The Relative Risk Trick

The Claim

Here is an advertisement for Lipitor, the best-selling prescription drug in history. The headline reads: “Lipitor reduces the risk of heart attack by 36%.”

Thirty-six percent. That sounds extraordinary. If you have high blood pressure and high cholesterol, and a drug could cut your heart attack risk by more than a third, you would want it. You would probably take it without much further thought.

Here is what the clinical trial actually found. In the ASCOT-LLA study, published in 2003, 10,305 patients with hypertension were randomised to Lipitor or placebo and followed for just over three years. In the placebo group, 3.0% of patients had a heart attack or died from coronary heart disease. In the Lipitor group, the figure was 1.9%. The difference is 1.1 percentage points.

The 36% reduction is real. It is also the least useful way to express the result.

If you read the trial honestly, what Lipitor achieved in this population, over this period, was moving 1.1 people out of every 100 from the “had a heart attack” column to the “did not.” Expressed the other way around: you would need to treat approximately 91 patients with Lipitor for three years for one person to benefit. The other 90 receive no benefit and are exposed to the drug’s side effects, including muscle pain, liver enzyme changes, and a modest increase in diabetes risk.

The 36% is the relative risk reduction. The 1.1% is the absolute risk reduction. Both numbers describe the same trial. Only one of them is what you need to make a decision.

You have almost certainly encountered this trick in the past month. Every pharmaceutical advertisement does it. Most health headlines do it. Once you see it, you cannot unsee it.

---

The Concept

To understand why these two numbers can both be true, you need four pieces of vocabulary. They are not complicated.

Absolute risk is the simplest of all: the probability that something happens to you. If 3 people out of every 100 in a particular group have a heart attack over five years, the absolute risk in that group is 3%. It is a direct statement of frequency, and it is the number that actually bears on your life.

Relative risk is a comparison. If the treated group has a 1.9% rate and the untreated group has a 3.0% rate, the relative risk of the treated group is 1.9 divided by 3.0, which is approximately 0.63. The treated group has about 63% of the risk of the untreated group. That means the relative risk was reduced by about 37% (rounding gives the advertised 36%). This is the relative risk reduction: how much smaller the treated group’s risk is as a proportion of the untreated group’s risk.

Absolute risk reduction (ARR) is the straightforward arithmetic: you subtract one absolute risk from the other. 3.0% minus 1.9% equals 1.1%. That is the actual reduction in probability that the treatment produced. One point one percentage points.

Now here is the fourth term, and it is the most honest measure of medical effect size ever devised.

Number Needed to Treat (NNT) asks: how many patients would you have to treat with this intervention, for the same duration as the trial, for one patient to benefit who would not have benefited otherwise? The formula is simple: divide 1 by the absolute risk reduction. In this case, 1 divided by 0.011 gives approximately 91.

The NNT of 91 means exactly this: treat 91 people, one benefits. The other 90 do not. They take the drug, pay for the drug, absorb whatever side effects come with it, and their outcome is identical to what it would have been without the drug.

The NNT is not a criticism of the drug. Some treatments with an NNT of 91 are excellent value, and some are poor value, depending on the cost of the drug, the severity of the outcome being prevented, and the side effect profile. The point is that the NNT gives you a real number in a real world where treatment has costs and risks. The relative risk reduction gives you a percentage that floats free of any of that.

Now look at why relative risk is always the number advertisers choose. Suppose a drug reduces the risk of a very common condition: say, from 40% to 26%. The ARR is 14 percentage points, and the NNT is approximately 7. Those are genuinely impressive numbers. The relative risk reduction is 35%. Now suppose a different drug reduces the risk of a rare condition: from 0.4% to 0.26%. The ARR is 0.14 percentage points, and the NNT is approximately 714. These numbers describe a drug with a very modest effect on most individuals. The relative risk reduction is also 35%.

