Absolute and relative effects
The same trial, three ways
Risk falls from 2 percent to 1 percent. The relative risk is 0.5, a 50 percent relative reduction. The absolute risk reduction is 1 percentage point. The number needed to treat is 100. Every one of those is correct, and they leave very different impressions.
The same relative reduction at two baseline risks
Why both are needed
Relative effects tend to be more stable across populations, which is what makes them useful for transporting a result from a trial to a different setting. Absolute effects depend on the baseline risk, which is exactly why they are what a decision needs: the same relative reduction produces a large benefit in a high-risk patient and a negligible one in a low-risk patient. The honest report gives the relative effect and applies it to a stated baseline risk.
Practical rules
- Report the absolute risks in both groups, not only the contrast between them.
- State the baseline risk any absolute figure is computed at, and choose one relevant to the reader's patients.
- Give harms in the same format as benefits. Presenting benefits relatively and harms absolutely is a well-documented asymmetry.
- Use natural frequencies rather than percentages where possible: 1 in 100 is understood better than 1 percent.
- Where risk varies widely, present the absolute effect across risk strata rather than at the average.
Odds ratios need care here
An odds ratio approximates a risk ratio only when the outcome is rare. With a common outcome it is further from 1 than the risk ratio, so reading it as one overstates the effect. Converting to absolute terms requires the baseline risk and is worth doing explicitly.
Estimating them from data
For two independent groups of individually sampled patients, the confidence interval for a risk difference is best calculated by Newcombe's method, which combines a Wilson interval for each arm and behaves well with small counts or risks near 0 or 1, where the simple normal (Wald) interval can be too narrow or run past the possible range. Matched pairs, or arms made of clusters, are not independent in this sense and need an interval or analysis that keeps the pairing or clustering. The interval for a risk ratio is calculated on the log scale and transformed back; when an arm has no events the ratio is zero or infinite and that interval does not exist, so state in advance how zero cells will be handled, for example with a continuity correction or a score-based interval. The number needed to treat is one divided by the risk difference, and its interval comes from inverting the risk difference's limits; when that interval includes no difference, the interval for the number needed to treat runs through infinity, and it is reported as a number needed to treat at one end and a number needed to harm at the other rather than as a single range. To adjust for covariates, an adjusted risk ratio can be estimated directly with a log-link Poisson model and a robust (sandwich) variance, called modified Poisson regression, because the ordinary Poisson variance is wrong for a binary outcome. An adjusted risk difference can come from a binomial model with an identity link, which estimates it directly but often fails to converge because predicted risks must stay between 0 and 1; standardising the predictions of a logistic model (g-computation) is the usual alternative.
What to watch out for
A relative reduction is the same number whether the risk falls from 20 percent to 10 or from 0.02 percent to 0.01, so it says nothing on its own about how much good the treatment does. It is also read as larger and is more persuasive than the identical result stated in absolute terms, by clinicians as well as patients. Reporting only the relative figure is therefore not a neutral choice of units; it reliably makes the treatment look better.
Clinical example
A drug is reported to reduce the risk of a complication by 30 percent. In a patient whose baseline risk is 3 percent, that is an absolute reduction of about 1 percentage point, and roughly 110 such patients would be treated for one to benefit. Both sentences describe the same trial.
- Using alternative statistical formats for presenting risks and risk reductions (opens in a new tab) · Cochrane Database Syst Rev · doi 10.1002/14651858.CD006776.pub2
- An assessment of clinically useful measures of the consequences of treatment (opens in a new tab) · N Engl J Med · doi 10.1056/NEJM198806303182605
- Interval estimation for the difference between independent proportions: comparison of eleven methods (opens in a new tab) · Stat Med · doi 10.1002/(sici)1097-0258(19980430)17:8<873::aid-sim779>3.0.co;2-i
- A modified poisson regression approach to prospective studies with binary data (opens in a new tab) · Am J Epidemiol · doi 10.1093/aje/kwh090
- Confidence intervals for the number needed to treat (opens in a new tab) · BMJ · doi 10.1136/bmj.317.7168.1309