Module 14 of 14 · 12 min
Biostatistics
Interpreting trial results for patients and prescribers means turning event rates into ARR, RRR and NNT; licensing exams routinely give a trial table and ask for one of these.
🧠 "NNT is 1 over the Absolute" — if it isn't absolute, it isn't NNT.
📌 Memorize these
- ARR
- CER − EER
- RRR
- (CER − EER) ÷ CER
- NNT
- 1 ÷ ARRround UP
- NNH
- 1 ÷ ARIround UP
- Relative risk
- $\frac{a/(a+b)}{c/(c+d)}$
- Odds ratio
- $\frac{a\times d}{b\times c}$
Event rates are proportions: control event rate (CER) and experimental event rate (EER). Convert percentages to decimals before taking 1/ARR.
ARR is the absolute difference; RRR expresses that difference as a fraction of the control rate, so RRR always looks bigger. NNT uses ARR, never RRR.
For harms, the same arithmetic gives the absolute risk increase (ARI) and number needed to harm, $\text{NNH}=1/\text{ARI}$. Round NNT and NNH up to the next whole patient.
From a 2×2 table (a = exposed with event, b = exposed without, c = unexposed with event, d = unexposed without): $RR=\dfrac{a/(a+b)}{c/(c+d)}$ and $OR=\dfrac{a\times d}{b\times c}$.
🧭 The method
- 1Identify the control and treatment groups and their event rates (as decimals).
- 2ARR (or ARI) = difference in rates.
- 3RRR = ARR ÷ CER; RR = EER ÷ CER.
- 4NNT (or NNH) = 1 ÷ ARR, rounded UP; state the time frame of the trial.
- 5For a 2×2 table, label a, b, c, d before calculating RR or OR.
Before each reveal, predict the next step — then check.
Over 2 years, stroke occurred in 12% of patients on placebo and 8% on the study drug. Calculate ARR, RRR and NNT.
- 1
Write the rates as decimals.
$$CER=0.12,\quad EER=0.08$$ Absolute risk reduction.
$$\text{ARR}=0.12-0.08=0.04\ (4\%)$$Relative risk reduction.
$$\text{RRR}=\frac{0.04}{0.12}=0.333\ (33.3\%)$$Number needed to treat (round up).
$$\text{NNT}=\frac{1}{0.04}=25$$
Same method — the last steps are yours. Work on paper, then reveal.
Bleeding occurred in 30 of 500 patients on the drug and 20 of 500 on placebo. What is the number needed to harm?
- 1
Event rates.
$$\frac{30}{500}=0.06,\quad\frac{20}{500}=0.04$$ - 2
Your turn
Now you: absolute risk increase.
Work it out on paper, then reveal.
$$\text{ARI}=0.06-0.04=0.02$$ - 3
Your turn
Now you: NNH.
Work it out on paper, then reveal.
$$\text{NNH}=\frac{1}{0.02}=50$$
Type your number. Your first try decides when this module comes back for review.
Event rate 20% with control and 15% with treatment. What is the ARR (%)?
Subtract the rates.
= 5 %
Event rate 10% with placebo and 7.5% with treatment. What is the RRR (%)?
ARR divided by the control rate.
= 25 %
Event rate 9% with placebo and 6% with treatment over 1 year. What is the NNT?
1/ARR, then round UP — never down.
= 34 patients
In a cohort, 40 of 200 exposed people and 20 of 200 unexposed people developed the outcome. What is the relative risk?
Risk in exposed ÷ risk in unexposed.
= 2
Using the same table (40 of 200 exposed and 20 of 200 unexposed with the outcome), what is the odds ratio?
a = 40, b = 160, c = 20, d = 180. OR = ad / bc.
= 2.25
A trial table reports 3-year mortality of 8.0% with placebo and 6.2% with treatment, and an RRR of 22.5%. How many patients must be treated for 3 years to prevent one death?
Ignore the RRR — NNT uses the absolute difference.
= 56 patients
⚠️ Tricky
In a 5-year trial, stroke occurred at 4.2% per year with placebo and 3.1% per year with treatment (assume constant annual rates, so 5-year risk = 5 × annual risk). How many patients must be treated for 5 years to prevent one stroke?
Match the NNT to the time frame asked: use the 5-year ARR, then round up.
= 19 patients
⚠️ The trap: Using the annual ARR (1.1%) gives an NNT of 91, which is the number to treat for one year, not five.
⚠️ Tricky
A harm was seen in 30 of 250 patients on the drug and 16 of 200 on placebo. What is the number needed to harm (NNH)?
The groups are different sizes: compare rates, not raw counts.
= 25 patients
⚠️ The trap: Subtracting the counts (30 − 16 = 14) and dividing by 250 gives an ARI of 5.6% and an NNH of 18.
⚠️ Tricky
A screening test has sensitivity 90% and specificity 95%. In the community being screened, prevalence is 2%. What is the positive predictive value (%)?
Picture 1000 people: 20 have the disease. Count true positives and false positives.
= 26.9 %
⚠️ The trap: Quoting the 90% sensitivity as the chance that a positive patient has the disease ignores the low prevalence; the real PPV is 26.9%.
⚠️ Tricky
A trial reports that the odds of responding to a drug are 0.6. What percentage of patients respond?
Odds = responders : non-responders. Probability = odds ÷ (1 + odds).
= 37.5 %
⚠️ The trap: Reading odds of 0.6 as a 60% response rate confuses odds with probability.
⚠️ Tricky
In a 10-year trial, the event rate was 20% with control and 15% with a statin (NNT 20). Your patient's own 10-year baseline risk is 8%. Assuming the relative risk reduction is the same for her, what is her 10-year NNT?
Carry the RRR, not the ARR or NNT, over to the new baseline risk.
= 50 patients
⚠️ The trap: Quoting the trial's NNT of 20 overstates the benefit for a lower-risk patient; her NNT is 50.
🕵️ Spot the mistake
Event rate 12% with placebo and 9% with treatment. What is the NNT?
A student wrote
⚠️ Traps examiners set
- Using RRR instead of ARR to calculate NNT.
- Rounding NNT or NNH down instead of up.
- Taking 1/ARR with ARR still in percent (1/4 instead of 1/0.04).
- Confusing RR (ratio of risks) with OR (ratio of odds) — they diverge when events are common.
- Reporting an NNT without the trial's time frame.
💬 Explain it in your own words
Why can a drug with a large RRR still have a large NNT, and what does that tell you about the baseline risk of the population studied?