Fundamental metrics of risk
| Metric | Symbol | Example calculation | Interpretation |
| Example 1: 1000 obese subjects, of whom 75 develop CVD during follow-up; 1000 non-obese subjects, of whom 30 develop CVD during follow-up. | |||
| Risk* | Obese: 75/1000=0.075; non-obese: 30/1000=0.03 | 75 in a 1000 obese, and 30 in a 1000 non-obese, develop CVD. | |
| Relative risk | RR | 0.075/0.03=2.5 | The obese have 2.5 times the risk of the non-obese. |
| Risk difference | RD | 0.075–0.03=0.045 | Obesity is associated with an additional risk of 45 in a 1000. |
| Example 2: half (500) of the obese were women, of whom 35 developed CVD; half (500) of the non-obese were women, of whom 10 developed CVD. | |||
| Risk for women | Obese: 35/500=0.07; non-obese: 10/500=0.02 | 7 in a 100 obese women, and 2 in a 100 non-obese women, develop CVD. | |
| Risk for men | Obese: 40/500=0.08; non-obese: 20/500=0.04 | 8 in a 100 obese men, and 4 in a 100 non-obese men, develop CVD. | |
| RR for women | RRwomen | 0.07/0.02=3.5 | Obese women have 3.5 times the risk of non-obese women. |
| RR for men | RRmen | 0.08/0.04=2 | Obese men have twice the risk of non-obese men. |
| RD for women | RDwomen | 0.07–0.02=0.05 | Female obesity is associated with an additional risk of 5 in a 100. |
| RD for men | RDmen | 0.08–0.04=0.04 | Male obesity is associated with an additional risk of 4 in a 100. |
| Ratio of relative risks, women to men | RRR | 3.5/2=1.75 | Women have a 75% greater proportional risk increase associated with obesity, compared with men. |
| Difference of risk differences, women to men | DRD | 0.05–0.04=0.01 | Women have an additional increased risk of 1 in a 100 associated with obesity, compared with men. |
The table includes a simple artificial example of a cohort study assuming no (or ignorable) censoring during a fixed duration of follow-up. In example 1, the sex of the subject is ignored; in example 2, sex differences are evaluated.
↵*Often called the ‘absolute risk’. I feel that the qualifier is unnecessary and inappropriate because it suggests some kind of truth, whereas in general the risk is merely an estimate subject to random error and, sometimes, bias error. It can also be confusing, as when absolute risk is incorrectly represented as an alternative to the RR (the true alternative to the RR is the RD).
Notes
1. With a cross-sectional study, replace ‘risk’ by ‘prevalence’.
2. With a case–control study, replace RR by ‘odds ratio’ (OR).
3. With a cohort study that is analysed using logistic regression, replace RR by OR. Censoring is ignored. Often the OR is assumed to be the same as the RR, which is reasonable if the disease analysed is rare in the study population, but the OR will always overestimate the RR. In example 1, the OR is (75/(1000–75))/(30/(1000–30))=2.62, slightly higher than the RR of 2.5.
4. With a cohort study that is analysed using log-binomial regression, risks and RRs are estimated. Censoring is ignored.
5. With a cohort study that is analysed using Cox or Weibull proportional hazards regression models, HRs are estimated. These are generally taken to be the same as the RR. Censoring is accounted for.
6. With a cohort study that is analysed using Poisson models, rates and relative rates are estimated. These are generally taken to be the same as risks and RRs. Censoring is accounted for.
CVD, cardiovascular disease.