Matching on poset-based average rank for multiple treatments to compare many unbalanced groups.

In this article, we propose an original matching procedure for multiple treatment frameworks based on partially ordered set theory (poset). In our proposal, called matching on poset-based average rank for multiple treatments (MARMoT), poset theory is used to summarize individuals' confounders and the relative average rank is used to balance confounders and match individuals in different treatment groups. This approach proves to be particularly useful for balancing confounders when the number of treatments considered is high. We apply our approach to the estimation of neighborhood effect on the fractures among older people in Turin (a city in northern Italy).