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Relative risk reduction

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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 (dark) reduced by 50% (RRR = 0.5) compared to the unexposed group (right).

Inepidemiology, therelative risk reduction (RRR) orefficacy is the relative decrease in therisk 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 termrelative 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 termrelative effect is used, and it is computed in the same way as relative risk increase.^[3]

Numerical examples

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Risk reduction

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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

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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, orRR − 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

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^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. Retrieved2018-05-09.
^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. pp. 59.ISBN 9780199754557.OCLC 750986180.{{cite book}}: CS1 maint: multiple names: authors list (link)

Clinical research andexperimental design

Overview

Controlled study
(EBM I to II-1)

Observational study
(EBM II-2 to II-3)

Measures

Occurrence	Incidence,Cumulative incidence,Prevalence,Point prevalence,Period prevalence
Association	Risk difference,Number needed to treat,Number needed to harm,Risk ratio,Relative risk reduction,Odds ratio,Hazard ratio
Population impact	Attributable fraction among the exposed,Attributable fraction for the population,Preventable fraction among the unexposed,Preventable fraction for the population
Other	Clinical endpoint,Virulence,Infectivity,Mortality rate,Morbidity,Case fatality rate,Specificity and sensitivity,Likelihood-ratios,Pre- and post-test probability