Evaluating inverse propensity score weighting in the presence of many treatments. An application to the estimation of the neighbourhood effect

In this paper we consider the problem of estimating causal effects in a framework with many treatments through a simulation study. We engage in Monte Carlo simulations to evaluate the performance of inverse probability of treatment weighting (IPTW) with 10 treatments, estimating the propensity scores using Generalized Boosted Models. We assess the performance of IPTW under three different scenarios representing treatment allocations, and compare it with a simple parametric approach, i.e. logistic regression. IPTW's estimates are less biased, even though they exhibit a higher variance than those based on logistic regression. Moreover, we apply IPTW to the estimation of the neighbourhood effect on the probability of older people experiencing at least one fracture requiring hospitalization during the year 2002 by comparing 10 neighbourhoods in the city of Turin (Italy). Our paper demonstrates that IPTW can be successfully applied to the estimation of neighbourhood effects, and, more generally, to the estimation of causal effects in the presence of many treatments.