Odds ratio, relative risk and the number needed to treat.
Enter the four cells of your 2×2 table and get the relative risk, the odds ratio, the absolute risk difference and the number needed to treat, each with a 95% confidence interval. Your counts never leave your browser.
A halved risk can still be a tiny benefit
Relative numbers sound dramatic and absolute numbers tell the patient what to expect. Reviewers increasingly ask for both, and for the intervals that go with them.
Both, not one
A relative risk of 0.5 is a halving whether the risk falls from 40% to 20% or from 0.4% to 0.2%. The absolute difference separates those two worlds, and it is the one patients feel.
An odds ratio is not a risk ratio
When the event is common, the odds ratio sits further from 1 than the relative risk. Reading it as a risk ratio overstates the effect, which is one of the most frequent errors reviewers catch.
NNT with an honest interval
When the interval for the risk difference includes zero, the interval for the number needed to treat is not a simple range. This tool reports it the way Altman set out, rather than hiding the problem.
Let a named physician-scientist run the analysis
Adjusted effects, logistic and Cox regression, matched designs and competing risks need more than a 2×2. Rigora’s statistics service delivers the analysis, the figures and the reporting, done by a publishing physician-scientist.
Questions
What is the difference between an odds ratio and a relative risk?
The relative risk compares the probability of the event in the two groups. The odds ratio compares the odds. When the event is rare the two are close, but when the event is common the odds ratio is further from 1 than the relative risk and overstates the effect if it is read as a risk.
When should I report the number needed to treat?
Report it whenever the absolute risk difference is meaningful for a clinical decision. The number needed to treat is one divided by the absolute risk difference, and it should always come with a confidence interval, because a relative effect alone hides how many patients actually benefit.
What do I do when a cell in the 2×2 table is zero?
The odds ratio and the relative risk are undefined with an empty cell. The usual fix is the Haldane-Anscombe correction, which adds 0.5 to every cell. This tool applies it automatically and tells you when it did, and it leaves the risks and the absolute difference uncorrected.