As I understand it, matching is one way to identify causality in observational studies. By matching observations that are "similar" and comparing ones that did or did not receive treatment, you can consider this as a quasi-experiment of sorts.

What is overmatching? What kind of bias does it introduce? I have mostly seen matching from an economics perspective, but have recently seen some papers on epidemiology suggesting that "overmatching" can result in bias. I find it hard to understand the terminology of the papers and would greatly appreciate if someone could help explain some of the main concepts. Below is an article that references the idea:

Over-matching can cause bias. BMJ. 2002 August 10; 325(7359)


2 Answers 2


From Modern Epidemiology 3rd Edition by Rothman, Greenland and Lash:

There are at least three forms of overmatching. The first refers to matching that harms statistical efficiency, such as case-control matching on a variable associated with exposure but not disease. The second refers to matching that harms validity, such as matching on an intermediate between exposure and disease. The third refers to matching that harms cost-efficiency.

The answer from AndyW is about the second form of overmatching. Briefly, here's how they all work:

1: In order to be a confounder, one of the criteria is that the covariate be associated with both the outcome and the exposure. If it's only associated with one of them, its not a confounder, and all you've succeeded in doing is widening your confidence interval.

To explore this type of overmatching further, consider a matched case-control study of a binary exposure, with one control matched to each case on one or more confounders. Each stratum in the analysis will consist of one case and one control unless some strata can be combined. If the case and its matched control are either both exposed or both unexposed, one margin of the 2 x 2 table will be 0 ... such a pair of subjects will not contribute any information to the analysis. If one stratifies on correlates of exposure, one will increase the chance that such tables will occur and thus tend to increase the information lost in stratified analysis.

2: This is partially discussed by AndyW. Matching on an intermediate factor will bias your estimate, as will matching on something affected by both the exposure and outcome. This is essentially controlling on a collider, and any technique that does so will bias your estimate.

If, however, the potential matching factor is affected by exposure and the factor in turn affects disease (i.e., is an intermediate variable), or is affected by both exposure and disease, then matching on the factor will bias both the crude and adjusted effect estimates. In these situations, case-control matching is nothing more than an irreparable form of selection bias.

3: This is more of a study design problem. Extensively matching on variables that you needn't match on for reasons 1 & 2 can cause you to reject easily obtained controls (friends, family, nearby social network, etc.) in favor of far harder to obtain controls that can be matched on the unnecessary set of covariates. That costs money - money that could have been spent on more subjects, better exposure or disease ascertainment, etc., for no appreciable gain in bias or precision, and indeed having threatened both.

  • 1
    $\begingroup$ (+1) Nice response. I'm not so surprised to see that Rothman & Greenland's textbook is again a good reference to keep on our desk, always within easy reach. $\endgroup$
    – chl
    Dec 10, 2011 at 20:48

While I was ignorant of the "over-matching" terminology as well, one example of the same idea I have heard in Economic and Statistic lingo could be matching on an "intermediate" outcome. See Andrew Gelman's posts on the subject

This is the same problem as described at the beginning of the article you cite (Marsh et al., 2002)

If the exposure itself leads to the confounder, or has equal status with it, then stratifying by the confounder will also stratify by the exposure, and the relation of the exposure to the disease will be obscured. This is called over-matching ...

Gelman gives a conceptually clear example in the "Does making sons make you more conservative" post. In just simple terms (absent of examples) it is just you have your causal directions backwards.

  • 1
    $\begingroup$ Right. In Josh Angrist's book Mostly Harmless Econometrics, he refers to the same phenomena as a "bad control." He gives the example of regressing wages on education and occupation. This is a horrible regression since it's identified off of differences in education within an occupation (e.g., if the occupation was lawyer, it'd be meaningless to analyze those education differences) and education is what enabled you to be a lawyer! I suspected over-matching bias may have been that. Perhaps an epidiomologist will come along to confirm. Thanks for the great Gelman links, I'll check them out. $\endgroup$
    – d_a_c321
    Dec 9, 2011 at 22:44
  • 1
    $\begingroup$ Very interesting and I think it's an important and under-discussed topic. $\endgroup$
    – rolando2
    Dec 10, 2011 at 14:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.