[Confounding and interaction in multiple regression]

In multiple regression the effect of an input (independent) variable on a continuous output (dependent or response) variable can be adjusted for the effect of confounding and modifying variables. This adjustment is useful to obtain either an unbiased estimate of the true association between an exposure and an outcome or to predict the outcome for given inputs after removing the influence of other factors. These factors are defined as confounders if they are associated with the exposure and are independent risk factors for the outcome, without being intermediates on the biological pathway between exposure and outcome. An interaction between exposure and another independent variable is present when the exposure-disease relationship varies across different values of this variable. Multivariable regression modeling removes the association between the confounder and the outcome eliminating the necessary condition for confounding. An interaction term can be also incorporated into the model to quantify any potential modifying effect.