What is it?

The common support in propensity score matching refers to the overlap in the propensity score distribution between the treatment and control groups. In other words, it is the range of propensity scores for which there are individuals in both the treatment and control groups.

Why is it important?

The common support is important for propensity score matching because it represents the range of scores for which it is possible to find a match between a treatment and a control individual. If there is no overlap in the propensity score distribution, then it would not be possible to find a match and the analysis would not be valid.

How to overcome a problem of common support assumption?

Here are some solutions for a lack of common support:

1. Change the eligibility criteria of your study to exclude patients that can not be matched. This should be clearly stated in your publication to inform readers that your results are not generalizable to the non-included population.
2. Remove matching variables for which no control subject matches: this should be done cautiously as it could introduce a bias and discrepancy between your control and treated subjects.
3. Increase the caliper for your matching algorithm
4. Merge some rare modalities for discrete variables to increase the number of available patients

In all cases, a lack of common support is a tough problem when using propensity score matching. If you find yourself in this situation, it would be wise to ask for help from a statistician or a clinician with both statistical and domain-related clinical knowledge.