*2.6. Spatial Analysis*

The number of attributable deaths (estimated following the methodology described in Section 2.5) was distributed in each census block, proportionally to the adult population size living in the census block. To investigate the spatial distribution of "premature" deaths at census block level in Paris, we used a spatial scan statistic approach. The Poisson probability model used in the SaTScan software [21] was chosen as a cluster analysis method to detect the presence of high avoidable death spatial clusters (called 'most likely clusters').

The null hypothesis (H0) tested was that the risk is equi-probable throughout the study area. In other words, the expected "premature" death rate would be randomly distributed over the area. The alternative hypothesis (H1) was that there is an elevated risk within the cluster in comparison with census blocks outside the cluster. The procedure works as follows: a circle or window of variable radius (from 0 up to 50% of the population size as recommended by Kulldorf [22]) is placed at every centroid of the census block and moves across the whole study area. For each window, the "premature" death risk estimated in the window is compared with expected "premature" death rate under the hypothesis of a random distribution. The statistically significant most likely clusters are identified using the likelihood ratio test [23]. The *p*-value associated to each detected cluster was obtained from a Monte Carlo replication [24]. ArcGis software was used to map and visualize the spatial location of the statistically significant most likely clusters.
