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.
Read more about this topic: Relative Risk
Famous quotes containing the word worked:
“Let a man learn to look for the permanent in the mutable and fleeting; let him learn to bear the disappearance of things he was wont to reverence; without losing his reverence; let him learn that he is here, not to work, but to be worked upon; and that, though abyss open under abyss, and opinion displace opinion, all are at last contained in the Eternal Cause.”
—Ralph Waldo Emerson (18031882)
“There is something singularly grand and impressive in the sound of a tree falling in a perfectly calm night like this, as if the agencies which overthrow it did not need to be excited, but worked with a subtle, deliberate, and conscious force, like a boa-constrictor, and more effectively then than even in a windy day.”
—Henry David Thoreau (18171862)