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This article is about an epidemiological concept. For other uses, see ARR.

In epidemiology, the absolute risk reduction or risk difference is the decrease in risk of a given activity or treatment in relation to a control activity or treatment.^[1] It is the inverse of the number needed to treat.^[2]

For example, consider a hypothetical drug which reduces the relative risk of colon cancer by 50% over five years. Even without the drug, colon cancer is fairly rare, maybe 1 in 3,000 in every five-year period. The rate of colon cancer for a five-year treatment with the drug is therefore 1/6,000, as by treating 6,000 people with the drug, one can expect to reduce the number of colon cancer cases from 2 to 1.

In general, absolute risk reduction is usually computed with respect to two treatments A and B, with A typically a drug and B a placebo (in our example above, A is a 5-year treatment with the hypothetical drug, and B is treatment with placebo, i.e. no treatment). A defined endpoint has to be specified (in our example: the appearance of colon cancer in the 5 year period). If the probabilities p_A and p_B of this endpoint under treatments A and B, respectively, are known, then the absolute risk reduction is computed as (p_B - p_A).

The inverse of the absolute risk reduction, NNT, is an important measure in pharmacoeconomics. If a clinical endpoint is devastating enough (e.g. death, heart attack), drugs with a low absolute risk reduction may still be indicated in particular situations. If the endpoint is minor, health insurers may decline to reimburse drugs with a low absolute risk reduction.

Presenting resultsEdit

The raw calculation of absolute risk reduction is a probability (0.003 fewer cases per person, using the colon cancer example above). Authors such as Ben Goldacre believe that this information is best presented as a natural number in the context of the baseline risk ("reduces 2 cases of colon cancer to 1 case if you treat 6,000 people for five years").^[3] Natural numbers, which are used in the number needed to treat approach, are easily understood by non-experts.

Worked exampleEdit

	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
CER − EER	< 0: absolute risk reduction	ARR	(−)0.3, or (−)30%	N/A
CER − EER	> 0: absolute risk increase	ARI	N/A	0.1, or 10%
(CER − EER) / CER	< 0: relative risk reduction	RRR	(−)0.75, or (−)75%	N/A
(CER − EER) / CER	> 0: relative risk increase	RRI	N/A	0.25, or 25%
1 / (CER − EER)	< 0: number needed to treat	NNT	(−)3.33	N/A
1 / (CER − EER)	> 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

ReferencesEdit

↑ An overview of measurements in epidemiology. URL accessed on 2010-02-01.
↑ Laupacis A, Sackett DL, Roberts RS. An assessment of clinically useful measures of the consequences of treatment. N Engl J Med 1988;318:1728-33. PMID 3374545.
↑ Ben Goldacre (2008). Bad Science, 239–260, New York: Fourth Estate.

External linksEdit

Measures of effect size of an intervention - unmc.edu.

es:Riesgo absoluto

nl:Absolute risicoreductie

[0] An overview of measurements in epidemiology. URL accessed on 2010-02-01.

[1] Laupacis A, Sackett DL, Roberts RS. An assessment of clinically useful measures of the consequences of treatment. N Engl J Med 1988;318:1728-33. PMID 3374545.

[isbn0-00-724019-8-2] Ben Goldacre (2008). Bad Science, 239–260, New York: Fourth Estate.

[1]

[2]

[3]

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Epidemiology/ methods	occurrence: Incidence (Cumulative incidence) Prevalence (Point prevalence, Period prevalence) association: absolute (Absolute risk reduction, Attributable risk, Attributable risk percent) relative (Relative risk, Odds ratio, Hazard ratio) other: Virulence Infectivity Mortality rate Morbidity Case fatality Specificity and sensitivity Likelihood-ratios Pre/post-test probability
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