Relative risk reduction

In epidemiology, the relative risk reduction is a measure calculated by dividing the absolute risk reduction by the control event rate.

Like many other epidemiological measures, the same equations can be used to measure a benefit or a harm (although the signs may need to be adjusted, depending upon how the data was collected.)

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
EER − CER	< 0: absolute risk reduction	ARR	(−)0.3, or (−)30%	N/A
	> 0: absolute risk increase	ARI	N/A	0.1, or 10%
(EER − CER) / CER	< 0: relative risk reduction	RRR	(−)0.75, or (−)75%	N/A
	> 0: relative risk increase	RRI	N/A	0.25, or 25%
1 / (EER − CER)	< 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