Why Would a Randomized Control Trial Report Odds Ratio, Not Risk Ratio?

In certain research studies, specifically randomized control trials (RCTs), odds ratio (OR) is often reported instead of risk ratio (RR) as a measure of association. This brief review aims to explain the reasons behind this practice and highlight the benefits of reporting OR in RCTs. It will also outline the conditions in which using OR is appropriate.

Benefits of Reporting Odds Ratio (OR) in Randomized Control Trials:

Useful for rare outcomes: OR is particularly valuable when studying rare outcomes. In such cases, the risk of an event occurring is low, making it challenging to calculate a precise RR. OR, on the other hand, can be estimated more reliably, ensuring accurate results.

Efficiency in small sample sizes: RCTs often involve a limited number of participants, especially when studying rare diseases or events. OR is less affected by small sample sizes and can provide more stable estimates compared to RR, which tends to have wider confidence intervals in such cases.

Consistency across multiple outcome measures: RCTs frequently assess multiple outcomes simultaneously. OR allows for consistent comparison across various outcomes, even if they have different baseline risks. This consistency facilitates better interpretation and comparison

## What is the difference between risk ratio and odds ratio in randomized controlled trials?

**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 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**.

## What is the difference between odds ratio and likelihood ratio?

## Why use hazard ratio instead of odds ratio?

**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.

## Can you use odds ratio in RCT?

**the odds ratio can be calculated as well**. The odds ratio is then defined as the odds of the outcome in the treated patients divided by the odds of the outcome in the untreated patients.

## How do you interpret a higher odds ratio?

**>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) In rare outcomes OR = RR (RR = Relative Risk)

## Frequently Asked Questions

#### How do you interpret odds calculations?

**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.

#### How do you know when to use relative risk vs odds 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.

#### What are the risk difference methods for meta-analysis?

**the two-step methods that estimate study-specific risk differences first, then followed by the univariate common-effect model, fixed-effects model, or random-effects models**; and (2) the one-step methods using bivariate random-effects

#### 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.

#### What is the odds ratio in the null hypothesis?

**1.0**for odds ratios and prevalence ratios (terms you will come across).

#### What is the null value for risk difference?

**A risk ratio or rate ratio that equals 1**(the null value) indicates that there is no difference in risk or rates between exposed and unexposed groups.

#### What does a risk ratio of 0.75 mean?

#### 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.

## FAQ

- Can you convert risk ratio to odds ratio?
- For example,
**a risk of 0.5 is equivalent to an odds of 1**; and a risk of 0.95 is equivalent to odds of 19. Measures of effect for clinical trials with dichotomous outcomes involve comparing either risks or odds from two intervention 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 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. - 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). - 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. - 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.- 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.- What is the misinterpretation of odds ratio?
- However, in cohort studies and RCTs, odds ratios are often interpreted as risk ratios. This is problematic because
**an odds ratio always overestimates the risk ratio**, and this overestimation becomes larger with increasing incidence of the outcome.

## Why would a randomized control trial report odds ratio not risk ratio

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. |

How do you calculate odds ratio for meta-analysis? | Among the measures of effect calculated from these frequency data, perhaps the most common is the odds ratio (OR = ad/bc). Meta-analyses have used various statistical techniques to estimate an overall effect that summarizes the effect sizes from the individual studies. |

How do you calculate the odds ratio from two proportions? | In a 2-by-2 table with cells a, b, c, and d (see figure), the odds ratio is odds of the event in the exposure group (a/b) divided by the odds of the event in the control or non-exposure group (c/d). Thus the odds ratio is (a/b) / (c/d) which simplifies to ad/bc. |

How do you interpret the odds ratio proportion? | 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) In rare outcomes OR = RR (RR = Relative Risk) |

How do you calculate odds ratio from effect size? | A systematic review may encompass both odds ratios and mean differences in continuous outcomes. A separate meta-analysis of each type of outcome results in loss of information and may be misleading. It is shown that a ln(odds ratio) can be converted to effect size by dividing by 1.81. |

How do I calculate odds ratio? | The odds ratio is calculated by dividing the odds of the first group by the odds in the second group. In the case of the worked example, it is the ratio of the odds of lung cancer in smokers divided by the odds of lung cancer in non-smokers: (647/622)/(2/27)=14.04. |

What does the odds ratio estimate in a case-control study? | In these case -control studies, the odds ratio estimates the rate ratio of cohort studies, without assuming that the disease is rare in the source population. Note that it is possible, albeit rare, that a control selected at a later time point could become a case during the remaining time that the study is running. |

What is odds ratio in epidemiology studies? | 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. |

- What does an odds ratio from a case-control study estimate quizlet?
- The odds ratio can be conceptualized as either a disease odds ratio or an exposure odds ratio. When case-base sampling is used for control selection in a case-control study, the odds ratio estimates:
**the odds ratio in the base population**.

- The odds ratio can be conceptualized as either a disease odds ratio or an exposure odds ratio. When case-base sampling is used for control selection in a case-control study, the odds ratio estimates:
- What is meant by odds of exposure in a case-control study?
- Odds ratio = [ (Number exposed with disease) x (Number not exposed without disease) ] / [ (Number exposed without disease ) x (Number not exposed with disease) ] The odds ratio tells us
**how strongly the exposure is related to the disease state**.

- Odds ratio = [ (Number exposed with disease) x (Number not exposed without disease) ] / [ (Number exposed without disease ) x (Number not exposed with disease) ] The odds ratio tells us
- 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**.

- Why use risk ratio instead of odds ratio?
- While
**risk reports the number of events of interest in relation to the total number of trials, odds report the number of events of interest in relation to the number of events not of interest**.

- While
- What is the significance of the incidence rate ratio?
- An incidence rate ratio (IRR) is
**a meaningful effect measure in epidemiology if it is adjusted for all important confounders**. For evaluation of the impact of adjustment, adjusted IRRs should be compared with crude IRRs.

- An incidence rate ratio (IRR) is
- What is the difference between odds ratio and prevalence ratio?
- Odds ratio (OR) and risk ratio (RR) are two commonly used measures of association reported in research studies. In cross-sectional studies,
**the odds ratio is also referred to as the prevalence odds ratio (POR) when prevalent cases are included, and, instead of the RR, the prevalence ratio (PR) is calculated**.

- Odds ratio (OR) and risk ratio (RR) are two commonly used measures of association reported in research studies. In cross-sectional studies,
- What are the limitations of 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 Are the Limitations of Odds Ratios? Several caveats must be considered when reporting results with odds ratios. First,