StatReason

Risk Ratio Confidence Interval Calculator

Estimate how many times more (or less) likely an event is in an exposed group compared to an unexposed group, using cohort-style counts where each group's own denominator is known.

What this answers

This calculator answers "how many times more likely is the event in the exposed group compared to the unexposed group?" It requires cohort-style data, where you know the full exposed and unexposed populations and their event counts, unlike a case-control study where that denominator is not available and an odds ratio is used instead.

How it is calculated

Risk in each group is simply events divided by that group's total. The risk ratio is the exposed group's risk divided by the unexposed group's risk. As with the odds ratio, the confidence interval is built on the log scale (where the sampling distribution is closer to normal) using a standard error derived from the four counts, then converted back with the exponential function.

Worked example

For 10 events out of 20 exposed subjects and 5 events out of 20 unexposed subjects, the risk in the exposed group is .5 and in the unexposed group is .25, giving a risk ratio of exactly 2: the event is twice as likely in the exposed group. The 95% confidence interval for this risk ratio spans roughly .83 to 4.8, still comfortably above 1 despite the modest sample size.

Assumption audit

Calculated from your data: each group's risk, the risk ratio, and its log-scale standard error from the four input counts.
Evidence to review: whether zero events occurred in the exposed group, which gives a risk ratio of exactly 0 with an undefined standard error, a genuinely different situation from a small but nonzero risk ratio.
You must verify: that your data is genuinely cohort-style (both group totals are known population sizes, not case-control sampling on the outcome), since this ratio is not valid for a case-control design.

What this result does not mean

A risk ratio above 1 shows the exposed group has a higher observed risk, not that the exposure caused that higher risk; confounding and reverse causation remain possible unless ruled out by design. Unlike the odds ratio, the risk ratio does not exaggerate the effect when the outcome is common, which is part of why it is generally preferred whenever cohort data makes it available.

Limitations

This calculator requires at least one event in the unexposed (denominator) group; a zero count there makes the risk ratio's log scale undefined. Table orientation matters: swapping which group is "exposed" inverts the reported ratio, so label your groups carefully before entering counts.