Relative Risk and Absolute Risk Are Not the Same Story

Three numbers from one 2x2 table

Everything in this article comes out of a table with four cells: how many people in each group did and did not have the outcome. Build one. This example is constructed for illustration and is not taken from any published study. Ten thousand exposed people, of whom 60 develop the outcome and 9,940 do not. Ten thousand unexposed people, of whom 40 develop it and 9,960 do not. From those four numbers, absolute risk in the exposed group is 60 ÷ 10,000 = 0.60%, and in the unexposed group 40 ÷ 10,000 = 0.40%.

Now the three derived quantities, each one line. Relative risk is one absolute risk divided by the other: 0.0060 ÷ 0.0040 = 1.50, so exposure multiplies the risk by 1.5, which is the same as a 50% increase. Absolute risk difference is one minus the other: 0.0060 − 0.0040 = 0.0020, or 0.20 percentage points. Number needed to harm is the reciprocal of that difference: 1 ÷ 0.0020 = 500, meaning one extra case for every 500 people exposed over the same period. All three are correct descriptions of the identical four cells. The relative figure is the largest-sounding, which is why it is the one that reaches a headline.

Baseline risk is the term that decides everything

A relative risk is a multiplier with no units and no scale. It tells you what to do to a baseline risk, but it says nothing about what that baseline is, so it cannot on its own tell you whether the change is trivial or enormous. Fix the relative effect at a 25% reduction and vary the baseline, and the practical consequences move by two orders of magnitude. On a baseline risk of 0.2%, a 25% reduction saves 0.05 percentage points and the number needed to treat is 2,000. On a baseline of 40%, the identical 25% reduction saves 10 percentage points and the number needed to treat is 10. Same headline, two hundred times the practical benefit.

This runs the other way too, and the reversal is the more useful half of the lesson. Compare two treatments. Treatment A cuts a common outcome — baseline 20% — by a modest 25%, taking it to 15%: an absolute gain of 5 percentage points and a number needed to treat of 20. Treatment B cuts a rare outcome — baseline 0.4% — by an impressive 50%, taking it to 0.2%: an absolute gain of 0.2 percentage points and a number needed to treat of 500. B has twice A's headline and one twenty-fifth of its practical value, because 500 ÷ 20 = 25. If you were choosing which to fund, or which to take, the relative numbers would rank them backwards.

NNT and NNH: the plain-language form of the same arithmetic

Number needed to treat, introduced by Cook and Sackett in the BMJ in 1995, is nothing more than one divided by the absolute risk reduction. Its value is linguistic rather than mathematical: it converts a small decimal into a count of people, which is a form most readers can hold in their head. An absolute risk reduction of 5 percentage points becomes an NNT of 20 — treat twenty people for one to benefit. An absolute risk reduction of 0.2 percentage points becomes an NNT of 500. Number needed to harm is the identical calculation applied to an increase, so the 0.20-point difference in the example above gives an NNH of 500.

Two conditions have to travel with any NNT or it becomes meaningless. The first is the time horizon: an NNT of 20 over five years and an NNT of 20 over five weeks describe entirely different interventions, and an NNT quoted without a period is uninterpretable. The second is the outcome: an NNT of 20 to prevent one death and an NNT of 20 to prevent one episode of mild nausea are not comparable, however identical the arithmetic. When you see an NNT quoted bare, those two omissions are usually where the persuasion is hiding. And a benefit NNT should be read next to the harm NNH from the same trial, because a treatment with an NNT of 20 and an NNH of 15 is doing more harm than good.

The odds ratio is a third quantity, and it drifts

Odds are not risk. Risk is events divided by everyone in the group; odds are events divided by non-events. In the constructed table above, the exposed odds are 60 ÷ 9,940 and the unexposed odds are 40 ÷ 9,960, so the odds ratio is 1.5030 against a relative risk of 1.5000 — an overstatement of 0.2%, which is nothing. That closeness is why odds ratios are routinely read as if they were relative risks. The approximation is genuinely good when the outcome is rare, and case-control studies, which cannot estimate absolute risk at all, can only report an odds ratio, so the habit has a real basis.

The approximation breaks as the outcome becomes common, and it is worth knowing exactly where. Hold the relative risk fixed at 1.50 and raise the baseline. At a 1% baseline the odds ratio is 1.508, overstating the relative risk by 0.5%. At 5% it is 1.541, overstating by 2.7%. At 10% it is 1.588, overstating by 5.9%. At 20% it is 1.714, overstating by 14.3%. At 40% it is 2.250 — a 50% overstatement, and by then reading it as a relative risk means reading a 50% increase as a 125% one. The rough rule that odds ratios approximate relative risks below about a 10% event rate is defensible; above that, the two numbers are answering different questions and should not be swapped.

