2 × 2 table — risk, RR, RRR, ARR, NNT, OR

Enter a single 2 × 2 table and obtain every standard measure of effect at once: risk in each group, relative risk, relative and absolute risk reduction, number needed to treat or harm, and the odds ratio.

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What is this for?

Almost every measure of a binary outcome derives from the same four numbers. Entering them once and reading all the measures together makes the relationship between them visible — in particular, how a large relative risk reduction can coexist with a trivial absolute benefit when the baseline risk is low.

How to use it

Enter the number of subjects with the outcome and the total number of subjects in each group.
State the time horizon over which the outcome was measured — an NNT is not interpretable without it.
Indicate whether the outcome is favourable or unfavourable, which determines whether the result is reported as a number needed to treat or a number needed to harm.

Worked example

In a five-year trial, 15 of 100 treated patients and 25 of 100 control patients had a myocardial infarction. Calculate the effect measures.

Answer: risk 15% vs 25%. ARR = 10%. RRR = 10/25 = 40%. RR = 0.15/0.25 = 0.60. NNT = 1/0.10 = 10 — treat 10 patients for five years to prevent one MI. OR = (15 × 75) ÷ (85 × 25) = 0.53.

Clinical pearls & pitfalls

Express ARR as a decimal when calculating NNT. Using the percentage gives an answer a hundred times too small — 1 ÷ 10 = 0.1 rather than 1 ÷ 0.10 = 10.
Always round NNT up, never down. Rounding 10.4 down to 10 overstates the benefit.
The relative risk reduction is independent of baseline risk, which is why it looks impressive in low-risk populations. A 50% RRR on a baseline risk of 0.2% is an ARR of 0.1% and an NNT of 1000.
The odds ratio approximates the relative risk only when the outcome is rare, roughly below 10%. For common outcomes the odds ratio systematically exaggerates the effect and should not be described as a risk ratio.
A confidence interval crossing 1 for a ratio measure, or crossing 0 for a difference measure, indicates the result is not statistically significant.
Odds ratios are what logistic regression and case-control studies produce, which is why they appear so often even when a relative risk would communicate better.

Assumptions & limitations

Applies to binary outcomes with complete follow-up. Time-to-event data with censoring require survival methods and a hazard ratio.
Confidence intervals use large-sample normal approximations (log method for RR and OR, Woolf standard errors). With small cell counts, especially any cell below 5, exact methods are preferable.
Zero cells make ratio measures undefined. A continuity correction is commonly applied, but this calculator reports the limitation rather than silently applying one.
These are measures of association within the data supplied. They say nothing about study quality, bias, confounding, or whether the result generalises to your patient.

References

Laupacis A, Sackett DL, Roberts RS. An assessment of clinically useful measures of the consequences of treatment. N Engl J Med. 1988;318(26):1728-1733.
Altman DG. Confidence intervals for the number needed to treat. BMJ. 1998;317(7168):1309-1312.
Guyatt G, Rennie D, Meade MO, Cook DJ. Users' Guides to the Medical Literature: A Manual for Evidence-Based Clinical Practice. 3rd ed. McGraw-Hill.
Schulz KF, Grimes DA. Sample size slippages in randomised trials. Lancet. 2005;365(9467):1348-1353.