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I am reviewing a paper where the authors compare cancer outcomes (binary) between two groups, one having a small sample size of 200 and the other having over 55,000.

The authors then claim that, due to the imbalance and in order to minimize confounding effects, they matched individuals from the larger group to the smaller.

My question is: is there a rule-of-thumb about how much efficiency can be gained by doing this? It was my understanding that if you matched on a factor, you would also have to adjust for it in a multivariate analysis. Assuming that the matching/adjustment factor is not in the causal pathway but it's not a confounder, then including that factor in the analysis leads to an efficiency loss with adjustment, but can the same be said of matching?

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The answer depends on what type of study this is. In a cohort study, matched factors do not need to be included in the analysis and can improve efficiency by ensuring positivity for all important confounders. In a case-control study, matching improves efficiency if the matched factors are actually confounders, but match factors must be included in the analysis in order to address confounding.

I suspect in the paper you describe the authors have matched to ensure positivity of important, since the first sample is so small, and not specifically to improve efficiency.

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