↓
 
Home→New Essays→RELATIVE RISK ASSESSMENT

RELATIVE RISK ASSESSMENT

56thst.com Posted on by

Main menu

Search

Personal tools

Contents

hide

Relative risk

24 languages

Tools

Appearancehide

Text

  • SmallStandardLarge

Width

  • StandardWide

Color (beta)

From Wikipedia, the free encyclopedia

Illustration of two groups: one exposed to treatment, and one unexposed. Exposed group has smaller risk of adverse outcome, with RR = 4/8 = 0.5.
The group exposed to treatment (left) has half the risk (RR = 4/8 = 0.5) of an adverse outcome (black) compared to the unexposed group (right).

The relative risk (RR) or risk ratio is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. Together with risk difference and odds ratio, relative risk measures the association between the exposure and the outcome.[1]

Statistical use and meaning

[edit]

Relative risk is used in the statistical analysis of the data of ecological, cohort, medical and intervention studies, to estimate the strength of the association between exposures (treatments or risk factors) and outcomes.[2] Mathematically, it is the incidence rate of the outcome in the exposed group, 𝐼𝑒{\displaystyle I_{e}}, divided by the rate of the unexposed group, 𝐼𝑢{\displaystyle I_{u}}.[3] As such, it is used to compare the risk of an adverse outcome when receiving a medical treatment versus no treatment (or placebo), or for environmental risk factors. For example, in a study examining the effect of the drug apixaban on the occurrence of thromboembolism, 8.8% of placebo-treated patients experienced the disease, but only 1.7% of patients treated with the drug did, so the relative risk is .19 (1.7/8.8): patients receiving apixaban had 19% the disease risk of patients receiving the placebo.[4] In this case, apixaban is a protective factor rather than a risk factor, because it reduces the risk of disease.

Assuming the causal effect between the exposure and the outcome, values of relative risk can be interpreted as follows:[2]

  • RR = 1 means that exposure does not affect the outcome
  • RR < 1 means that the risk of the outcome is decreased by the exposure, which is a “protective factor“
  • RR > 1 means that the risk of the outcome is increased by the exposure, which is a “risk factor“

As always, correlation does not mean causation; the causation could be reversed, or they could both be caused by a common confounding variable. The relative risk of having cancer when in the hospital versus at home, for example, would be greater than 1, but that is because having cancer causes people to go to the hospital.

Usage in reporting

[edit]

Relative risk is commonly used to present the results of randomized controlled trials.[5] This can be problematic if the relative risk is presented without the absolute measures, such as absolute risk, or risk difference.[6] In cases where the base rate of the outcome is low, large or small values of relative risk may not translate to significant effects, and the importance of the effects to the public health can be overestimated. Equivalently, in cases where the base rate of the outcome is high, values of the relative risk close to 1 may still result in a significant effect, and their effects can be underestimated. Thus, presentation of both absolute and relative measures is recommended.[7]

Inference

[edit]

Relative risk can be estimated from a 2×2 contingency table:

 Group
Intervention (I)Control (C)
Events (E)IECE
Non-events (N)INCN

The point estimate of the relative risk is𝑅𝑅=𝐼𝐸/(𝐼𝐸+𝐼𝑁)𝐶𝐸/(𝐶𝐸+𝐶𝑁)=𝐼𝐸(𝐶𝐸+𝐶𝑁)𝐶𝐸(𝐼𝐸+𝐼𝑁).{\displaystyle RR={\frac {IE/(IE+IN)}{CE/(CE+CN)}}={\frac {IE(CE+CN)}{CE(IE+IN)}}.}

The sampling distribution of the log⁡(𝑅𝑅){\displaystyle \log(RR)}is closer to normal than the distribution of RR,[8] with standard error𝑆𝐸(log⁡(𝑅𝑅))=𝐼𝑁𝐼𝐸(𝐼𝐸+𝐼𝑁)+𝐶𝑁𝐶𝐸(𝐶𝐸+𝐶𝑁).{\displaystyle SE(\log(RR))={\sqrt {{\frac {IN}{IE(IE+IN)}}+{\frac {CN}{CE(CE+CN)}}}}.}

The 1−𝛼{\displaystyle 1-\alpha } confidence interval for the log⁡(𝑅𝑅){\displaystyle \log(RR)} is then𝐶𝐼1−𝛼(log⁡(𝑅𝑅))=log⁡(𝑅𝑅)±𝑆𝐸(log⁡(𝑅𝑅))×𝑧𝛼,{\displaystyle CI_{1-\alpha }(\log(RR))=\log(RR)\pm SE(\log(RR))\times z_{\alpha },}

where 𝑧𝛼{\displaystyle z_{\alpha }} is the standard score for the chosen level of significance.[9][10] To find the confidence interval around the RR itself, the two bounds of the above confidence interval can be exponentiated.[9]

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

Comparison to the odds ratio

[edit]

Risk ratio vs odds ratio

The relative risk is different from the odds ratio, although the odds ratio asymptotically approaches the relative risk for small probabilities of outcomes. If IE is substantially smaller than IN, then IE/(IE + IN) ≈{\displaystyle \scriptstyle \approx } IE/IN. Similarly, if CE is much smaller than CN, then CE/(CN + CE) ≈{\displaystyle \scriptstyle \approx } CE/CN. Thus, under the rare disease assumption𝑅𝑅=𝐼𝐸(𝐶𝐸+𝐶𝑁)𝐶𝐸(𝐼𝐸+𝐼𝑁)≈𝐼𝐸⋅𝐶𝑁𝐼𝑁⋅𝐶𝐸=𝑂𝑅.{\displaystyle RR={\frac {IE(CE+CN)}{CE(IE+IN)}}\approx {\frac {IE\cdot CN}{IN\cdot CE}}=OR.}

