Question

How can size of a sample hide a confounder? Is this a paradox?

Answer 1

It depends on fact if you are asking about randomized or non-randomized study.

In randomized study sample size decreases any bias and also confounding. But also randomized studies are not immune to confounding even if the randomization process helps protect them against it.

For observational studies, study size has a less clear impact on confounding. But a study with larger sample size has greater power => we could easily detect any confounding. For example, if I have a study of 100 people, there are only so many covariates I can include in the model, and I might be hesitant to use second or third-order terms for some of those covariates, because it will start to erode the precision of my final estimate. With a study of 100000 people, you can go to town, and start using far more sophisticated methods of controlling for confounding without really harming the qualitative precision of your estimate.

So in non-randomized studies it is usually opposite than in randomized => large sample size leads to fact that we are able to detect more confounding factors.

So yes the statement is slightly paradoxical but not completely.