve true positives, but they divide by different groups.

Translate each answer into a sentence

In our example, the test detects 90% of people who have disease. However, only about 69% of positive results occur in people with disease. Those statements answer different questions, so there is no contradiction.

Similarly, approximately 97.3% of people with a negative result are disease-free in this study. The remaining 2.7% have disease despite testing negative. A useful self-check is that NPV and the probability of disease among test-negative people add to 100%.

3. Why prevalence changes the answer

Repeat the same test in a lower-prevalence population

Now consider another hypothetical population of 1,000 people, with disease present in only 20. For this exercise, hold sensitivity and specificity at 90%. The test detects 18 of the 20 people with disease and misses two. Among the 980 without disease, 98 test positive and 882 test negative.

The lower-prevalence population contains many more people without disease. Even a 10% false-positive rate therefore generates substantially more false positives than true positives. The test characteristics in our model have not deteriorated, but the meaning of a positive result has changed.

Distinguish prevalence from individual pre-test probability

Prevalence describes a population. A patient's pre-test probability also reflects their symptoms, signs, risk factors and selection into a diagnostic pathway. Population prevalence may inform that estimate, but it should not automatically replace a clinical assessment.

Holding sensitivity and specificity constant makes the arithmetic comparison clear. In real studies, different patient spectra, thresholds and methods may change measured performance. Do not turn a simplifying assumption into a promise that the test performs identically in every setting.

4. Likelihood ratios and post-test probability

Calculate LR+ and LR−

A likelihood ratio compares how often a particular test result occurs with disease versus without disease. For a binary test, LR+ = sensitivity / (1 − specificity), while LR− = (1 − sensitivity) / specificity. Use proportions consistently. These relationships are described in the Cochrane diagnostic-test handbook chapter.

For our 90% sensitive and 90% specific test, LR+ = 0.90 / 0.10 = 9. LR− = 0.10 / 0.90 = 1/9, approximately 0.111. The positive result multiplies disease odds by nine; the negative result reduces them to one ninth of their starting value.

Convert probability to odds, multiply, then convert back

The critical point is that a likelihood ratio multiplies odds, not probability. The three-step method is: pre-test odds = p / (1 − p); post-test odds = pre-test odds × LR; post-test probability = post-test odds / (1 + post-test odds). The BMJ likelihood-ratio teaching paper describes this Bayesian update.

Start with a pre-test probability of 20%, so p = 0.20. Pre-test odds are 0.20 / 0.80 = 0.25. After a positive result, post-test odds are 0.25 × 9 = 2.25. Convert back: 2.25 / 3.25 = 0.6923, approximately 69.2%.

This agrees with the PPV from our original table. The count-based method and the odds-based method reach the same answer when their assumptions match. Multiplying 20% directly by nine would give 180%, which immediately signals a faulty method.

Interpret a negative result

Using the same 20% pre-test probability, the odds after a negative result are 0.25 × 1/9 = 1/36. The resulting probability is (1/36) / (1 + 1/36) = 1/37, approximately 2.7%. This is the probability of disease after a negative result, not the NPV. The NPV is its complement, approximately 97.3%.

Now change only the starting probability to 80%. Pre-test odds become 0.80 / 0.20 = 4. After a negative result, they become 4/9. The post-test disease probability is (4/9) / (13/9) = 4/13, approximately 30.8%. The same test result can leave very different residual risks.

5. Avoid the common traps

Go beyond “rule in” and “rule out” mnemonics

SnNout and SpPin are reminders, not guarantees. Whether a result provides enough reassurance depends on the complete test characteristics, starting probability and the decision threshold. Oxford's CEBM discussion is useful further reading. Our 80% pre-test example shows why a negative result cannot be interpreted without context.

Check what the number actually represents

6. Five original MRCEM Primary practice SBAs

These are original educational questions, not official or recalled RCEM examination material. Each uses hypothetical data. Attempt them before reading the explanations.

Questions

Question 1. A test is evaluated in 600 people. Disease is present in 150. The test is positive in 120 people with disease and 90 people without disease. What is its sensitivity?

• A. 20%

• B. 35%

• C. 57.1%

• D. 80%

• E. 92.3%

Question 2. Using the same study, what is the probability that a person with a positive result has disease?

• A. 20%

• B. 35%

• C. 57.1%

• D. 80%

• E. 92.3%

Question 3. A test has sensitivity 96% and specificity 80%. What is its negative likelihood ratio?

