7.6 Controlling confounding

Confounding can be prevented in the design or removed in the analysis.

In the design: randomisation, which makes exposure independent of every pre-existing variable; restriction to one level of the confounder (only non-smokers), which removes it at the cost of generalisability; and matching (Section 6.3), which must be followed by a matched analysis.
In the analysis: standardisation (Section 8), stratification with pooled estimates such as the Mantel–Haenszel estimators, and regression models, which do the same with many variables at once.

Each analytic method removes confounding only by the variables that were measured, and only as well as they were measured: adjusting for a confounder measured with error leaves residual confounding. No analysis removes confounding by variables that were not recorded, which is why Cornfield’s argument and its modern relatives remain necessary.

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