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WordNet

expose to a chance of loss or damage; "We risked losing a lot of money in this venture"; "Why risk your life?"; "She laid her job on the line when she told the boss that he was wrong" (同)put on the line, lay on the line
a venture undertaken without regard to possible loss or injury; "he saw the rewards but not the risks of crime"; "there was a danger he would do the wrong thing" (同)peril, danger
the probability of being exposed to an infectious agent (同)risk of exposure
the probability of becoming infected given that exposure to an infectious agent has occurred (同)risk of infection
give (hair) the appearance of being fuller by using a rat
a pad (usually made of hair) worn as part of a womans coiffure
any of various long-tailed rodents similar to but larger than a mouse
catch rats, especially with dogs
desert ones party or group of friends, for example, for ones personal advantage
employ scabs or strike breakers in
newly come into prominence; "a rising young politician"
advancing or becoming higher or greater in degree or value or status; "a rising trend"; "a rising market"
the relative magnitudes of two quantities (usually expressed as a quotient)

PrepTutorEJDIC

『危険』;危害(損害)を受ける可能性《+『of』+『名』(do『ing』)》 / 〈生命など〉‘を'『危険にさらす』 / …‘を'危険(失敗,損失など)を覚悟してする
『ネズミ』 / ひきょう者,裏切り者 / ネズミをつかまえる / 《話》(人を)裏切る,密告する《+『on』+『名』〈人〉》
〈U〉(…が)上がること,(…の)上昇;昇進《+『of』+『名』》 / 〈U〉起床 / 〈C〉蜂起,反乱 / 上がる,強まる,高まる / 成長する,発達中の,上り坂にある
ほぼ(…)歳
『比』,比率,『割合』;『比例』

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2019/03/30 02:42:35」(JST)

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The group exposed to treatment (left) has half the risk (RR = 0.5) of an adverse outcome (black) compared to the unexposed group (right).

In epidemiology, risk ratio (RR) or relative risk is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. It is computed as $I_{e}/I_{u}$ , where $I_{e}$ is the incidence in the exposed group, and $I_{u}$ is the incidence in the unexposed group.^[1] Together with risk difference and odds ratio, risk ratio measures the association between the exposure and the outcome.^[2]

Statistical use and meaning

Risk ratio is used in the statistical analysis of the data of experimental, cohort and cross-sectional studies, to estimate the strength of the association between treatments or risk factors, and outcome.^[2]^[3] For example, it is used to compare the risk of an adverse outcome when receiving a medical treatment versus no treatment (or placebo), or when exposed to an environmental risk factor versus not exposed.

Assuming the causal effect between the exposure and the outcome, values of RR can be interpreted as follows:

RR = 1 means that exposure does not affect the outcome;
RR < 1 means that the risk of the outcome is decreased by the exposure;
RR > 1 means that the risk of the outcome is increased by the exposure.

Usage in reporting

Risk ratio is commonly used to present the results of randomized controlled trials.^[4] This can be problematic, if risk ratio is presented without the absolute measures, such as absolute risk, or risk difference.^[5] In the case when the base rate of the outcome is low, large or small values of risk ratio may not translate to significant effect, and the importance of the effect to the public health can be overestimated. Equivalently, in the case when the base rate of the outcome is high, values of the risk ratio close to 1 may still result in a significant effect and can be underestimated. Thus, presentation of both absolute and relative measures is recommended.^[6]

Inference

Risk ratio can be estimated from a 2x2 contingency table:

	Group
	Experimental (E)	Control (C)
Events (E)	EE	CE
Non-events (N)	EN	CN

The point estimate of the risk ratio is

RR={\frac {EE/(EE+EN)}{CE/(CE+CN)}}={\frac {EE(CE+CN)}{CE(EE+EN)}}.

The sampling distribution of the $\log(RR)$ is approximately normal,^[7]^{[not in citation given]} with standard error

SE(\log(RR))={\sqrt {{\frac {EN}{EE(EE+EN)}}+{\frac {CN}{CE(CE+CN)}}}}.

The $1-\alpha$ confidence interval for the $\log(RR)$ is then

CI_{1-\alpha }(\log(RR))=\log(RR)\pm SE(\log(RR))\times z_{\alpha },

where $z_{\alpha }$ is the standard score for the chosen level of significance^[8]^[9]. To find the confidence interval around the RR itself, the two bounds of the above confidence interval can be exponentiated.^[8]

In regression models, the exposure is typically included as an indicator variable along with other factors that may affect risk. The risk ratio is usually reported as calculated for the mean of the sample values of the explanatory variables.

Comparison to the odds ratio

Risk ratio is different from the odds ratio, although it asymptotically approaches it for small probabilities of outcomes. If EE is substantially smaller than EN, then EE/(EE + EN) $\scriptstyle \approx$ EE/EN. Similarly, if CE is much smaller than CN, then CE/(CN + CE) $\scriptstyle \approx$ CE/CN. Thus, under the rare disease assumption

RR={\frac {EE(CE+CN)}{CE(EE+EN)}}\approx {\frac {EE\cdot CN}{EN\cdot CE}}=OR.

