Relative Risk - Worked Example

Worked Example

Example 1: risk reduction Example 2: risk increase
Experimental group (E) Control group (C) Total (E) (C) Total
Events (E) EE = 15 CE = 100 115 EE = 75 CE = 100 175
Non-events (N) EN = 135 CN = 150 285 EN = 75 CN = 150 225
Total subjects (S) ES = EE + EN = 150 CS = CE + CN = 250 400 ES = 150 CS = 250 400
Event rate (ER) EER = EE / ES = 0.1, or 10% CER = CE / CS = 0.4, or 40% EER = 0.5 (50%) CER = 0.4 (40%)
Equation Variable Abbr. Example 1 Example 2
CER − EER < 0: absolute risk reduction ARR (−)0.3, or (−)30% N/A
> 0: absolute risk increase ARI N/A 0.1, or 10%
(CER − EER) / CER < 0: relative risk reduction RRR (−)0.75, or (−)75% N/A
> 0: relative risk increase RRI N/A 0.25, or 25%
1 / (CER − EER) < 0: number needed to treat NNT (−)3.33 N/A
> 0: number needed to harm NNH N/A 10
EER / CER relative risk RR 0.25 1.25
(EE / EN) / (CE / CN) odds ratio OR 0.167 1.5
EER − CER attributable risk AR (−)0.30, or (−)30% 0.1, or 10%
(RR − 1) / RR attributable risk percent ARP N/A 20%
1 − RR (or 1 − OR) preventive fraction PF 0.75, or 75% N/A
  • Example 3: Ratios are presented for each of experimental and control groups. In the disease-risk 2 × 2 table above, suppose a + c = 1 and b + d = 1 and the total number of patients and healthy people be m and n, respectively. Then prevalence ratio becomes p = m/(m + n). We can put q = m/n = p/(1 − p). Thus
If p is small enough, then q would be small enough and either of (b/d)q and (a/c)q would be small enough to be regarded as 0 compared with 1. RR would be reduced to the odd ratio as above.
Among Japanese, not a small fraction of patients of Behçet's disease are bestowed with a specific HLA type, namely HLA-B51 gene. In a survey, the proportion is 63% of the patients with this gene, while in healthy people the ratio is 21%. If the figures are considered to be representative for most Japanese, using the values of 12,700 patients in Japan in 1984 and the Japanese population about 120 million in 1982, then RR = 6.40. Compare with the odd ratio 6.41.

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