Absolute Risk, Relative Risk, NNT, and NNH
Reading Past the Headline Number
Absolute Risk, Relative Risk, NNT, and NNH
Drug trials report the same result in multiple ways. Relative risk reduction makes a drug look impressive. Absolute risk reduction and NNT tell you what actually happens to patients. You need to know all three.
Part 1 — Definitions and Formulas
| Term | Formula | What It Means |
|---|---|---|
| EER (Experimental Event Rate) | Events in treatment group / total in treatment group | The event rate in patients who received the drug |
| CER (Control Event Rate) | Events in control group / total in control group | The event rate in patients who received placebo |
| ARR (Absolute Risk Reduction) | CER − EER | The actual percentage-point reduction in events |
| RRR (Relative Risk Reduction) | ARR ÷ CER | The proportion of control-group risk that was eliminated |
| NNT (Number Needed to Treat) | 1 ÷ ARR | Patients who must receive treatment for 1 event to be prevented |
| NNH (Number Needed to Harm) | 1 ÷ ARI | Patients who must be treated for 1 additional harm to occur |
Note: ARI = Absolute Risk Increase (calculated the same way as ARR, but for an adverse outcome).
Part 2 — The Same Trial, Three Different Headlines
ASCOT-LLA (2003) randomized 10,305 patients with hypertension and cardiovascular risk factors to atorvastatin 10 mg vs. placebo. Primary outcome: nonfatal MI or fatal CHD.
| Metric | Calculation and Result |
|---|---|
| CER | 154 / 5137 = 3.0% (events in placebo group over 3.3 years) |
| EER | 100 / 5168 = 1.9% (events in atorvastatin group over 3.3 years) |
| ARR | 3.0% − 1.9% = 1.1% |
| RRR | 1.1% ÷ 3.0% = 36% |
| NNT | 1 ÷ 0.011 = 91 (over 3.3 years) |
- Drug rep version: “This statin reduces cardiovascular events by 36%.” (RRR)
- Journal abstract version: “Atorvastatin reduced the absolute risk of events by 1.1%.” (ARR)
- Patient counseling version: “91 patients need to take this pill every day for 3 years to prevent 1 heart attack or cardiac death.” (NNT)
All three are mathematically true. They do not feel the same.
RRR scales with baseline risk. A 36% RRR means something very different in a patient with 3% baseline risk (NNT = 91) vs. a patient with 15% baseline risk (NNT = 18). The higher the baseline risk, the lower the NNT, and the more compelling the case for treatment.
Part 3 — NNH: Applying the Same Logic to Harms
NNH uses the same arithmetic, applied to an adverse outcome. If a drug causes bleeding in 2% of treated patients vs. 0.5% of controls:
| Metric | Result |
|---|---|
| ARI | 2.0% − 0.5% = 1.5% |
| NNH | 1 ÷ 0.015 = 67 |
Using NNT and NNH together is the most direct way to frame a benefit-harm tradeoff at the bedside. A drug with NNT of 25 and NNH of 200 has a favorable profile. A drug with NNT of 200 and NNH of 25 does not. Put the numbers side by side.
NNT is the number you use to counsel patients. “This drug reduces your risk by 33%” (RRR) sounds very different from “91 patients need to take this drug for 3 years to prevent 1 event” (NNT). Both are true. Know which one you are saying.
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