Randomised trials: Risk of unknown confounders in large comapred to small studies

Question

My understanding is that in a randomised trial, one aim of randomisation is to reduce the chance of baseline imbalances (i.e. possible confounding factors) between groups.

Obviously known confounders, such as age, sex or any other difference of which we are aware can be dealt with before randomisation with methods to ensure that they are distibuted randomly between intervention and control groups.

Possible unkown factors, however cannot, and so we rely and randomisation for this. It is well documented that randomisation cannot be sure to eliminate these (ref: Howick, The Philosopy of Evidence Based Medicine) however it is the better at reducing them than a non randomised study.

Howick claims that additionally, as study sizes increase, the law of large numbers will increase the likelihood that basline differences between the groups that could be confounding factors will remain. This seems to make sense to me.

However I seem to have found a paper http://www.ncbi.nlm.nih.gov/pubmed/2727470 that seems to suggest this is not true. You may not be able to access the whole thing, but the abstract staes that they conclude:

covariate imbalance is just as much a problem for large studies as for small ones in terms of effect on size

Am I correct in thinking that this is saying that larger studies do not deal with possible unkown confounding factors better than small ones?

If so, does anybody know why this might be the case, or any other papers on this issue? (I realise this might be difficult as you may not have access for the paper)

Just to put things in context I am coming from a philosophy of science position.

Answer 1

As the number of potential baseline factors is infinite, and we can afford to look at more factors as $n \rightarrow \infty$, one could say that more imbalance will be found in larger studies, although the magnitude of imbalance of any one factor is likely to decrease. In some ways the problem is not fully defined. Stephen Senn has written much about this topic. The fact that apparent imbalances can be counter-balanced by imbalances in the other direction if one looks at enough factors (including examining data not entered in the database) means that imbalances tend to cancel, and looking for imbalances is futile. We enjoy the benefits of randomization at all sample sizes.