Stat Moment

Odds ratio

Risk is measured in 2 ways:

1)Odds Ratio

2) Relative Risk

1) Relative risk is frequently used to express the number of times risk is increased or decreased in one group being studied as compared to another in clinical trials. It is the probability of the outcome of interest occurring. Practically speaking this is the

experimental event rate (A/ (A+ B))/ control event rate (C/(C+D)).

However, in case-control studies, the risk ratio (relative risk) cannot be obtained directly and the odds ratio is used and frequently interpreted as the relative risk.

In order to calculate the Relative Risk, we need to know the population at risk. This information is not available in a case-control study as the group without disease is CHOSEN by the investigator and not randomly assigned.

Relative risk is defined as the percentage of the baseline risk (ie the risk of an event in the control patient) removed as a result of therapy or intervention.

Absolute risk reduction is the difference in the risk of an event between 2 groups.

2)Odds Ratio measures the odds of an event occurring to the odds of an event not occurring. The odds ratio is the measure of choice in case-control studies. In a case control study, the odds ration gives the ratio of the odds of an event in the experimental group to those in the control group - usually for a rare condition. When the outcome of interest is common in a STUDY population (even though rare in the general population, ie a case-control study) the odds ratio may exaggerate a risk or treatment effect. Stated in another way, if the event is rare (<10% is the often quoted rate) the odds ratio is a good estimate of the relative risk.

Odds Ratio is often used in logistic regression analysis, due to mathematical modelling. It can show more of an effect than Relative Risk.

Odds Ratio

exposure/risk factor/ / treatment
disease/outcome / positive / negative
positive / A / B
negative / C / D

(A/B) divided by (C/D)-People with risk factor AND disease divided by people with risk factor and NO disease

Or (AxD)/(BxC)

Exaggeration of treatment effect or risk factor

Results from a randomised trial comparing sclerotherapy and ligation

Death / Survival / Total Treated
Ligation / 18 / 46 / 64
Sclerotherapy / 29 / 36 / 65

What is the risk of event/death for each group?

And the Relative Risk?

What is the Odds Ratio for death after ligation vs death after sclerotherapy?

Let’s assume that the number of patients who died in both groups was 50% less (ie 14% and 22.3%)....

Death / Survival / Total treated
Ligation / 9 / 46 / 55
Sclerotherapy / 14.5 / 36 / 51

The Relative risk is now?

What is the Odds Ratio now?