NNT calculator: relative vs absolute risk, and how a trial is spun

A playground: two sliders, 100 patients, and the three numbers a drug trial can be reported as.

RRR — relative risk reduction

How much the risk shrinks in proportional terms. The number press releases love: it can be large while the real change is tiny.

ARR — absolute risk reduction

The actual percentage-point drop in risk. This is what changes for a real patient.

NNT — number needed to treat

How many patients you must treat to prevent one event. NNT = 1 / ARR. A blunt, honest summary.

The trap: a drug cuts risk from 2% to 1%. The headline says 50% lower risk (RRR). The reality is a 1 point drop (ARR), and you would treat 100 people to spare one event (NNT). Same trial, three very different feelings.

Risk without treatment (control)

Risk with treatment

100 patients, all treated

helped: event preventedevent despite treatmentharmed by treatmentfine either way

When the news says a drug cuts risk by 50%, it is almost always reporting the relative reduction, because that figure comes out largest. The absolute reduction and the NNT are what a patient actually gains, and they rarely make the headline. This is not a hypothetical worry: in 1995, exactly this misreading, a doubling reported without the tiny absolute risk behind it, triggered a national panic and an estimated 13,000 extra abortions. The 1995 pill scare

Why do the same numbers feel so different? Here is each one, then the formulas.

What the three numbers mean

Relative risk reduction (RRR) divides the drop in risk by the starting risk, so it hides how common the event was to begin with. A fall from 2% to 1% and a fall from 40% to 20% are both a 50% RRR, but they mean wildly different things for a patient. Absolute risk reduction (ARR) is the plain difference, the percentage points that actually changed. NNT is just its reciprocal: treat 1/ARR people to prevent one event.

$$\text{RRR}=\frac{\text{CER}-\text{EER}}{\text{CER}}=1-\text{RR} \qquad \text{ARR}=\text{CER}-\text{EER} \qquad \text{NNT}=\frac{1}{\text{ARR}}$$

Two more you will meet: relative risk (RR), the ratio of the two risks, and the odds ratio (OR), the ratio of the odds. For rare events OR and RR are close; as events get common, the OR drifts further from the RR and tends to look more dramatic, which is worth remembering when a paper reports odds ratios.

$$\text{RR}=\frac{\text{EER}}{\text{CER}} \qquad \text{OR}=\frac{\text{EER}/(1-\text{EER})}{\text{CER}/(1-\text{CER})}$$

Work one by hand

Problem

A trial of a preventive drug reports that it lowers the risk of a heart attack over five years from 4 in 100 to 3 in 100. The press release says the drug cuts risk by 25%. What actually changes, and how many people must take it for one to benefit?

Work it in people, out of 100 treated:

• Without the drug, 4 of 100 have a heart attack. With it, 3 of 100 do.
• ARR = 4% − 3% = 1 percentage point. NNT = 1 / 0.01 = 100.
• RRR = 1 / 4 = 25% — true, but it is one prevented event per hundred treated.
• So: 1 helped, 3 have the attack anyway, 96 were never going to.

The 25% headline and the NNT of 100 describe the exact same trial. Neither is wrong; only one tells the patient what to expect. Press the pharma headline preset above to watch it on the dots.

Common questions

What is the number needed to treat (NNT)?

The NNT is how many patients you must treat for one to benefit, meaning to prevent one extra event. It equals 1 divided by the absolute risk reduction, so a smaller NNT means a more effective treatment.

What is the difference between relative and absolute risk reduction?

Relative risk reduction is the proportional drop in risk, such as 50% lower. Absolute risk reduction is the actual percentage-point drop for a patient. The same 50% relative reduction can be only a 1-point absolute reduction at low baseline risk, which is why the absolute figure is what matters for a real decision.

How is NNT calculated from a trial?

Take the control event rate minus the treated event rate, which is the absolute risk reduction, then the NNT is 1 divided by that. If risk falls from 2% to 1%, the absolute reduction is 1 point and the NNT is 100.

One trap down. Stat Exam Pro drills relative-vs-absolute risk and the rest of medical statistics as exam questions with worked answers, in English and French.

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