When Can Odds Ratio Approximate Relative Risk?

Benefits of Understanding When Odds Ratio Approximates Relative Risk:

Simplified Interpretation:

When odds ratio approximates relative risk, it simplifies the interpretation of study results. Instead of dealing with complex odds ratios, researchers can communicate the findings in terms of relative risk, which is easier for both professionals and the general public to grasp.

Enhanced Comparability:

By approximating relative risk, odds ratio allows for easier comparisons between different studies. Researchers can compare findings from various sources, even if they report different measures, by converting odds ratios to relative risk. This enhances the comparability of studies and facilitates meta-analyses.

Useful in Case-Control Studies:

Odds ratio is commonly used in case-control studies, where it is more practical to calculate compared to relative risk. Understanding when odds ratio approximates relative risk is particularly beneficial in these

## Odds ratio good estimate of relative risk when

## Why are the relative risk and odds ratio approximately equal?

**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 is the risk ratio larger than the odds ratio?

**when the study outcome is common and the risk ratio is not close to 1, the odds ratio will be further from 1 compared with the risk ratio**.

## Is relative risk the same as rate ratio?

**The term "relative risk" is sometimes used as a synonym for risk ratio, and rate ratio is one of the relative risk measures too**.

## Why is odds ratio used in case control studies instead of relative risk?

**provides a valid estimate of the risk ratio without assuming that the disease is rare in the source population**.

## Would you say that your odds ratio is an accurate approximation of the risk ratio?

**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.**

## Frequently Asked Questions

#### Can you use odds ratio to estimate the risk ratio if this is a case-control study?

**You can only calculate an odds ratio**. However, in certain situations a case-control study is the only feasible study design.

#### Can odds ratio approximate risk?

**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.

#### What is the difference between odds ratio and relative risk in meta analysis?

**The risk ratio (RR, or relative risk) is the ratio of the risk of an event in the two groups, whereas the odds ratio (OR) is the ratio of the odds of an event**(see Box 6.4. a). For both measures a value of 1 indicates that the estimated effects are the same for both interventions.

#### Why do we use probability instead of odds ratio?

**a linear model can be fit**.

#### Why do we use odds ratio over 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.

#### Why do we calculate odds ratio?

**to compare the relative odds of the occurrence of the outcome of interest**(e.g. disease or disorder), given exposure to the variable of interest (e.g. health characteristic, aspect of medical history).

#### What is the significance of the odds ratio value?

**If the 95% CI for an odds ratio does not include 1.0, then the odds ratio is considered to be statistically significant at the 5% level**.

#### What is the significance of relative risk?

**provides an increase or decrease in the likelihood of an event based on some exposure**. Relative risk has the benefit of being a ratio of risks which means it can be applied to populations with differing disease prevalence. Relative risk does not specify the absolute risk of the event occurring.

#### Why would you use an odds ratio in a case-control study and not a relative risk ratio?

**by simple virtue of the fact that ratios of outcomes are controlled**, cannot have a risk ratio reported.

## FAQ

- 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**. - 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 it mean when the odds ratio is greater than 1?
- Odds Ratio is a measure of the strength of association with an exposure and an outcome. OR > 1 means
**greater odds of association with the exposure and outcome**. OR = 1 means there is no association between exposure and outcome. OR < 1 means there is a lower odds of association between the exposure and outcome. - Under what conditions would odds ratio be a good approximation for relative risk?
**The probability of the event of interest is small (< 0.1)**. This condition guarantees that the odds ratio will make a good approximation to the relative risk. In this example, the event of interest is a response to the mailing.- 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]. - When should odds ratio be used?
- Odds ratios are most commonly used in
**case-control studies**, however they can also be used in cross-sectional and cohort study designs as well (with some modifications and/or assumptions). - 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.
- Does the odds ratio give a good approximation to the relative risk for these data why OR why not?
- Odds ratios often are mistaken for relative risk ratios. 2,3 Although for rare outcomes odds ratios approximate relative risk ratios,
**when the outcomes are not rare, odds ratios always overestimate relative risk ratios**, a problem that becomes more acute as the baseline prevalence of the outcome exceeds 10%. - Why does odds ratio approximate 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 can odds ratio approximate relative risk

Why do we use relative risk? | Thus relative risk provides an increase or decrease in the likelihood of an event based on some exposure. Relative risk has the benefit of being a ratio of risks which means it can be applied to populations with differing disease prevalence. Relative risk does not specify the absolute risk of the event occurring. |

Can risk ratio and odds ratio be the same? | 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]. When there is an association between an exposure and an outcome, OR exaggerates the estimate of their relationship (is farther from 1.0 than RR). |

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). |

Can the odds ratio estimate the risk ratio when the outcome is rare? | Odds ratios often are mistaken for relative risk ratios. 2,3 Although for rare outcomes odds ratios approximate relative risk ratios, when the outcomes are not rare, odds ratios always overestimate relative risk ratios, a problem that becomes more acute as the baseline prevalence of the outcome exceeds 10%. |

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 +. |

What happens when an odds ratio is used to estimate the relative risk? | The odds ratio will always overstate the case when interpreted as a relative risk, and the degree of overstatement will increase as both the initial risk increases and the size of any treatment effect increases. |

What are the limitations of odds ratio? | The authors illustrate that a single measure of association such as an odds ratio does not meaningfully describe a marker's ability to classify subjects. Appropriate statistical methods for assessing and reporting the classification power of a marker are described. |

When can odds ratio provide an acceptable approximation of the relative risk? | Relative risk can be directly determined in a cohort study by calculating a risk ratio (RR). In case-control studies, and in cohort studies in which the outcome occurs in less than 10% of the unexposed population, the OR provides a reasonable approximation of the RR. |

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. |

- What are the advantages of odds ratio?
- The odds ratio is a versatile and robust statistic. For example, it can calculate the odds of an event happening given a particular treatment intervention (1). It can calculate the odds of a health outcome given exposure versus non-exposure to a substance or event (2).

- How do you calculate relative risk from 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
- 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**.

- 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
- What is relative risk equal to?
- 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.

- Why use odds ratio instead of relative 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**.

- “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.
- Why do we use odds ratio in logistic regression?
- Logistic regression is used
**to obtain odds ratio in the presence of more than one explanatory variable**. The procedure is quite similar to multiple linear regression, with the exception that the response variable is binomial. The result is the impact of each variable on the odds ratio of the observed event of interest.

- Logistic regression is used
- What is the purpose of the odds ratio?
- An odds ratio (OR) is
**a measure of association between an exposure and an outcome**. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.

- An odds ratio (OR) is
- In which kind of study should you use odds ratio instead of the relative risk?
- In contrast to clinical trials and cohort studies, odds ratios are not only preferred in case-control studies, but are often the only measure of association that can be applied to this type of study design.