Odds ratio

In statistics, the words probability and odds are often confused with each other, because they help measure the same thing - the chance that an outcome will occur - and in both cases, we need to know the same two things - the number of times an outcome actually happened, or didn’t happen, and the total number of times an outcome could have happened.

The probability is the number of times an outcome happened divided by the number of times the outcome could have happened, and is often represented by a capital P.

For example, let’s say we want to figure out the probability of having a heart attack for people with hypertension - or high blood pressure.

To do this, we could carry out a cohort study which is where we start with two exposure groups and follow them over time to see if they develop a certain outcome.

We could recruit 100 people with hypertension, The exposed group - and 100 people without hypertension - the non-exposed group - and organize our results in a 2 by 2 table, and keep track of how many of them have heart attacks in the next year.

The two outcomes - heart attack or no heart attack - labeled on the top, and the two exposure groups - hypertension or no hypertension - on the side, and each of the cells inside the box labeled as a, b, c, or d.

Now, let’s say there are 9 people that have heart attacks in the group with hypertension - cell a - and 3 people that have heart attacks in the group without hypertension - cell c.

That means that there are 100 minus 9, or 91, people that didn’t have heart attacks in the group with hypertension - cell b - and 100 minus 3, or 97, people that didn’t have heart attacks in the group without hypertension - cell d.

To calculate the relative risk, we need the probability of having a heart attack in the group with hypertension - so cell a, 9, divided by cell a plus cell b or 100, which gives us 0.09.