Ignoring the matching variables in cohort studies - when is it valid and why?

In observational studies of the effect of an exposure on an outcome, the exposure-outcome association is usually confounded by other causes of the outcome (potential confounders). One common method to increase efficiency is to match the study on potential confounders. Matched case-control studies are relatively common and well covered by the literature. Matched cohort studies are less common but do sometimes occur. It is often argued that it is valid to ignore the matching variables, in the analysis of matched cohort data. In this paper, we provide analyses delineating the scope and limits of this argument. We discuss why the argument does not carry over to effect estimation in matched case-control studies, although it does carry over to null-hypothesis testing. We also show how the argument does not extend to matched cohort studies when one adjusts for additional confounders in the analysis. Ignoring the matching variables can sometimes reduce variance, even though this is not guaranteed. We investigate the trade-off between bias and variance in deciding whether adjustment for matching factors is advisable.