Risk Ratio from a Two-by-Two Table: Audit Before Calculating

Establish what each person contributes

A risk ratio compares the proportion experiencing a defined event in one group with that proportion in another. Before opening a calculator, write a sentence naming the event, follow-up window, and comparison. For example: “First readmission within 30 days, intervention versus control.” This prevents a valid calculation from answering the wrong question.

Use a cohort or randomized comparison with identifiable group denominators. A conventional case-control sample does not directly provide the group risks needed here. CDC explains how design determines the appropriate association measure in its field epidemiology guidance.

Reconstruct the four cells

Record events and non-events separately in each group. Reconcile their sums against the outcome-specific analysis population. Do not assume that everyone randomized had an observed 30-day outcome, or silently classify an unobserved outcome as a non-event.

Use the two-by-two audit worksheet to record the source table, population, window, and unresolved discrepancy. Keep the original labels beside any shortened labels entered into software. If the source reports recurrent admissions, determine whether it counts people admitted or total admissions; those are different endpoints.

Work through a fictional example

Suppose 12 of 100 intervention participants and 24 of 100 controls experience the event. Non-events are 88 and 76. Risks are 0.12 and 0.24, so the intervention-to-control risk ratio is 0.50. Reversing the groups produces 2.00.

For these independent groups, the conventional log-scale Wald calculation gives an approximate 95% confidence interval of 0.265 to 0.944. The risk-ratio calculator reproduces this arithmetic. This example is invented for instruction, not evidence of a treatment effect.

Check the calculation's boundary

The tool requires all four cells to be positive and flags cells below five. A zero cell or sparse sample needs an appropriate analysis strategy; adding a constant without documenting it changes the result. A calculator cannot resolve missing outcomes, clustering, matching, or confounding. The crude table also cannot replace a prespecified adjusted model.

Save the group order, four counts, calculation method, and rounding alongside the result. Describe the observed comparison without making a causal claim that the study design cannot support. Before submission, ask another reader to reconstruct the same table from the cited page.

Source checked on 30 October 2026; numerical example independently recalculated.