Measuring chances: Wai-Ching Leung explains odds and probabilities

Introduction

In my latest article in the Student BMJ, I noted that statistics are useful when events are not entirely predictable.1 An important use of medical statistics is to measure this level of certainty and estimate how likely certain events are to happen. One clinical example is our attempt to estimate from our clinical assessment how likely it is that a patient is suffering from a given disease. If a 70 year old woman is admitted to an emergency department with central chest pain but with a normal electrocardiogram, how likely is it that has she had a heart attack? Another example relates to hypothesis testing. Suppose we wish to find out whether brain tumours are associated with use of mobile phones. But no matter how many people we get data on, we can never be absolutely certain. Instead we measure the level of certainty by estimating how likely the data we obtain would have occurred if brain tumours were not associated with mobile phone use.

I will discuss these two specific examples in more detail in future articles. In this article, I will look at how chance can be measured, some examples and one pitfall in interpretation that should be avoided.

Probability and odds

Chance can be measured in two ways. Probability is the more commonly used measure, and almost all medical students should have come across it. We can think of it as the number of ways an event can occur compared with the total number of possible outcomes. Suppose we throw a dice, we expect the probability that it will land on a “1” is 1/6, that it is an even number is 3/6=1/2, and that it is greater than 2 is 4/6=2/3. Sometimes, we may estimate probability by observations-the number of events to the total number of possible …