Signature
ARR = p_C - p_I
| Inputs | Definition | Unit |
|---|---|---|
p_C | Risk of the adverse event in the comparator group over the follow-up period | probability from 0 to 1 |
p_I | Risk of the adverse event in the intervention group over the same period | probability from 0 to 1 |
ARR | Difference between the comparator and intervention risks, positive when the intervention lowers risk | probability difference from minus 1 to 1, over the stated period |
|---|
Function
Absolute risk reduction function
Maps the risks of an adverse event with the comparator and with the intervention, over the same period, to their difference, oriented so that a benefit is positive. The difference converts a relative treatment effect into events avoided per person treated, the quantity that costs and QALYs in an economic evaluation are built from.
Try this function
Implementations
Excel
Absolute risk reduction from event counts
With comparator events and totals in ComparatorEvents and ComparatorN, and intervention events and totals in InterventionEvents and InterventionN, Excel returns the ARR.
=ComparatorEvents/ComparatorN-InterventionEvents/InterventionN
Assumptions
Same outcome, population and period in both arms
Both risks refer to the same event definition, the same randomised population and the same follow-up period. An ARR is reported with that period, because events accrue and the ARR changes as follow-up lengthens.
Adverse outcome orientation
The event is one the intervention aims to prevent. For a beneficial outcome, such as response, the subtraction is reversed so that a benefit remains positive.
Worked examples
OSIRIS trial reported in CONSORT 2010
Death or oxygen dependence occurred in 514 of 1,346 infants with delayed selective surfactant and 429 of 1,344 with early administration, risks of about 0.38187 and 0.31920. The ARR of 0.06267 matches the risk difference of minus 6.3 per cent reported in the CONSORT 2010 explanation for item 17b.
p_C = 0.38187; p_I = 0.31920; ARR = 0.06267
Common errors
Pooling events across trials before subtracting
Adding events and participants across trials and then computing one ARR ignores randomisation within studies and can mislead when allocation ratios differ. The Cochrane Handbook advises using the pooled result of a meta-analysis instead.
Sources
Absolute and relative effects for binary outcomes in CONSORT 2010
Moher D, Hopewell S, Schulz KF, Montori V, Gøtzsche PC, Devereaux PJ, Elbourne D, Egger M, Altman DG. CONSORT 2010 explanation and elaboration: updated guidelines for reporting parallel group randomised trials. BMJ. 2010;340:c869. Item 17b (for binary outcomes, presentation of both absolute and relative effect sizes is recommended), its example and table 7 from the OSIRIS trial, and the explanation that the risk difference is less generalisable than the relative risk because it depends on baseline risk.
Absolute and relative effect sizes in CONSORT 2025
Hopewell S, Chan AW, Collins GS, Hróbjartsson A, Moher D, Schulz KF, et al. CONSORT 2025 statement: updated guideline for reporting randomised trials. BMJ. 2025;389:e081123. Checklist item 26: for binary outcomes, presentation of both absolute and relative effect size.
Risk difference and absolute risk reduction in the Cochrane Handbook
Schünemann HJ, Vist GE, Higgins JPT, Santesso N, Deeks JJ, Glasziou P, Akl EA, Guyatt GH. Chapter 15: Interpreting results and drawing conclusions (last updated August 2023). In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.5. Cochrane; 2024. Section 15.4.1 (the risk difference is often referred to as the absolute risk reduction or absolute risk increase) and section 15.4.4 (not computing risk differences from aggregated totals across trials).
Canonical Identity
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