# Measure of Assocation - Risk Ratio

## 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:
1. in the exposed and
2. 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.