Methods and Applications of Statistics in Clinical Trials, Volume 1: Concepts, Principles, Trials, and Designs

Chapter 22

Confounding

Sander Greenland

22.1 Introduction

The word confounding has been used to refer to at least three distinct concepts. In the oldest usage, confounding is a bias in estimating causal effects. This bias is sometimes informally described as a mixing of effects of extraneous factors (called confounders) with the effect of interest. This usage predominates in nonexperimental research, especially in epidemiology and sociology. In a second and more recent usage, confounding is a synonym for noncollapsibility, although this usage is often limited to situations in which the parameter of interest is a causal effect. In a third usage, originating in the experimental-design literature, confounding refers to inseparability of main effects and interactions under a particular design. The term aliasing is also sometimes used to refer to the latter concept; this usage is common in the analysis of variance literature.

The three concepts are closely related and are not always distinguished from one another. In particular, the concepts of confounding as a bias in effect estimation and as noncollapsibility are often treated as identical, although there are many examples in which the two concepts diverge [8,9,14]; one is given below.

22.2 Confounding as a Bias in Effect Estimation

22.2.1 Confounding

A classic discussion of confounding in which explicit reference is made to “confounded effects” is Mill [15, Chapter X] (although in Chapter III Mill lays out the primary issues and ...