Two groups, one outcome, four numbers. That is the whole of a simple comparative result, and yet it is where a surprising share of manuscripts go wrong. The same table can be summarised as a relative risk, an odds ratio, an absolute difference or a number needed to treat, and those four tell rather different stories about the same patients. Reviewers notice when only the flattering one is reported.

1Everything starts with the 2×2 table

Lay out the two groups as rows and the outcome as columns. Every measure below is a different way of dividing or subtracting the two row percentages, so once the table is right the rest is arithmetic.

The first thing to write down is the plain risk in each group. In the example here 15 of 100 treated patients had the event and 30 of 100 controls did, so the risks are 15% and 30%. Report these two numbers. They are the raw material a reader needs to check everything else, and they cost you one sentence.

From one 2×2 table to four effect measures Event No event Risk % Treated 15 85 15% Control 30 70 30% Relative risk 0.50 Odds ratio 0.41 Absolute difference 15% Number needed to treat 6.7 The blue pair are relative and answer how many times. The green pair are absolute and answer how many patients.
Figure 1. The four measures are not competing answers, they are four views of the same table. Trouble starts when a paper shows only the view that looks best.

2An odds ratio is not a relative risk

The relative risk divides one probability by the other, 15% divided by 30%, which gives 0.50. The odds ratio divides one odds by the other. Odds compare the event against its absence rather than against the whole group, so 15 against 85 divided by 30 against 70 gives 0.41. Same table, two numbers, and the odds ratio looks like the bigger effect.

How far apart they drift depends entirely on how common the event is. When the outcome is rare, the odds and the risk are almost the same thing and the two measures nearly coincide. As the event becomes common the odds ratio pulls away from 1 and exaggerates what the treatment actually does to a patient’s chances.

This matters because logistic regression, which most people reach for by default, produces odds ratios. A perfectly correct analysis then gets written up in the discussion as though the odds ratio were a risk, and the reported effect quietly inflates.

The same halved risk, seen as an odds ratio 0.5 0.4 0.3 0.2 Relative risk stays at 0.50 Odds ratio drifts further from 1 2% 20% 40% 60% 80% How common the event is in the control group
Figure 2. Every point on both lines comes from a treatment that halves the risk. Only the odds ratio changes, which is why it cannot be read as a risk once the outcome is common.

3A relative effect hides the size of the benefit

A relative risk of 0.50 is a halving. It is also completely silent about whether that halving is worth anything to a patient. Halving a risk that starts at 40% prevents an event in one patient out of every five treated. Halving a risk that starts at 0.4% prevents one in five hundred. The relative number is identical and the clinical reality is not remotely comparable.

This is why the absolute risk difference belongs in the abstract next to the relative one. It is the subtraction rather than the division, 30% minus 15% in our example, so 15 percentage points. Write percentage points and not percent, because a fall from 30% to 15% is 15 percentage points and also a 50% reduction, and readers who confuse the two will misread the result by a factor of three.

Two trials, both halving the risk When the event is common Control Treated 40% 20% NNT 5 When the event is rare Control Treated 0.4% 0.2% NNT 500 Same relative risk, one hundred times the work per patient helped
Figure 3. Both panels are drawn to the same scale. The bars on the right are almost invisible, and that is precisely the information a relative risk of 0.50 throws away.

4The NNT needs an interval, and it is an odd one

The number needed to treat is one divided by the absolute risk difference. In our example that is one divided by 0.15, so about 7 patients treated to prevent one event. It is the most intuitive number in the whole set and the one most often reported bare, without any measure of uncertainty.

Giving it an interval is easy when the treatment clearly works. Take the confidence interval of the risk difference and invert both ends. Our interval runs from 3.6 to 26.4 percentage points, so the NNT runs from about 4 to about 28. Wide, but honest.

The awkward case is when the risk difference is not significant, which means its interval includes zero. Inverting a difference of zero gives infinity, so the NNT interval is not a range at all. It runs from a benefit bound out to infinity and comes back in from the harm side. The convention Altman set out is to write it as a benefit bound, then infinity, then a harm bound, rather than pretending it is an ordinary pair of limits. Calculators that print a tidy range here are hiding the fact that the trial did not settle the question.

  • Report the two group risks first, in plain percentages.
  • Give one relative measure and one absolute measure, both with intervals.
  • Say explicitly whether your ratio is a risk ratio or an odds ratio.
  • Use percentage points for a difference and percent for a ratio.
  • If the interval for the difference crosses zero, say so rather than reporting a clean NNT.

5What reviewers send back

Almost every problem in this area is visible from the manuscript alone, without seeing a single row of the raw data. That is what makes these errors so easy for a reviewer to spot and so cheap for you to avoid.

Five effect measure mistakes reviewers catch An odds ratio described as a risk, when the event is common Only the relative effect reported, never the absolute one A number needed to treat given without any confidence interval An empty cell corrected silently, with no note in the methods Percent and percentage points used as if they meant the same
Figure 4. The last one looks pedantic and is not. A reader who takes 15 percentage points for a 15 percent reduction has misunderstood the result by a wide margin.

The empty cell deserves a word of its own. When nobody in one group had the event, the odds ratio and the relative risk are undefined, because the arithmetic divides by zero. The usual repair is to add half a count to every cell, which is known as the Haldane-Anscombe correction. It is a perfectly respectable thing to do and an entirely unrespectable thing to do quietly. Say in the methods that you did it.

6Get the numbers in seconds, free

You can produce every measure in this guide from your own table with our free odds ratio and relative risk calculator. Enter the four counts and it returns the relative risk, the odds ratio, the absolute risk difference and the number needed to treat, each with a 95% confidence interval, plus the matching R code. It applies the Haldane-Anscombe correction when a cell is empty and tells you that it did, and it reports the NNT interval the way Altman set out when the difference crosses zero. Everything runs in your browser. Adjusted effects, regression and matched designs are where a statistician earns their fee.