How to read a health headline in thirty seconds

Ask four questions in order. What is the baseline risk — the chance of the outcome without the exposure or treatment? What is the absolute difference in percentage points? Over what period, and in whom? And is the reported figure a relative risk, an odds ratio or a hazard ratio? If the article does not answer the first two, it has not told you enough to judge anything, and the honest move is to go and find the abstract, where the absolute event counts are usually available even when the press release omits them. CONSORT has asked trialists to report both absolute and relative effect sizes for binary outcomes since 2010, so for a well-reported trial the numbers exist.

One caution against overcorrecting. Concluding that small absolute differences never matter is its own error, and a dangerous one. Absolute differences scale with baseline risk, so a change that is negligible in a low-risk population can be substantial in a high-risk one — the same relative effect that gives an NNT of 2,000 at a 0.2% baseline gives an NNT of 10 at 40%. Absolute differences also scale with population size: 0.20 percentage points across ten million people is 20,000 cases. And a person's own baseline is rarely the population average. The point of computing both numbers is not to become dismissive. It is to stop letting one of them do the arguing on its own.

Frequently asked questions

What is the difference between a percentage and a percentage point?

It is the whole confusion in miniature. A percentage point is an absolute difference between two percentages; a percentage change is a relative one. Going from 0.40% to 0.60% is a rise of 0.20 percentage points and a rise of 50%, because 0.20 ÷ 0.40 = 0.50. Both statements are true about the same pair of numbers. This is why the wording of a report matters as much as its arithmetic: risk rose by 50% and risk rose by 0.2 points describe the identical change, but they leave completely different impressions. When you write about risk, use points for absolute differences and reserve percent for relative ones, and say which you mean rather than trusting the reader to infer it.

Is relative risk ever the right number to quote?

Yes, and it is not a villain. Relative risk is the more stable of the two across different populations, which is precisely what makes it useful in research: an effect expressed relatively often transfers reasonably well from a trial population to another group, whereas an absolute difference does not, because it depends on a baseline risk that changes with age, sex and comorbidity. That is why meta-analyses usually pool relative measures. The correct practice is to combine them: take the relative effect from the evidence, apply it to the baseline risk of the person or population in front of you, and report the resulting absolute difference. Quoting the relative figure alone is the failure. Discarding it in favour of a single absolute number that only applies to one group is also a failure.

When can I read an odds ratio as if it were a relative risk?

When the outcome is rare, and the usual working threshold is an event rate below about 10%. The drift is computable, so you can check rather than guess. Hold the relative risk at 1.50 and the odds ratio comes out at 1.508 on a 1% baseline, 1.541 on 5%, 1.588 on 10%, 1.714 on 20% and 2.250 on 40%. The overstatement is therefore 0.5%, 2.7%, 5.9%, 14.3% and 50% respectively. Below a 10% event rate the substitution costs you a few percent and rarely changes a conclusion; above 20% it becomes seriously misleading, and at a 40% baseline reading the odds ratio as a relative risk turns a 50% increase into an apparent 125% one. When the outcome is common, ask for risks rather than odds.

Does a small absolute difference mean the finding does not matter?

No, and treating it that way is the mirror-image error. Three things can make a small absolute difference consequential. Population size: 0.20 percentage points across ten million people is 20,000 cases, which is a public health matter even if it is a negligible personal one. Baseline risk: the same relative effect that produces a 0.05-point difference at a 0.2% baseline produces a 10-point difference at 40%, so your own risk profile decides which of those you are. Severity: a tiny absolute increase in a fatal outcome is not equivalent to a tiny increase in a self-limiting one. Absolute numbers exist to let you weigh the finding, not to let you dismiss it, and how it weighs for you personally is a conversation with a clinician who knows your history.

Where do I find the absolute numbers when a news article omits them?

Almost always in the abstract of the study itself, which is usually free even when the full text is not. Look for the event counts and the group sizes — the four cells of the 2x2 — because from those you can compute every measure in this article yourself. If the abstract gives only percentages, the group sizes in the methods will let you reconstruct the counts. CONSORT has asked trialists since 2010 to report both absolute and relative effect sizes for binary outcomes, and the Cochrane Handbook takes the same position for systematic reviews, so a well-conducted study will normally have the numbers somewhere even if the press release does not. If you cannot find them anywhere in the paper, that absence is itself information about how the result is being presented.