Both drugs produce the same headline number. Their actual usefulness is completely different. The relative risk reduction tells you nothing about how common the condition is in the first place. Without the baseline risk, a percentage reduction is close to meaningless.

Use the tool below to explore how the same relative risk reduction can represent very different absolute benefits depending on the baseline.

Set the baseline risk to 0.5% and apply a 50% relative risk reduction. The NNT is 200. Now raise the baseline to 10% and apply the same 50% reduction. The NNT drops to 20. The intervention looks identical in relative terms. In absolute terms, one is ten times more valuable than the other.

---

Why It Matters

The pharmaceutical industry did not invent relative risk. It is a legitimate statistical measure with genuine uses, particularly in comparing interventions across populations with different baseline risks. But the industry has used it systematically and strategically for decades, because the law in most jurisdictions only requires that advertising not be false, and relative risk reduction is not false. It is just incomplete in a way that consistently flatters the product.

The statin story is the clearest case study. For many years, the dominant public health message was that statins reduce heart attack risk by “around 30 to 36 percent.” The raw statistics are from trials like WOSCOPS (1995), which found a 31% relative risk reduction in first heart attacks for pravastatin in middle-aged men with high cholesterol. What the press releases did not emphasise was that the absolute risk reduction was 1.9 percentage points, giving an NNT of approximately 53 over five years. For secondary prevention (people who have already had a heart attack), the numbers look better. The 4S trial of simvastatin found a 34% relative risk reduction in major coronary events, but the absolute risk reduction in all-cause mortality was 3.3 percentage points, with an NNT of approximately 30. These patients already had established heart disease and were at much higher baseline risk, which is why treating them produces a far larger absolute benefit from the same relative reduction.

The distinction matters enormously for how we think about prescribing. A drug with an NNT of 30 in a high-risk secondary prevention population is not the same drug, in practical terms, as an NNT of 91 in a lower-risk primary prevention population, even if both treatments produce a “36% reduction.” Policy decisions about who should receive statins, at what cost to the health system, cannot be made sensibly from relative risk figures alone.

The COVID-19 vaccine efficacy claims during 2020 and 2021 provide a more recent and more politically charged illustration. The Pfizer BNT162b2 vaccine was reported as “95% effective” against symptomatic COVID-19, based on the Phase 3 trial published in the New England Journal of Medicine in December 2020. This headline figure was the relative risk reduction: 8 cases in the vaccine group versus 162 in the placebo group, out of approximately 21,700 participants in each arm. The absolute risk reduction was 0.7 percentage points, giving a number needed to vaccinate of approximately 119 to prevent one case of symptomatic COVID-19 during the trial period.

This does not mean the vaccine was ineffective. At population scale, preventing one case per 119 vaccinated people across hundreds of millions of vaccinations prevents an enormous number of cases. The effectiveness also varied significantly with infection rates: as the virus became more prevalent in communities, the absolute risk reduction grew, and the NNT fell. The point is not that the vaccine was oversold. The point is that “95% effective” and “0.7% absolute risk reduction” describe the same result, and a member of the public who understood both numbers was better equipped to think about the policy trade-offs than someone who only heard the first.

Cancer screening adds another layer. When screening programmes report “survival rates,” they often mean the proportion of diagnosed patients still alive five years after diagnosis. This is not the same as the proportion who avoided dying from cancer. Early detection shifts the clock forward: a cancer found in year one of a five-year survival window looks like a survivor, even if the patient dies in year six having gained nothing from early diagnosis. This is lead time bias, and it is how a screening programme can report improving five-year survival rates while reducing mortality not at all. The relative risk framing compounds this: “screening reduces cancer mortality by 20%” is a relative figure, and the baseline matters enormously.

---

How to Spot It

The tell is a large percentage reduction paired with no mention of the baseline risk.

