246 PART 5 Looking for Relationships with Correlation and Regression

Synergy and anti-synergy

Sometimes, two predictor variables exert a synergistic effect on an outcome. That is,

if both predictors were to be associated with an increase in the outcome by one

unit, the outcome would change by more than the sum of the two increases, which

is what you’d expect from changing each value individually by one unit. You can

test for synergy between two predictors with respect to an outcome by fitting a

model that contains an interaction term, which is the product of those two vari-

ables. In this equation, we predict SBP using Age and Weight, and include an

interaction term for Age and Weight:

SBP = Age + Weight + Age * Weight

If the estimate of the slope for the interaction term has a statistically significant

p value, then the null hypothesis of no interaction is rejected, and the two variables

are interpreted to have a significant interaction. If the sign on the interaction term

is positive, it is a synergistic interaction, and if it is negative, it is called an anti-

synergistic or antagonistic interaction.

Introducing interaction terms into a fitted model and interpreting their

­significance  — both clinically and statistically  — must be done contextually.

Interaction terms may not be appropriate for certain models, and may be required

in others.

Collinearity and the mystery of the

disappearing significance

When developing multiple regression models, you are usually considering more

predictors than just two as we used in our example. You develop iterative models,

MODEL BUILDING

If you have a big data set with many variables, how do you plan which predictors to try

to include in your multiple regression model? Once you choose the ones you want to

consider, how do you decide which ones to keep and which ones to remove to achieve

the best-fitting model? Biostatisticians approach model building using different meth-

ods, but the goal of all of these is to achieve the best-fitting model that explains the rela-

tionship between the predictors and outcome, and to do it in a transparent way.

Chapter 20 includes a section explaining how to develop a modeling plan if you have a

choice of many potential predictor variables.