Propensity score techniques in multiple treatments framework: the estimation of neighbourhood effect

Neighbourhood effects have been defined by Oakes (2004) as the independent causal effects of neighbourhood on a given number of health or social outcome(s). The aim of this thesis is to estimate the neighbourhood effect on old population in Turin with a propensity score approach. To achieve this goal, we need to work on adapting propensity score techniques to work well in a framework with many treatments (with ten or more treatments). Data used in the thesis come from the Turin Longitudinal Study (SLT), described in chapter 3. Our main goal is to understand if the observed differences in health outcomes across neighbourhoods can be causally attributed to neighbourhoods' as opposed to their different composition, i.e. to the fact that individuals with different risks factors live in different areas. In order to adjust for confounders and simulate an experimental approach, we focused on propensity score techniques that are briefly described in chapter 2. The first part of the analysis focuses on the performance evaluation of an inverse probability of treatment approach (IPTW) in a 10-treatment framework (chapter 4) and its application on real data on two different health outcomes: hospitalized fractures and mental health (chapter 5). In the second part of the thesis we propose a novel method that consists on a matching based on partially ordered sets (poset) (chapter 6). The Matching on Poset based Average Rank for Multiple Treatment (MARMoT), tested with some simulations, has revealed to be really useful to estimate neighbourhood effect, reducing bias of estimates because of the initial improvement of covariates' balance between groups