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# Why is the odds ratio an indirect measure of risk

Why is the Odds Ratio an Indirect Measure of Risk?

The odds ratio is a statistical measure used to assess the association between two variables in research studies. While it is not a direct measure of risk, it provides valuable insights into the relationship between variables. In this article, we will explore the positive aspects and benefits of using the odds ratio as an indirect measure of risk, along with the conditions in which it is applicable.

Benefits of Using Odds Ratio as an Indirect Measure of Risk:

1. Easy Interpretation:

• The odds ratio provides a straightforward interpretation, making it easier for researchers, healthcare professionals, and policymakers to understand and communicate the results.
• It quantifies the strength and direction of the association between variables, allowing for meaningful comparisons.
2. Suitable for Case-Control Studies:

• The odds ratio is particularly useful in case-control studies, where the prevalence of the outcome is determined by comparing cases (individuals with the outcome) and controls (individuals without the outcome).
• It helps estimate the odds of exposure in cases compared to controls, providing valuable information about the association between the exposure and the outcome.
3. Identifying Risk Factors:

• By calculating the odds ratio, researchers can identify potential risk factors associated with a
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Table of Contents

## 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].

## Under which conditions are the values for the relative risk and odds ratio the most similar?

If there's absolutely no difference between the groups in the probability of an outcome, then both the OR and the RR are 1.0. That's the only situation in which they can be exactly equal.

## 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.

## 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 is an example of odds ratio and relative risk?

Despite the fact that the relative risk and odds ratio have the same range, they represent totally different measures of differential risks and, therefore, have quite different interpretations. For example, if p1=0.40 and p2=0.25, then the relative risk is r=1.60, but the odds ratio is θ =2.00.

## How does the odds ratio measure risk?

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.

## Frequently Asked Questions

#### What is the problem with odds ratios?

Unfortunately, there is a recognised problem that odds ratios do not approximate well to the relative risk when the initial risk (that is, the prevalence of the outcome of interest) is high. Thus there is a danger that if odds ratios are interpreted as though they were relative risks then they may mislead.

#### 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 is the relative risk ratio in a case-control study?

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.

#### Can you use odds ratio in case-control?

Many epidemiologists and statisticians believe that the odds ratio is the only measure that can be reliably estimated from case-control studies.

#### What is the risk ratio or odds ratio for a cohort study?

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 are the limitations of the odds ratio?

What Are the Limitations of Odds Ratios? Several caveats must be considered when reporting results with odds ratios. First, the interpretation of odds ratios is framed in terms of odds, not in terms of probabilities. Odds ratios often are mistaken for relative risk ratios.

#### What does odds ratio tell you?

What is an 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.

#### 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).

#### 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.

#### 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.

#### What is the difference between likelihood ratio and odds 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 +.

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

## FAQ

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.
Why use 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.
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.
Can the odds ratio be used to approximate?
Odds ratios are used 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).
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.
How do you interpret odds ratio and risk ratio?
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 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.
What is the relationship between odds ratio and probability?
Odds are the probability of an event occurring divided by the probability of the event not occurring. An odds ratio is the odds of the event in one group, for example, those exposed to a drug, divided by the odds in another group not exposed. Odds ratios always exaggerate the true relative risk to some degree.
How do you explain odds ratio results?
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.
Why use odds ratio instead of risk ratio?
“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.
Why use an odds ratio in a RCT?
Researchers often present ORs to quantify the treatment effect in a RCT, because they have applied logistic regression to adjust for baseline covariables. Logistic regression models yield odds ratios.
When not to use relative risk?
When the event is an improvement in health due to a health exposure, then the relative benefit is usually reported rather than the relative risk. The relative benefit is 1 – relative risk. A relative risk of one implies there is no difference of the event if the exposure has or has not occurred.

## Why is the odds ratio an indirect measure of risk

 Can you use odds ratio in cohort study? Key Concept: Remember that in a cohort study you can calculate either a risk ratio or an odds ratio, but In a case-control study: you can only calculate an odds ratio. What is a clinical trial odds ratio OR relative risk? 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. Why would you use an odds ratio in a case control study and not a relative risk ratio? Firstly, RRs cannot be applied in all cases. Because risk in a sample is an estimate of risk in a population, the sample must be reasonably representative of the population. As such, case-control studies, by simple virtue of the fact that ratios of outcomes are controlled, cannot have a risk ratio reported. Is odds ratio a measure of 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. What does odds ratio measure? What is an 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. Do cohort studies measure odds ratio? Odds ratios, often used in cohort studies and randomized controlled trials (RCTs), are often interpreted as risk ratios but always overestimate the risk ratio. Does odds ratio measure correlation? Odds ratio and correlation don't measure the same thing- correlation looks at how much one variable is explained by another (for example, is how much is wieght explaine by height?). Odds ratio compare the odds of a specific outcome in two groups, one exposied an done unexposed to a specific exposure. What is the measure of relative risk? Relative risk is the ratio of the risks for an event for the exposure group to the risks for the non-exposure group. Thus relative risk provides an increase or decrease in the likelihood of an event based on some exposure. What is the difference between risk ratio and odds ratio? The basic difference is that the odds ratio is a ratio of two odds (yep, it's that obvious) whereas the relative risk is a ratio of two probabilities. (The relative risk is also called the risk ratio). 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 is the difference between an odds ratio and a hazard 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. What is the difference between odds ratio and absolute risk? The absolute risk is the probability of an event in a sample or population of interest. 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.
• What is an example of odds ratio and risk ratio?
• 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. In a sample of 100, about 9 individuals will have the event and 91 will not.
• When can odds ratio estimate 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.
• 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 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.
• What does the odds ratio suggest?
• 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.
• 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 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.
• Is it important to distinguish between a risk ratio and an odds ratio?
• Yes, as Graham says, odds ratios (ORs) are not intuitive and frequently misinterpreted as risk ratios (RRs). ORs are always farther from 1 than RRs, unless both are equal to 1. Even if you use a logistic regression model, you can present your results with RRs or risk differences (RDs), but it's tricky.
• Why is the odds ratio important?
• Odds ratios are used 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 difference between risk ratio and rate ratio?
• Rate ratio: ratio of the rate of an event in one group (exposure or intervention) to that in another group (control). Risk ratio: ratio of the risk of an event in one group (exposure or intervention) to that in another group (control).
• Why is risk ratio bigger than odds ratio?
• The figures show that the odds ratio will always exaggerate the size of the effect compared with a relative risk. 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.

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February 8, 2024
February 8, 2024
February 8, 2024