When Does Relative Risk Equal Odds Ratio: An Informative Guide

When conducting research or analyzing data in the field of statistics and epidemiology, understanding the relationship between relative risk and odds ratio is crucial. The phrase "When does relative risk equal odds ratio?" refers to the circumstances under which these two important measures of association become equal. This brief review aims to explain the concept, highlight its positive aspects, list the benefits, and provide insights into the conditions in which it can be used.

I. Understanding the Concept:

Definition of Relative Risk:

- Relative risk (RR) measures the likelihood of an event or outcome occurring in one group compared to another.
- It helps determine the strength of the association between an exposure and a health outcome.

Definition of Odds Ratio:

- Odds ratio (OR) also measures the association between an exposure and an outcome.
- It estimates the odds of an event occurring in one group compared to another.

II. When Does Relative Risk Equal Odds Ratio?

- Rare Disease Assumption:
- When the outcome of interest is rare (e.g., less than 10%), the odds of the event are approximately equal to the relative risk.
- This assumption allows for the approximation of the odds

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## 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.

## 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.

## Is relative risk the same as rate ratio?

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 does a relative risk of 2.5 mean?

0.1 = 2.5. This means that. those in the control group were 2.5 times more likely to die than those in the treatment group. The relative risk is interpreted in terms of the risk of the group in the numerator.

## What does relative risk of 0.5 mean?

For example, when the RR is 2.0 the chance of a bad outcome is twice as likely to occur with the treatment as without it, whereas an RR of 0.5 means that

**the chance of a bad outcome is twice as likely to occur without the intervention**. When the RR is exactly 1, the risk is unchanged.## What is the difference between odds and risk in statistics?

Odds is the likelihood of a new case occurring rather than not occurring. It differs from risk in that the denominator does not include the patients with the condition. Ratios (risk, rate and odds) provide a relative effect of an intervention or risk factor.

## Frequently Asked Questions

#### Do you use odds ratio OR relative risk in 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.#### What is the relationship between odds ratio and relative risk?

The relative risk (also known as risk ratio [RR]) is the ratio of risk of an event in one group (e.g., exposed group) versus the risk of the event in the other group (e.g., nonexposed group). 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.

#### In what case will the relative risk be similar to the odds ratio?

**If the study outcome is rare among those exposed**(Table 1), then A will be small relative to B, so the risk (A/[A + B]) will be close to the odds (A/B). Similarly, if the outcome is rare among those not exposed, then C will be small relative to D and [C/(C + D)] will be close to (C/D).

#### Should relative risk and odds ratio be the same?

For example: “

**The odds ratio is approximately the same as the relative risk if the outcome of interest is rare**. For common events, however, they can be quite different.”3 How close is “approximately the same,” how uncommon does an event have to be to qualify as “rare,” and how different is “quite different”?#### Under what circumstances does the odds ratio approximate the risk ratio?

**When a study outcome is rare in all strata used for an analysis**, the odds ratio estimate of causal effects will approximate the risk ratio; therefore, odds ratios from most case-control studies can be interpreted as risk ratios.

#### When interpreting a relative risk or odds ratio if the calculation is equal to OR less than 1.0 then which of the following is true?

The odds ratio is interpreted in the same manner as the risk ratio or rate ratio with an OR of 1.0 indicating no association, an OR greater than 1.0 indicating a positive association, and an OR less than 1.0 indicating

**a negative, or protective association**.#### Why odds ratio instead of relative risk?

The relative risk (RR) is the risk of the event in an experimental group relative to that in a control group. The odds ratio (OR) is the odds of an event in an experimental group relative to that in a control group.

**An RR or OR of 1.00 indicates that the risk is comparable in the two groups**.#### What is the risk ratio odds ratio rare disease assumption?

The rare disease assumption is a mathematical assumption in epidemiologic case-control studies where the hypothesis tests the association between an exposure and a disease. It is assumed that,

**if the prevalence of the disease is low, then the odds ratio (OR) approaches the relative risk (RR)**.#### Should I use odds ratio or risk ratio?

**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).

#### Is a higher or lower odds ratio better?

Important points about Odds ratio:

**OR >1 indicates increased occurrence of an event**. OR <1 indicates decreased occurrence of an event (protective exposure) Look at CI and P-value for statistical significance of value (Learn more about p values and confidence intervals here)## FAQ

- What is a good estimate of relative risk when the disease is rare?
- 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.
- What is odds ratio for disease?
- Odds of disease is
**the ratio between the probability of disease and the probability of no disease**. From surveys, it is estimated by the number of cases divided by the number of non- cases. - How do you interpret the odds ratio in epidemiology?
- The odds ratio is interpreted in the same manner as the risk ratio or rate ratio with
**an OR of 1.0 indicating no association, an OR greater than 1.0 indicating a positive association, and an OR less than 1.0 indicating a negative, or protective association**. - What is the interpretation of risk ratio and odds ratio?
- RELATIVE RISK AND ODDS RATIO An RR (or OR) more than 1.0 indicates an increase in risk (or odds) among the exposed compared to the unexposed, whereas a RR (or OR) <1.0 indicates a decrease in risk (or odds) in the exposed group. As for other summary statistics, confidence intervals can be calculated for RR and OR.
- What does risk ratio mean in epidemiology?
- Risk ratios. When risks are computed in a study, the risk ratio is
**the measure that compares the Riskexposed to the Riskunexposed**. The risk ratio is defined as the risk in the exposed cohort (the index group) divided by the risk in the unexposed cohort (the reference group). - What is the significance of the odds ratio?
**An odds ratio greater than 1 indicates that the condition or event is more likely to occur in the first group**. And an odds ratio less than 1 indicates that the condition or event is less likely to occur in the first group. The odds ratio must be nonnegative if it is defined.- How do you interpret odds ratio for dummies?
- The blog explains that an odds ratio (OR) is a relative measure of effect, which allows the comparison of the intervention group of a study relative to the comparison or placebo group.
**If the OR is > 1 the control is better than the intervention.****If the OR is < 1 the intervention is better than the control.** - What is the difference between odds ratio and incident risk ratio?
- The relative risk (also known as risk ratio [RR]) is the ratio of risk of an event in one group (e.g., exposed group) versus the risk of the event in the other group (e.g., nonexposed group). 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.
- Why is the rate ratio different to the risk ratio?
- A rate measures the rapidity of health outcome occurrence in the population. Two-by-two tables are generally used to organize the data from a study as shown below. Risk ratios.
**When risks are computed in a study, the risk ratio is the measure that compares the Riskexposed to the Riskunexposed**.