In epidemiological research, the odds ratio is commonly used for case-control studies, as the risk ratio cannot be estimated.^[2]

In fact, the odds ratio has much broader use in statistics, since logistic regression, often associated with clinical trials, works with the log of the odds ratio, not risk ratio. Because the (natural log of the) odds of a record is estimated as a linear function of the explanatory variables, the estimated odds ratio for 70-year-olds and 60-year-olds associated with the type of treatment would be the same in logistic regression models where the outcome is associated with drug and age, although the risk ratio might be significantly different. In cases like this, statistical models of the odds ratio often reflect the underlying mechanisms more efficiently.

Since risk ratio is a more intuitive measure of effectiveness, the distinction is important especially in cases of medium to high probabilities. If action A carries a risk of 99.9% and action B a risk of 99.0% then the risk ratio is just over 1, while the odds associated with action A are more than 10 times higher than the odds with B.

In statistical modelling, approaches like poisson regression (for counts of events per unit exposure) have risk ratio interpretations: the estimated effect of an explanatory variable is multiplicative on the rate and thus leads to a risk ratio. Logistic regression (for binary outcomes, or counts of successes out of a number of trials) must be interpreted in odds-ratio terms: the effect of an explanatory variable is multiplicative on the odds and thus leads to an odds ratio.

Bayesian interpretation

We could assume a disease noted by $D$ , and no disease noted by $\neg D$ , exposure noted by $E$ , and no exposure noted by $\neg E$ . Risk ratio can be written as

RR={\frac {P(D\mid E)}{P(D\mid \neg E)}}={\frac {P(E\mid D)/P(\neg E\mid D)}{P(E)/P(\neg E)}}.

This way the risk ratio can be interpreted in Bayesian terms as the posterior ratio of the exposure (i.e. after seeing the disease) normalized by the prior ratio of exposure.^[10] If the posterior ratio of exposure is similar to that of the prior, the effect is approximately 1, indicating no association with the disease, since it didn't change beliefs of the exposure. If on the other hand, the posterior ratio of exposure is smaller or higher than that of the prior ratio, then the disease has changed the view of the exposure danger, and the magnitude of this change is the risk ratio.

Numerical example

	Example of risk reduction
	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%

Equation	Variable	Abbr.	Value
CER - EER	absolute risk reduction	ARR	0.3, or 30%
(CER - EER) / CER	relative risk reduction	RRR	0.75, or 75%
1 / (CER − EER)	number needed to treat	NNT	3.33
EER / CER	risk ratio	RR	0.25
(EE / EN) / (CE / CN)	odds ratio	OR	0.167
(CER - EER) / CER	preventable fraction among the unexposed	PFu	0.75

References

^ Porta M, ed. (2014). Dictionary of Epidemiology (6th ed.). Oxford University Press. pp. 245, 252. doi:10.1093/acref/9780199976720.001.0001. ISBN 978-0-19-939006-9.
^ ^a ^b ^c Sistrom CL, Garvan CW (January 2004). "Proportions, odds, and risk". Radiology. 230 (1): 12–9. doi:10.1148/radiol.2301031028. PMID 14695382.
^ Riegelman RK (2005). Studying a study and testing a test: how to read the medical evidence (5th ed.). Philadelphia: Lippincott Williams & Wilkins. p. 389. ISBN 978-0-7817-4576-5. OCLC 56415070.
^ Nakayama T, Zaman MM, Tanaka H (April 1998). "Reporting of attributable and relative risks, 1966-97". Lancet. 351 (9110): 1179. doi:10.1016/s0140-6736(05)79123-6. PMID 9643696.
^ Noordzij M, van Diepen M, Caskey FC, Jager KJ (April 2017). "Relative risk versus absolute risk: one cannot be interpreted without the other". Nephrology, Dialysis, Transplantation. 32 (suppl_2): ii13–ii18. doi:10.1093/ndt/gfw465. PMID 28339913.
^ Moher D, Hopewell S, Schulz KF, Montori V, Gøtzsche PC, Devereaux PJ, Elbourne D, Egger M, Altman DG (March 2010). "CONSORT 2010 explanation and elaboration: updated guidelines for reporting parallel group randomised trials". BMJ. 340: c869. doi:10.1136/bmj.c869. PMC 2844943. PMID 20332511.
^ "Standard errors, confidence intervals, and significance tests". StataCorp LLC.
^ ^a ^b Szklo, Moyses; Nieto, F. Javier (2019). Epidemiology : beyond the basics (4th. ed.). Burlington, Massachusetts: Jones & Bartlett Learning. p. 488. ISBN 9781284116595. OCLC 1019839414.
^ Katz, D.; Baptista, J.; Azen, S. P.; Pike, M. C. (1978). "Obtaining Confidence Intervals for the Risk Ratio in Cohort Studies". Biometrics. 34 (3): 469–474. doi:10.2307/2530610. JSTOR 2530610.
^ Armitage P, Berry G, Matthews JN (2002). Statistical Methods in Medical Research (Fourth ed.). Blackwell Science Ltd. doi:10.1002/9780470773666. ISBN 978-0-470-77366-6. PMC 1812060.

External links

Relative risk online calculator

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