Table 1.

Controlling for confounders in three study designs

Study design	Inherent control for confounders	Interpretation of unadjusted effect size	Interpretation of adjusted effect size
Randomized	Controls for observed and, by assumption, unobserved confounders	Effect size is unbiased estimate of unconfounded population effect size	Effect size is unbiased estimate of unconfounded population effect size Power of the test of treatment effect may increase*
Case–control	Controls for observed confounders on which groups are matched. Does not control for unmatched or unobserved confounders	Effect size is unbiased estimate of population effect size if groups are matched on all observed confounders	Effect size is unbiased if all observed confounders are adjusted for either by matching or in analysis
Quasi-experimental or observational cohort	No inherent control for confounders	Effect size is biased, and usually artificially large, except in the rare case in which there are no confounders (observed or unobserved)	Effect size is unbiased if adjustment is for all confounders and there are no unobserved confounders

^*In a linear model, this increase in power is due to the potential increase in precision of the effect size estimate. In a non-linear model (e.g. logistic regression, Poisson regression, Cox models), adjustment for covariates in a randomized study cannot increase (and is likely to decrease) the precision of the treatment effect, but it can be expected to increase the treatment effect size in randomized trials, leading to increased power [27,34].