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Risk, odds & NNT 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. Absolute risk reduction = ______; number needed to treat = 1 / ARR.

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   CER − EER

   Why? CER is the control event rate and EER the experimental event rate. NNT is the number of patients treated to prevent one bad outcome; round it up.

2. Absolute risk reduction = CER − EER; number needed to treat = ______.

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   1 / ARR

   Why? CER is the control event rate and EER the experimental event rate. NNT is the number of patients treated to prevent one bad outcome; round it up.

3. In an RCT, 20% of the placebo group and 15% of the treatment group have a stroke over 5 years. Calculate the ARR, RRR and NNT.

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   ARR = 20% − 15% = 5%. RRR = 5/20 = 25%. NNT = 1/0.05 = 20 (over 5 years).

   Why? RRR = (CER − EER)/CER, i.e. ARR divided by the control event rate. The same RRR can mean very different ARRs depending on baseline risk.

4. Of 100 smokers, 60 develop cancer. Of 80 non-smokers, 20 develop cancer. Calculate the odds ratio for cancer in smokers versus non-smokers.

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   Odds in smokers = 60/40 = 1.5; odds in non-smokers = 20/60 ≈ 0.33; OR = 1.5/0.33 = 4.5.

   Why? Odds = people with the outcome ÷ people without it (not ÷ the total).

5. Of 100 smokers, 60 develop cancer. Of 80 non-smokers, 20 develop cancer. Calculate the relative risk of cancer in smokers versus non-smokers.

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   Risk in smokers = 60/100 = 0.60; risk in non-smokers = 20/80 = 0.25; RR = 0.60/0.25 = 2.4.

   Why? Risk = people with the outcome ÷ everyone in the group. The OR (4.5) exaggerates the RR (2.4) here because the outcome is common.

6. Of 100 smokers, 60 develop cancer. Of 80 non-smokers, 20 develop cancer. Calculate the absolute risk increase and the number needed to harm.

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   ARI = 0.60 − 0.25 = 0.35 (35%). NNH = 1/0.35 ≈ 2.9 (about 3): roughly 1 extra cancer for every 3 people who smoke.

   Why? For a harmful exposure the risk difference is an absolute risk increase, and its reciprocal is the number needed to harm.

7. Which measure of association does a case-control study produce, and which does a cohort study produce?

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   Case-control: odds ratio. Cohort (or RCT): relative risk.

   Why? Case-control studies start from outcome status, so true risks cannot be calculated; cohorts follow exposed and unexposed people forward.

8. In an RCT, 10% of the placebo group and 6% of the treatment group have a myocardial infarction over 3 years. Calculate the ARR, RRR and NNT.

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   ARR = 10% − 6% = 4%. RRR = 4/10 = 40%. NNT = 1/0.04 = 25 (over 3 years).

   Why? ARR = CER − EER; RRR = ARR/CER; NNT = 1/ARR, always quoted with its time frame.

9. A drug causes a rash in 7% of treated patients; 2% of the placebo group also develop a rash. Calculate the number needed to harm.

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   Absolute risk increase = 7% − 2% = 5%; NNH = 1/0.05 = 20.

   Why? For every 20 patients treated, one extra patient gets a rash because of the drug.

10. A trial reports a hazard ratio of 0.7 for death with treatment. What does this mean?

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    At any point during follow-up, the treated group's rate (hazard) of death is about 70% of the control group's — 30% lower (assuming the hazards stay proportional).

    Why? Hazard ratios compare event rates over time in time-to-event (survival) analysis, shown on Kaplan–Meier curves. HR < 1 favours treatment; HR > 1 means more events.

11. A cohort study reports a relative risk of 1.4 with a 95% confidence interval of 0.9 to 2.1. Is the result statistically significant at the 5% level?

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    No — the 95% CI includes 1, the value of no effect.

    Why? For ratios (RR, OR, HR) no effect = 1; for differences (ARR, mean difference) no effect = 0. A 95% CI that excludes the no-effect value corresponds to p < 0.05.

12. In a town of 10,000 people, 200 new cases of flu occur in one month. Flu lasts about one week (0.25 month). Estimate the incidence and the prevalence.

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    Incidence = 200/10,000 = 2% per month. Prevalence ≈ incidence × duration = 2% × 0.25 = 0.5%.

    Why? Short illnesses have a low prevalence even with a high incidence; long-lasting diseases such as diabetes have a high prevalence despite a low incidence.