Relative risk reduction

Illustration of two groups: one exposed to a treatment, and one unexposed. Exposed group has smaller risk of adverse outcome (RRR = 0.5). — The group exposed to treatment (left) has the risk of an adverse outcome (black) reduced by 50% (RRR = 0.5) compared to the unexposed group (right).

In epidemiology, the relative risk reduction (RRR) or efficacy is the relative decrease in the risk of an adverse event in the exposed group compared to an unexposed group. It is computed as $(I_{u}-I_{e})/I_{u}$ , where $I_{e}$ is the incidence in the exposed group, and $I_{u}$ is the incidence in the unexposed group. If the risk of an adverse event is increased by the exposure rather than decreased, the term relative risk increase (RRI) is used, and it is computed as $(I_{e}-I_{u})/I_{u}$ .^[1]^[2] If the direction of risk change is not assumed, the term relative effect is used, and it is computed in the same way as relative risk increase.^[3]

Numerical examples

Risk reduction

Example of risk reduction
Quantity	Experimental group (E)	Control group (C)	Total
Events (E)	EE = 15	CE = 100	115
Non-events (N)	EN = 135	CN = 150	285
Total subjects (S)	ES = EE + EN = 150	CS = CE + CN = 250	400
Event rate (ER)	EER = EE / ES = 0.1, or 10%	CER = CE / CS = 0.4, or 40%	—

Variable	Abbr.	Formula	Value
Absolute risk reduction	ARR	CER − EER	0.3, or 30%
Number needed to treat	NNT	1 / (CER − EER)	3.33
Relative risk (risk ratio)	RR	EER / CER	0.25
Relative risk reduction	RRR	(CER − EER) / CER, or 1 − RR	0.75, or 75%
Preventable fraction among the unexposed	PFu	(CER − EER) / CER	0.75
Odds ratio	OR	(EE / EN) / (CE / CN)	0.167

Risk increase

Example of risk increase
Quantity	Experimental group (E)	Control group (C)	Total
Events (E)	EE = 75	CE = 100	175
Non-events (N)	EN = 75	CN = 150	225
Total subjects (S)	ES = EE + EN = 150	CS = CE + CN = 250	400
Event rate (ER)	EER = EE / ES = 0.5, or 50%	CER = CE / CS = 0.4, or 40%	—

Variable	Abbr.	Formula	Value
Absolute risk increase	ARI	EER − CER	0.1, or 10%
Number needed to harm	NNH	1 / (EER − CER)	10
Relative risk (risk ratio)	RR	EER / CER	1.25
Relative risk increase	RRI	(EER − CER) / CER, or RR − 1	0.25, or 25%
Attributable fraction among the exposed	AF_e	(EER − CER) / EER	0.2
Odds ratio	OR	(EE / EN) / (CE / CN)	1.5

References

^ Porta, Miquel, ed. (2014). "A Dictionary of Epidemiology". Dictionary of Epidemiology - Oxford Reference. Oxford University Press. doi:10.1093/acref/9780199976720.001.0001. ISBN 9780199976720. Retrieved 2018-05-09.
^ Szklo, Moyses; Nieto, F. Javier (2019). Epidemiology : beyond the basics (4th. ed.). Burlington, Massachusetts: Jones & Bartlett Learning. p. 97. ISBN 9781284116595. OCLC 1019839414.
^ J., Rothman, Kenneth (2012). Epidemiology : an introduction (2nd ed.). New York, NY: Oxford University Press. p. 59. ISBN 9780199754557. OCLC 750986180.{{cite book}}: CS1 maint: multiple names: authors list (link)

[:02-1] Porta, Miquel, ed. (2014). "A Dictionary of Epidemiology". Dictionary of Epidemiology - Oxford Reference. Oxford University Press. doi:10.1093/acref/9780199976720.001.0001. ISBN 9780199976720. Retrieved 2018-05-09.

[2] Szklo, Moyses; Nieto, F. Javier (2019). Epidemiology : beyond the basics (4th. ed.). Burlington, Massachusetts: Jones & Bartlett Learning. p. 97. ISBN 9781284116595. OCLC 1019839414.

[:12-3] J., Rothman, Kenneth (2012). Epidemiology : an introduction (2nd ed.). New York, NY: Oxford University Press. p. 59. ISBN 9780199754557. OCLC 750986180.{{cite book}}: CS1 maint: multiple names: authors list (link)

[1]

[2]

[3]

Numerical examples

Risk reduction

Risk increase

See also

References