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Relative risk
U N DE R S T AN D I N G S T A T IS T IC S
Relative risk The relative risk is a commonly used measure for reporting the size of an effect seen when the outcomes in two groups in a prospective study are compared. It provides a quantitative estimate of the effect of treatment. Risk is a concept that expresses the probability that a health outcome or event will occur. It is calculated simply as the number of those who experience the event, divided by the total number of people at risk of having the event; it is usually expressed as a proportion or percentage. A hypothetical example can be used to illustrate the concept. In a cohort of women examined periodically and followed for more than 5 years, osteoporosis-related hip fractures were observed in 124 of 226 women in the control (untreated) group and in 42 of 222 women in the experimental group (given hormone replacement therapy) (Table 1). Using these data, risk can be calculated as follows: risk of event (in the experimental group)"a/a#b"42/222"0.19 risk of event (in the control group)"c/c#d"124/226"0.55 The relative risk (RR), which is also known as the risk ratio or the event rate ratio, is an expression of the probability that an event will occur when one group of subjects is compared with another. Mathematically, the relative risk can be calculated as follows: risk of event in experimental group relative risk" risk of event in control group
In the osteoporosis example, the relative risk of hip fractures with hormone replacement therapy is: (42/222)/(124/226)"0.19/0.55"0.34 The relative risk gives one an indication of how much the risk is increased or decreased from a baseline level (i.e. risk without treatment) and is a concept that is readily understood. For example, a relative risk of 0.5 demonstrates that the baseline risk has been halved, whereas a relative risk of 4 indicates that the baseline risk has been increased fourfold. The complement of the relative risk (i.e. 1-relative risk) is the relative risk reduction (RRR), which expresses the proportionate risk difference. Thus, a relative risk of 0.34 (and RRR of 0.66) represents a 66% reduction in the event rate (rate of hip fracture) in the experimental (treated) group, compared to the control (untreated) group. The relative risk reduction, therefore, is the reduction in adverse events achieved by treatment, expressed as a proportion of the control rate. In numerical terms, it is the absolute difference in event rates between the control and experimental groups, divided by the event rate in the control group: relative risk reduction" control group event rate!experimental group event rate control group event rate The main disadvantages of using RRR in clinical decision-making is that it does not reflect the magnitude of the baseline risk.
even rate in experimental group " event rate in control group
Salim Daya, MB, MSc McMaster University, Hamilton ON, Canada
a/a#b " c/c#d
Table 1. Effect of post-menopausal hormone replacement therapy on the prevention of osteoporosis-related hip fractures Hip fractures Allocation group Hormone replacement therapy Control (no treatment) Total
60
Yes 42 124 162
No a c a#c
Evidence-based Obstetrics and Gynecology (2000) 2, 60 doi:10.1054/ebog.2000.0172, available online at http://www.idealibrary.com on
180 102 282
Total b d b#d
222 226 448
a#b c#d a#b#c#d
^ 2000 Harcourt Publishers Ltd
Relative risk The relative risk is a commonly used measure for reporting the size of an effect seen when the outcomes in two groups in a prospective study are compared. It provides a quantitative estimate of the effect of treatment. Risk is a concept that expresses the probability that a health outcome or event will occur. It is calculated simply as the number of those who experience the event, divided by the total number of people at risk of having the event; it is usually expressed as a proportion or percentage. A hypothetical example can be used to illustrate the concept. In a cohort of women examined periodically and followed for more than 5 years, osteoporosis-related hip fractures were observed in 124 of 226 women in the control (untreated) group and in 42 of 222 women in the experimental group (given hormone replacement therapy) (Table 1). Using these data, risk can be calculated as follows: risk of event (in the experimental group)"a/a#b"42/222"0.19 risk of event (in the control group)"c/c#d"124/226"0.55 The relative risk (RR), which is also known as the risk ratio or the event rate ratio, is an expression of the probability that an event will occur when one group of subjects is compared with another. Mathematically, the relative risk can be calculated as follows: risk of event in experimental group relative risk" risk of event in control group
In the osteoporosis example, the relative risk of hip fractures with hormone replacement therapy is: (42/222)/(124/226)"0.19/0.55"0.34 The relative risk gives one an indication of how much the risk is increased or decreased from a baseline level (i.e. risk without treatment) and is a concept that is readily understood. For example, a relative risk of 0.5 demonstrates that the baseline risk has been halved, whereas a relative risk of 4 indicates that the baseline risk has been increased fourfold. The complement of the relative risk (i.e. 1-relative risk) is the relative risk reduction (RRR), which expresses the proportionate risk difference. Thus, a relative risk of 0.34 (and RRR of 0.66) represents a 66% reduction in the event rate (rate of hip fracture) in the experimental (treated) group, compared to the control (untreated) group. The relative risk reduction, therefore, is the reduction in adverse events achieved by treatment, expressed as a proportion of the control rate. In numerical terms, it is the absolute difference in event rates between the control and experimental groups, divided by the event rate in the control group: relative risk reduction" control group event rate!experimental group event rate control group event rate The main disadvantages of using RRR in clinical decision-making is that it does not reflect the magnitude of the baseline risk.
even rate in experimental group " event rate in control group
Salim Daya, MB, MSc McMaster University, Hamilton ON, Canada
a/a#b " c/c#d
Table 1. Effect of post-menopausal hormone replacement therapy on the prevention of osteoporosis-related hip fractures Hip fractures Allocation group Hormone replacement therapy Control (no treatment) Total
60
Yes 42 124 162
No a c a#c
Evidence-based Obstetrics and Gynecology (2000) 2, 60 doi:10.1054/ebog.2000.0172, available online at http://www.idealibrary.com on
180 102 282
Total b d b#d
222 226 448
a#b c#d a#b#c#d
^ 2000 Harcourt Publishers Ltd