## When does relative risk equal odds ratio

What is the difference between incidence rate and incidence risk? | Rate is defined as the number of new cases that occur per the total amount of time a person is at risk of becoming a case. It differs from risk in that it accounts for the sum total of time that study members are at risk of developing the outcome of interest. |

What is the difference between odds ratio and likelihood ratio? | The odds ratio is the effect of going from “knowing the test negative” to “knowing it's positive” whereas the likelihood ratio + is the effect of going from an unknown state to knowing the test is +. |

Is odds ratio always larger than risk ratio? | That is, if the odds ratio is less than one then it is always smaller than the relative risk. Conversely, if the odds ratio is greater than one then it is always bigger than the relative risk. |

How do you choose between odds ratio and relative risk? | The relative risk (RR) is the risk of the event in an experimental group relative to that in a control group. The odds ratio (OR) is the odds of an event in an experimental group relative to that in a control group. An RR or OR of 1.00 indicates that the risk is comparable in the two groups. |

How can you determine whether an odds ratio OR relative risk is statistically significant using a confidence interval? | If the RR, OR, or HR = 1, or the confidence interval (CI) = 1, then there is no statistically significant difference between treatment and control groups. If the RR/OR/HR >1, and the CI does not include 1, events are significantly more likely in the treatment than the control group. |

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. |

Do you use odds ratio OR relative risk in 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 use odds ratio and not relative risk? | When the outcome is not rare in the population, if the odds ratio is used to estimate the relative risk it will overstate the effect of the treatment on the outcome measure. The odds ratio will be greater than the relative risk if the relative risk is greater than one and less than the relative risk otherwise. |

When can you not use risk ratio? | In retrospective (case-control) studies, where the total number of exposed people is not available, RR cannot be calculated and OR is used as a measure of the strength of association between exposure and outcome. |

- Why are odds ratios misleading?
**The discrepancy between a relative risk reduction and the equivalent relative odds reduction**(100×(1−odds ratio)%) can be misleading. When event rates are high (commonly the case in trials and systematic reviews) the relative odds reduction can be many times larger than the equivalent relative risk reduction.

- Why use relative risk instead of odds ratio?
- 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).

- 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
- Why use hazard ratio instead of odds ratio?
- Hazard ratios differ from relative risks (RRs) and odds ratios (ORs) in that
**RRs and ORs are cumulative over an entire study, using a defined endpoint**, while HRs represent instantaneous risk over the study time period, or some subset thereof.

- Hazard ratios differ from relative risks (RRs) and odds ratios (ORs) in that
- What is the rare disease assumption of odds ratio?
- The rare disease assumption is a mathematical assumption in epidemiologic case-control studies where the hypothesis tests the association between an exposure and a disease. It is assumed that,
**if the prevalence of the disease is low, then the odds ratio (OR) approaches the relative risk (RR)**.

- The rare disease assumption is a mathematical assumption in epidemiologic case-control studies where the hypothesis tests the association between an exposure and a disease. It is assumed that,
- How do you convert odds ratio to risk ratio?
- To convert an odds ratio to a risk ratio, you can use "
**RR = OR / (1 – p + (p x OR)), where p is the risk in the control group**" (source: http://www.r-bloggers.com/how-to-convert-odds-ratios-to-relative-risks/).

- To convert an odds ratio to a risk ratio, you can use "
- What is the odds ratio of a risk factor?
- The relative risk (also known as risk ratio [RR]) is the ratio of risk of an event in one group (e.g., exposed group) versus the risk of the event in the other group (e.g., nonexposed group). 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**.

- The relative risk (also known as risk ratio [RR]) is the ratio of risk of an event in one group (e.g., exposed group) versus the risk of the event in the other group (e.g., nonexposed group). The odds ratio (OR) is
- What does an odds ratio of 5.2 mean?
- Consequently, an odds ratio of 5.2 with a confidence interval of 3.2 to 7.2 suggests that
**there is a 95% probability**that the true odds ratio would be likely to lie in the range 3.2-7.2 assuming there is no bias or confounding.

- Consequently, an odds ratio of 5.2 with a confidence interval of 3.2 to 7.2 suggests that
- How do you calculate relative risk with odds ratio?
- Thus the odds ratio is (a/b) / (c/d) which simplifies to ad/bc. This is compared to the relative risk which is
**(a / (a+b)) / (c / (c+d))**. 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.

- Thus the odds ratio is (a/b) / (c/d) which simplifies to ad/bc. This is compared to the relative risk which is
- How do you calculate risk ratio?
- The risk ratio is defined as
**the risk in the exposed cohort (the index group) divided by the risk in the unexposed cohort (the reference group)**.

- The risk ratio is defined as