2025 – PAGE 392 – STATISTICS
RELATIVE RISK
The relative risk (AKA risk ratio) is the ratio of the risk of having a particular outcome (usually a negative outcome) in one group to the risk of having the same outcome in another group. Usually this is used to compare an intervention to a control. The risk is the number of events (such as death) divided by the total population in that group.
| Disease | No Disease | Total | |
| Exposed | Exposed-disease | Exposed-healthy | Exposed-Total |
| Unexposed | Unexposed-disease | Unexposed-healthy | Unexposed-Total |
Relative Risk Formula:
For example, if 3% of patients who are given Antibiotic A (intervention) experience renal failure (outcome) compared with 1% of patients experiencing renal failure with NO antibiotics given (control), then the risk of Antibiotic A resulting in renal failure is 3% and the risk of having renal failure without antibiotics is 1%. The relative risk of using Antibiotic A is 3% divided by 1%, which comes out to 3.
| Renal failure | No Renal Failure | Total | |
| Antibiotic A | 3 | 97 | 100 |
| No Antibiotic | 1 | 99 | 100 |
The RR in this example would be (3/100) / (1/100) = 3.
PEARL: If the RR is less than 1, then the exposure seems to be protective (or less likely to cause the measured outcome). If the relative risk is greater than 1, then the exposure seems to be harmful (or at least more likely to cause the measured outcome).
CASE-CONTROL STUDIES
In case-control studies, the researcher starts by selecting individuals in whom the disease is present (case) and those in whom the disease is not present (control). He then looks backwards for evidence of exposure versus non-exposure. A researcher can limit confounding factors by controlling for various factors (sex, age, etc.) during the selection process. Other strengths include the limited expense involved, the ability to perform the study quickly, and its usefulness to study rare diseases. A potential weakness has to do with lower internal validity when the history of exposure relies on the recall of the subject or a loved one. For example, if researching 5-year-old boys with and without peanut allergies with plans to assess for first-time peanut exposure, the researcher must rely on parental recall of first-time exposure to any peanut-based product. That’s quite variable. Furthermore, parents of a peanut-allergic child might be more likely to recall exposures than parents of a non-allergic child (recall bias).
IMAGE: www.pbrlinks.com/CASECONTROL1 (compares cohorts vs. case-controlled studies)