• A. 0.04

• B. 0.05

• C. 0.20

• D. 1.20

• E. 4.80

Question 4. A patient has a pre-test disease probability of 25%. A positive test has LR+ = 6. What is the post-test probability, to the nearest whole percentage?

• A. 40%

• B. 60%

• C. 67%

• D. 86%

• E. 150%

Question 5. A test is applied to a population with lower disease prevalence. Assume its sensitivity and specificity remain fixed, both strictly between 0% and 100%. Which change is expected?

• A. PPV rises and NPV falls

• B. PPV falls and NPV rises

• C. Both PPV and NPV rise

• D. Both PPV and NPV fall

• E. Both remain unchanged

Answers and explanations

1. D — 80%. Sensitivity = 120 / 150 = 80%. A is the false-negative rate: 30 / 150. B is the overall positive-test proportion: 210 / 600. C is PPV: 120 / 210. E is NPV: 360 / 390. Although specificity also happens to be 80% here, sensitivity is justified by the disease-present denominator.

2. C — 57.1%. There are 120 + 90 = 210 positive tests, of which 120 are true positives. PPV = 120 / 210 ≈ 57.1%. A describes the false-negative rate in this dataset; B describes how often the test is positive across the entire sample. D is sensitivity, and also specificity in this example. E describes the disease-free proportion among negative results. None answers the question about positive results.

3. B — 0.05. LR− = (1 − 0.96) / 0.80 = 0.04 / 0.80 = 0.05. A stops at the false-negative rate without dividing by specificity. C is the false-positive rate. D divides sensitivity by specificity, which is neither of the requested likelihood-ratio formulas. E is LR+: 0.96 / 0.20 = 4.80.

4. C — 67%. Pre-test odds = 0.25 / 0.75 = 1/3. Post-test odds = (1/3) × 6 = 2. Probability = 2 / 3 ≈ 66.7%, which rounds to 67%. A and B do not follow the odds conversion. D approximates 6 / 7, treating the LR itself as the post-test odds and ignoring the initial odds. E results from multiplying 25% directly by six and is not a possible probability.

5. B — PPV falls and NPV rises. With fewer disease cases relative to non-cases, a smaller proportion of positive results are true positives, while a larger proportion of negative results are true negatives. A reverses both effects. C gets NPV right but PPV wrong. D gets PPV right but NPV wrong. E confuses fixed sensitivity and specificity with fixed predictive values. The earlier 1,000-person comparison demonstrates this numerically.

7. Frequently asked questions and revision plan

Is sensitivity the same as positive predictive value?

No. Sensitivity asks how many people with disease test positive. PPV asks how many people with a positive test have disease. Underline the group named in the question before choosing the denominator.

Can a likelihood ratio exceed one?

Yes. It compares two probabilities and is not itself a probability. In our worked example LR+ is nine. An LR of one leaves the odds unchanged; an LR above one raises them and an LR below one lowers them.

Does a negative result exclude disease?

Not automatically. Calculate or estimate the residual risk in the relevant clinical context. Our hypothetical test reduced disease probability from 20% to 2.7%, but from 80% to 30.8%. Whether the remaining risk is acceptable depends on the condition and diagnostic pathway.

How should I practise diagnostic-statistics questions?

Start by drawing an empty table from memory. Populate it from a short stem, check the totals and write down the denominator in words. Calculate the four basic measures, then work through one positive and one negative likelihood-ratio update. Finally, change the prevalence while keeping test characteristics fixed and predict what will happen before doing the arithmetic.

When you make a mistake, record the reasoning error rather than only the correct percentage. “I used all positive tests when the question asked about people with disease” is a useful revision note. “The answer was 80%” is much less transferable. For other EBM topics, read our broader statistics and evidence-based medicine guide.

Put your revision into practice

Build on these examples with the StudyMedical MRCEM Primary question bank. It offers over 7,800 questions, explanations with teaching diagrams, custom topic-based quizzes, timed quizzes and the option to revisit previously incorrect answers. Try free sample questions without signing up, then choose a plan that suits your revision.

References and further reading

• RCEM: MRCEM examination information.

• RCEM: New Basic Sciences Syllabus to Apply from 2027, 3 August 2026.

• Cochrane: What are diagnostic test accuracy reviews?

• Cochrane DTA Handbook: Chapter 10, diagnostic-accuracy measures and synthesis.

• Deeks and Altman: Diagnostic tests 4 — likelihood ratios, BMJ 2004;329:168.

• Oxford CEBM: SpPin and SnNout.