Statistical
Relative Risk (RR), Odds Ratio (OR), ARR & Number Needed to Treat (NNT)
Compare fictional adverse-event counts over the same follow-up period using risk ratio, odds ratio, absolute risk reduction and a benefit-only NNT estimate.
Define the event, population and follow-up before comparing risks
The fictional example counts an adverse event over the same follow-up period: 12/200 in the treatment group and 30/200 in the control group. Risks are 0.06 and 0.15, so the risk ratio is 0.4 and control-minus-treatment risk reduction is 0.09, or 9 percentage points. These are point estimates, not evidence that a treatment should be prescribed.
For positive absolute risk reduction, this worksheet rounds 1/ARR upward to an integer NNT for an additional beneficial outcome. NNT depends on the follow-up horizon and baseline risk. If ARR is zero there is no finite benefit estimate; if negative, events increased and a benefit NNT is inappropriate. This sheet returns No benefit in either case, without claiming statistical significance or estimating uncertainty.
Odds ratio compares event odds rather than event probabilities. It is not generally interchangeable with risk ratio. In a case-control sample, sampled event proportions do not ordinarily estimate population risks, so do not use that table to compute ARR or NNT. This example is a trial/cohort-style table with comparable follow-up.
Counts must be nonnegative integers and both groups must contain observations. Zero denominators return Not estimable; no arbitrary continuity correction is applied. All effect measures are unadjusted. This educational worksheet does not model censoring, confounding or confidence intervals.
| Epidemiology Effect Measure | Formula | Trial Data (12/200 Treated vs 30/200 Control) | Null Effect (30/200 vs 30/200) |
|---|---|---|---|
| Relative Risk (RR) | (B2/(B2+B3)) / (B4/(B4+B5)) | 0.06 / 0.15 = 0.4000 (60% RRR) | 1.0000 (No difference) |
| Cross-Product Odds Ratio (OR) | (B2 * B5) / (B3 * B4) | 2,040 / 5,640 = 0.3617 | 1.0000 |
| Absolute Risk Reduction (ARR) | (B4/(B4+B5)) - (B2/(B2+B3)) | 0.15 - 0.06 = 0.0900 (9.0% pts) | 0.0000 |
| Number Needed to Treat (NNT) | CEILING.MATH(1 / ARR, 1) | CEILING(11.11, 1) = 12 patients | No benefit (no finite benefit NNT) |
Risk ratio for comparable trial or cohort groups
Divide the treatment event proportion by the control event proportion. A zero control risk has no finite ratio in this example.
=IF(COUNT(B2:B5)<>4,"Invalid inputs",IF(OR(MIN(B2:B5)<0,B2<>INT(B2),B3<>INT(B3),B4<>INT(B4),B5<>INT(B5)),"Invalid inputs",IF(OR(B2+B3=0,B4+B5=0,B4=0),"Not estimable",ROUND((B2/(B2+B3))/(B4/(B4+B5)),4))))Benefit-only number needed to treat
Calculate from the unrounded positive risk reduction, then round the reciprocal upward. A nonpositive reduction returns No benefit, not a negative number of patients.
=IF(COUNT(B2:B5)<>4,"Invalid inputs",IF(OR(MIN(B2:B5)<0,B2<>INT(B2),B3<>INT(B3),B4<>INT(B4),B5<>INT(B5)),"Invalid inputs",IF(OR(B2+B3=0,B4+B5=0),"Not estimable",IF(B4/(B4+B5)-B2/(B2+B3)<=0,"No benefit",CEILING.MATH(1/(B4/(B4+B5)-B2/(B2+B3)),1)))))Odds ratio
Compare event-to-nonevent odds using the cross-product. The denominator must be positive.
=IF(COUNT(B2:B5)<>4,"Invalid inputs",IF(OR(MIN(B2:B5)<0,B2<>INT(B2),B3<>INT(B3),B4<>INT(B4),B5<>INT(B5)),"Invalid inputs",IF(OR(B2+B3=0,B4+B5=0,B3=0,B4=0),"Not estimable",ROUND((B2*B5)/(B3*B4),4))))Absolute risk reduction
Control event risk minus treatment event risk. Negative values indicate increased adverse-event risk in this sample.
=IF(COUNT(B2:B5)<>4,"Invalid inputs",IF(OR(MIN(B2:B5)<0,B2<>INT(B2),B3<>INT(B3),B4<>INT(B4),B5<>INT(B5)),"Invalid inputs",IF(OR(B2+B3=0,B4+B5=0),"Not estimable",B4/(B4+B5)-B2/(B2+B3))))Try the example
Use the original values or change them to test your understanding.