Does it matter if my independent variables are related to each other?

As discussed in Section 1.1, the strength of multivariable analysis is its ability to determine how multiple independent variables, which are related to one another, are related to an outcome. We would not need multivariable analysis to determine the independent effect of exercise on mortality if it weren't for the fact that exercise, smoking, age, hypertension, and cholesterol level were all related to each other and the outcome of interest. Multivariable analysis helps us to separate the effects of these different variables on outcomes such as mortality.

However, if two variables are so closely correlated that if you know the value for one variable you know the value of the other, multivariable analysis cannot separately assess the impact of these two variables on the outcome. This problem is called multicollinearity. I can best illustrate it with an extreme example.

Let's say you were studying factors that affected length of hospital stay among patients with pneumonia. At your hospital, to accommodate the different preferences of the staff, the nurses record patients' temperature in both Fahrenheit and Celsius. When you do your medical abstraction, you record both Fahrenheit and Celsius temperatures. If you entered both variables in a model assessing length of stay, your model would be incorrect, and you would get an error message or unpredictable answers. This is because temperature in Celsius and temperature in Fahrenheit is the same variable even though the numbers are different.