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:
“He worked for twenty years to get his contemporaries to believe—and in the end he succeeded. Meanwhile, however, his adversaries also succeeded: he could no longer believe in himself.”
—Friedrich Nietzsche (1844–1900)
“... often in the heat of noonday, leaning on a hoe, looking across valleys at the mountains, so blue, so close, my only conscious thought was, “How can I ever get away from here? How can I get to where they have books, where I can be educated?” I worked hard, always waiting for something to happen to change things. There came a time when I knew I must make them happen; that no one would do anything about it for me. And I did.”
—Belinda Jelliffe (1892–1979)