Matching on poset-based Average Rank for Multiple Treatments (MARMoT) 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 particularly useful for balancing confounders, even in situations in which the number of treatments considered is high. We apply our approach to the estimation of neighbourhood effect on the fractures among older people in Turin (a city in northern Italy).