Why do odds ratio and relative risk have similar values?

When conducting statistical analysis in various fields, researchers often come across two important measures: odds ratio and relative risk. Both these measures provide valuable insights into the association between variables. This review aims to explain why odds ratio and relative risk have similar values, highlighting their benefits and suitable conditions for their use.

I. Understanding Odds Ratio and Relative Risk:

Odds Ratio:

- The odds ratio compares the odds of an event occurring in one group to the odds of the same event occurring in another group.
- It is commonly used in case-control studies and logistic regression analyses.
- The formula for calculating odds ratio is: (ad)/(bc), where a, b, c, and d represent the frequencies of different outcomes.

Relative Risk:

- Relative risk measures the ratio of the probability of an event occurring in the exposed group to the probability of the same event occurring in the unexposed group.
- It is frequently used in cohort studies and epidemiological research.
- The formula for calculating relative risk is: (a/(a+b))/(c/(c+d)), where a, b, c, and d represent the frequencies of different outcomes.

II. Similarity in Values

RELATIVE RISK AND ODDS RATIO
The odds ratio (OR) is the ratio of odds of an event in one group versus the odds of the event in the other group. An RR (or OR) of 1.0 indicates that

**there is no difference in risk (or odds) between the groups being compared**.## Under which conditions are the values for the relative risk and odds ratio the most similar?

If the disease condition (event) is rare, then the odds ratio and relative risk may be comparable, but the odds ratio will overestimate the risk if the disease is more common. In such cases, the odds ratio should be avoided, and the relative risk will be a more accurate estimation of risk.

## Are rate ratio and relative risk the same?

Risk ratio: ratio of the risk of an event in one group (exposure or intervention) to that in another group (control). So it depends on your definitions of rate and risk. The term "relative risk" is sometimes used as a synonym for risk ratio, and

**rate ratio is one of the relative risk measures too**.## What is the difference between odds ratio risk ratio and risk?

The risk difference (RD) is the difference between the absolute risks of 2 interventions or risk factors. The RD represents excess risk attributed to the group with the higher risk.

**The odds ratio can estimate the risk ratio when the probability of an event is ≤10%.**## Is odds ratio similar to risk ratio?

The odds ratio is mathematically similar to the risk ratio

**when the outcome is rare**, because A+B will be similar to B, and C+D will be similar to D. But when the outcome is common, the odds ratio and risk ratio can be very different.## When can the risk ratio be approximated by the odds ratio?

**When the risks (or odds) in the two groups being compared are both small (say less than 20%)**then the odds will approximate to the risks and the odds ratio will approximate to the relative risk.

## What does a relative risk of 1.5 mean?

For example, a relative risk of 1.5 means that

**the risk of the outcome of interest is 50% higher in the exposed group than in the unexposed group**, while a relative risk of 3.0 means that the risk in the exposed group is three times as high as in the unexposed group.## Frequently Asked Questions

#### Is odds ratio a measure of risk?

Odds ratios (OR) are commonly reported in the medical literature as the measure of association between exposure and outcome. However,

**it is relative risk that people more intuitively understand as a measure of association**. Relative risk can be directly determined in a cohort study by calculating a risk ratio (RR).#### What does odds ratio of 1.5 mean?

If something has a 25% chance of happening, the odds are 1:3. You interpret an odds ratio the same way you interpret a risk ratio. An odds ratio of 1.5 means

**the odds of the outcome in group A happening are one and a half times the odds of the outcome happening in group B**.#### What does odds ratio tell you?

Odds ratios frequently are used to present strength of association between risk factors and outcomes in the clinical literature. Odds and odds ratios are related to the probability of a binary outcome (an outcome that is either present or absent, such as mortality).

#### Is the odds ratio an approximation to relative risk?

Odds ratio as an approximation of relative risk
Even with initial risks as high as 50% and very large reductions in this risk (odds ratios of about 0.1),

**the odds ratio is only 50% smaller than the relative risk**(0.1 for the odds ratio compared with a true value for the relative risk of 0.2).## FAQ

- Can you use odds ratio to estimate risk ratio?
- When the risks (or odds) in the two groups being compared are both small (say less than 20%) then the odds will approximate to the risks and the odds ratio will approximate to the relative risk.
- Why do we use odds instead of risk?
- “Risk” refers to the probability of occurrence of an event or outcome. Statistically, risk = chance of the outcome of interest/all possible outcomes. The term “odds” is often used instead of risk. “Odds” refers to the probability of occurrence of an event/probability of the event not occurring.
- Can you use odds ratio to estimate the risk ratio if this is a case-control study?
- Key Concept: In a study that is designed and conducted as a case-control study, you cannot calculate incidence. Therefore, you cannot calculate risk ratio or risk difference.
**You can only calculate an odds ratio**. However, in certain situations a case-control study is the only feasible study design.

## Why do odds ratio and relative risk have similar values

Would you say that your odds ratio is an accurate approximation of the risk ratio? | As a result, risks, rates, risk ratios or rate ratios cannot be calculated from the typical case-control study. However, you can calculate an odds ratio and interpret it as an approximation of the risk ratio, particularly when the disease is uncommon in the population. |

When an odds ratio is used to estimate the relative risk quizlet? | When can OR be used to estimate RR? The odds ratio always approximates the relative risk if the disease is frequent. In a cohort study of obesity and myocardial infarction, the odds ratio was calculated to be 4.5 while the relative risk was 2.5. |

When an odds ratio is used to estimate the relative risk? | When the risks (or odds) in the two groups being compared are both small (say less than 20%) then the odds will approximate to the risks and the odds ratio will approximate to the relative risk. |

- Can you convert odds ratio to risk ratio?
- The simplest way to ensure that the interpretation is correct is to
**first convert the odds into a risk**. For example, when the odds are 1:10, or 0.1, one person will have the event for every 10 who do not, and, using the formula, the risk of the event is 0.1/(1+0.1) = 0.091.

- The simplest way to ensure that the interpretation is correct is to
- When odds ratio equal relative risk?
- RELATIONSHIP OF RISK RATIO AND ODDS RATIO
**When there is no association between exposure and outcome**, both OR and RR are identical and equal to 1.0 [Table 3a].

- RELATIONSHIP OF RISK RATIO AND ODDS RATIO
- Why is odds ratio used in case control studies instead of relative risk?
- In these case-control studies, the odds ratio
**provides a valid estimate of the risk ratio without assuming that the disease is rare in the source population**.

- In these case-control studies, the odds ratio