Single outcome with multiple variables

Why is it important?

So far, we have only discussed comparing one outcomes and one variable (e.g. death versus surgical group), however outcomes can be influenced by multiple variables. Regression analyses are multivariable methods that allow us to compare an outcome adjusting for multiple different variables (e.g. death versus surgical group, age and lung function).

How is it done?

There are a family of regression methods appropriate to the type and distribution of the outcome of interest. Linear regression is the basic model that is applied to a continuous normally distributed outcome (e.g. serum potassium) and the measures of association are usually given in the same units as the outcome measure (e.g. each year of age increases serum potassium by 0.011 mmol/l). For binary outcomes, logistic regression is used and the measure of association is given as an odds ratio (the odds of an event happening versus the odds of an event not happening). The odds ratio is a difficult ratio for most to interpret (unless you are an experienced gambler) and often it is (incorrectly) interpreted as a relative risk. The discussion is out of the scope of this article, but as an illustration the two ratios of 2/4 and 1/4 is expressed as a relative risk of 2/4 ÷ 1/4= 2 and an odds ratio of 2/2 ÷ 1/3 = 3. Therefore the output of a measure of association in a logistic regression model is interpreted for example in men, the odds ratio of developing ischaemic heart disease is 4.3 compared to women.

What is the relevance?

It is important to be able to appreciate the correct regression method for the correct type and distribution of outcomes. Often clinicians who are less experienced try to convert outcomes from continuous to binary simply to apply a different method of analyses for example, instead of using a linear regression for serum potassium, they would convert it into high versus low serum potassium (above or below 4.5 mmol/l) and apply logistic regression methods.