# Measure of Assocation - Risk Ratio

*Lead Author(s):* Jeff Martin, MD
## Definition of Risk

In a cohort study:
**Risk is based on proportion of persons with disease = cumulative incidence**
The concept of **risk** reflects the proportion of persons experiencing the event or outcome or disease.
## Definition of Risk Ratio

**Risk ratio** = ratio of 2 cumulative incidence estimates = **relative risk**
If the concept of **risk** reflects the proportion of persons experiencing the event or outcome or disease,
- it follows that two cumulative incidences are needed for a
**risk ratio** or **relative risk**.

## Why Use Risk Ratio?

**Risk ratio** gives a **relative measure**
- Relative measure gives better sense of
**strength of an association** between exposure and disease for inferences about causes of disease

Because a ratio measure gives the incidence in one group relative to another, the magnitude of the ratio reflects the strength of the association between the exposure and the disease.
- The strength of association is one of the criteria considered in assessing causality in the relationship between an exposure and a disease.
- So ratio measures are more useful in making inferences about the causes of disease.
- Ratio measures are also given by the most commonly used multivariate analyses such as logistic regression and proportional hazards regression.

## Example of Absolute versus Relative Measure of Risk

In practice many risk factors have a relative measure in the range of **2 to 5.**
In the table below it looks like a **ratio of about 3**, treating more than 3 months really does make a difference,
- but because TB recurrence is a relatively
**rare event** in treated patients, the **absolute difference of 2.6%** is not so impressive.
- The
**absolute measure** is important when cost effectiveness is being evaluated.

**If incidence is very low, relative measure can be large but difference measure small.**
## Example of Risk Ratio in a Cohort with Complete Follow-up

This is an example (below) from an outbreak of gastrointestinal illness of a risk ratio from cohort data.
- We have equal follow-up on everyone in the cohort.

Because the follow-up is short and identical for everyone, the risk ratio is just the ratio of the proportion
- With disease in the exposed group (those who ate the potato salad) and
- With disease in the unexposed group (those who did not eat the potato salad).

**Eleven is a large value for a risk ratio** but that might be expected in a study such as this looking for a single likely food source for the outbreak.
So the RR=11 is taken as **strong evidence for assigning causality to eating the potato salad**. It is highly likely that the potato salad caused the outbreak of gastroenteritis.
## Risk Ratio in a Cohort with Censoring

In many cohort studies there is unequal follow-up time and consequently censoring.
Follow-up in these cohorts, which are not very short term outbreak investigations, have differing amounts of follow-up time on the subjects.
**The risk of the event has to be estimated:**
- in the exposed and
- in the unexposed group

## Example of Risk Ratio in a Cohort with Censoring

In the Kaplan-Meier analysis of the survival in two groups (below), you have to choose a point in time.
**For Example:** At 6 years, % dead in low CD4 group = 0.70 and in high CD4 group = 0.26.
**Risk ratio at 6 years = 0.70/0.26 = 2.69**
As you can see from inspecting the curve, the risk ratio will be different for different points in time.
- If one point in time is selected, then the risk ratio becomes the ratio of the two proportions failing (or surviving, if you prefer) at that point in time.
- IN reporting Kaplan-Meier results you
**must always specify at what amount of follow-up time**.
- This applies to the risk ratio as well.

NOTE : **Risk ratio would be different for different follow-up times**.