In practice the odds ratio is commonly used for case-control studies, as the relative risk cannot be estimated.[1]

In fact, the odds ratio has much more common use in statistics, since logistic regression, often associated with clinical trials, works with the log of the odds ratio, not relative risk. 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 relative risk might be significantly different.[citation needed]

Since relative risk 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 relative risk is just over 1, while the odds associated with action A are more than 10 times higher than the odds with B.[citation needed]

In statistical modelling, approaches like Poisson regression (for counts of events per unit exposure) have relative risk interpretations: the estimated effect of an explanatory variable is multiplicative on the rate and thus leads to a relative risk. 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.[citation needed]

Bayesian interpretation

[edit]

We could assume a disease noted by 𝐷{\displaystyle D}, and no disease noted by ¬𝐷{\displaystyle \neg D}, exposure noted by 𝐸{\displaystyle E}, and no exposure noted by ¬𝐸{\displaystyle \neg E}. The relative risk can be written as𝑅𝑅=𝑃(𝐷∣𝐸)𝑃(𝐷∣¬𝐸)=𝑃(𝐸∣𝐷)/𝑃(¬𝐸∣𝐷)𝑃(𝐸)/𝑃(¬𝐸).{\displaystyle 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 relative risk 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.[11] 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 relative risk.

Numerical example

[edit]

QuantityExperimental group (E)Control group (C)Total
Events (E)EE = 15CE = 100115
Non-events (N)EN = 135CN = 150285
Total subjects (S)ES = EE + EN = 150CS = CE + CN = 250400
Event rate (ER)EER = EE / ES = 0.1, or 10%CER = CE / CS = 0.4, or 40%—
VariableAbbr.FormulaValue
Absolute risk reductionARRCER − EER0.3, or 30%
Number needed to treatNNT1 / (CER − EER)3.33
Relative risk (risk ratio)RREER / CER0.25
Relative risk reductionRRR(CER − EER) / CER, or 1 − RR0.75, or 75%
Preventable fraction among the unexposedPFu(CER − EER) / CER0.75
Odds ratioOR(EE / EN) / (CE / CN)0.167

See also

[edit]

Wikimedia Commons has media related to Statistics for relative risk.

References

[edit]

  1. ^ Jump up to:a b Sistrom CL, Garvan CW (January 2004). “Proportions, odds, and risk”. Radiology. 230 (1): 12–9. doi:10.1148/radiol.2301031028. PMID 14695382.
  2. ^ Jump up to:a b Carneiro, Ilona. (2011). Introduction to epidemiology. Howard, Natasha. (2nd ed.). Maidenhead, Berkshire: Open University Press. p. 27. ISBN 978-0-335-24462-1. OCLC 773348873.
  3. ^ Bruce, Nigel, 1955- (29 November 2017). Quantitative methods for health research : a practical interactive guide to epidemiology and statistics. Pope, Daniel, 1969-, Stanistreet, Debbi, 1963- (Second ed.). Hoboken, NJ. p. 199. ISBN 978-1-118-66526-8. OCLC 992438133.
  4. ^ Motulsky, Harvey (2018). Intuitive biostatistics : a nonmathematical guide to statistical thinking (Fourth ed.). New York. p. 266. ISBN 978-0-19-064356-0. OCLC 1006531983.
  5. ^ 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. S2CID 28195147.
  6. ^ 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.
  7. ^ 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.
  8. ^ “Standard errors, confidence intervals, and significance tests”. StataCorp LLC.
  9. ^ Jump up to: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.
  10. ^ Katz, D.; Baptista, J.; Azen, S. P.; Pike, M. C. (1978). “Obtaining Confidence Intervals for the relative risk in Cohort Studies”. Biometrics. 34 (3): 469–474. doi:10.2307/2530610. JSTOR 2530610.
  11. ^ Armitage P, Berry G, Matthews JN (2002). Armitage P, Berry G, Matthews J (eds.). Statistical Methods in Medical Research. Vol. 64 (Fourth ed.). Blackwell Science Ltd. p. 1168. doi:10.1002/9780470773666. ISBN 978-0-470-77366-6. PMC 1812060. {{cite book}}: |journal= ignored (help)

[edit]

showvteClinical research and experimental design
showvtePublic health

Categories: 

Posted in New Essays permalink

About joelsnell99

Who's Who in all U.S and U.K. Honoraries (Marquis) Numerous publications in over 80 venues DANA SPIRIT AWARD/2009 Oxford Roundtable, Editor of FOCUS, a student Social Science Journal Author Snell Life Cycle Lonliness Curve Professor Emeritus - Kirkwood College Omicron Delta Kappa Grants Online Editor for Psychology and Education.com Research Fellow - Arlington Institute Outstanding Teacher at Kirkwood College Membership in numerous editorial boards or a reviewer of manuscripts Associate Editor - Psychology and Education Co-Author of Snell-Green Professor Index Author of Snell Educator Effectiveness Index Contributer to FutureEdition.com Co-Author of Snell-Allen Medical Rank Index Fellow in Kennedy Foundation Co-Author of Snell-Allen Subjective Assessment Sex Role Index Honors >>> Positions and Courses Taught >>> joelsnell@hotmail.com http://www.socialvibes.net Research Council, Advisory Board

Comments are closed.

↑