In 2003, Pfizer ran newspaper advertisements for Lipitor in the United States that prominently featured a 36% reduction in heart attack risk. The small print disclosed that this figure came from the ASCOT-LLA trial and that the actual event rates were 3% in the placebo group and 2% in the Lipitor group. (The rounding in the advertisement overstated the absolute difference slightly.) The advertisements were technically compliant with FDA requirements. They were also constructed so that no casual reader would carry away any number except 36%.

The pattern is consistent across decades of pharmaceutical advertising. The relative risk reduction goes in the headline, on the billboard, and in the television spot. The absolute risk figures, when disclosed at all, appear in fine print accompanied by caveats about study populations and duration that further obscure the practical significance.

In scientific papers, the same pattern appears: relative risk reductions are typically reported in the abstract, which is what most readers and almost all journalists read. The absolute figures are usually present, but buried in the results tables. A 2015 analysis of cardiovascular drug trial reports found that abstracts were significantly more likely to feature relative than absolute risk measures when the relative figure was more favourable.

When you read any health claim, ask immediately: is this a relative or absolute figure? If a percentage reduction is given without the baseline risk, you cannot evaluate it. The baseline is always available if the research was done honestly. If it is not provided, that is itself informative.

---

Your Challenge

A drug manufacturer publishes the following claim in an advertisement for a new blood-thinning drug:

“In the PROTECTA trial of 8,600 patients with atrial fibrillation, [Drug Name] reduced the risk of stroke by 30% compared with placebo.”

The trial results section of the full prescribing information contains this passage: “Stroke occurred in 2.8% of patients in the [Drug Name] group and 4.0% of patients in the placebo group over the 24-month study period.”

Calculate: the absolute risk reduction, and the Number Needed to Treat.

What would a doctor need to weigh against the NNT before deciding whether to prescribe this drug to a given patient?

---

References

1. Sever PS, Dahlöf B, Poulter NR, et al. Prevention of coronary and stroke events with atorvastatin in hypertensive patients who have average or lower-than-average cholesterol concentrations, in the Anglo-Scandinavian Cardiac Outcomes Trial (ASCOT-LLA). Lancet. 2003;361(9364):1149–1158. The source for the 36% relative risk reduction, 1.9% vs 3.0% event rates, 1.1% ARR, and NNT of 91 cited in this unit.

2. Shepherd J, Cobbe SM, Ford I, et al. Prevention of coronary heart disease with pravastatin in men with hypercholesterolaemia (WOSCOPS). New England Journal of Medicine. 1995;333(20):1301–1307. Source for the 31% relative risk reduction and 1.9% ARR in primary prevention with pravastatin.

3. Scandinavian Simvastatin Survival Study Group. Randomised trial of cholesterol lowering in 4444 patients with coronary heart disease: the Scandinavian Simvastatin Survival Study (4S). Lancet. 1994;344(8934):1383–1389. Source for the 34% relative risk reduction and 3.3% ARR in all-cause mortality in secondary prevention.

4. Polack FP, Thomas SJ, Kitchin N, et al. Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine. New England Journal of Medicine. 2020;383(27):2603–2615. Source for the 95% relative risk reduction and 0.7% ARR in the Pfizer Phase 3 trial, and the calculated NNV of approximately 119.

5. Brown JB, Shye D, McFarland BH. The paradox of guideline-based prescribing: a study of patients in clinical practice. Archives of Internal Medicine. 1995. Background on the gap between relative and absolute risk reporting in pharmaceutical communications.

6. Barratt A, Wyer PC, Hatala R, et al. Tips for learners of evidence-based medicine: 1. Relative risk reduction, absolute risk reduction and number needed to treat. CMAJ. 2004;171(4):353–358. A clear clinical introduction to ARR, RRR, and NNT as decision-making tools.

7. Prasad V, Vandross A, Toomey C, et al. A decade of reversal: an analysis of 146 contradicted medical practices. Mayo Clinic Proceedings. 2013;88(8):790–798. Background on how relative risk framing contributes to overestimation of medical interventions.