where = (4) i = RR 1 for = and RR is the relative risk of disease within the cluster6. For  i – 1,…,I, we consider the conditional alternative hypothesis unknown λ ~ multinomial(c+, (5)  1,…,I) H1: C1,…,CI c+ where = , = (6) i i 1,…, spatial scan statistic 2.3 Kulldorff’s Kulldorff11 defines a spatial scan statistic to detect the most likely cluster based on locally observed likelihood ratio test statistics. The scan statistic is constructed based on circles of increasing radii centered at each tract centroid until a maximum radius, selected is attained. Kulldorff and Nagarwalla7 suggest a largest circle a priori, containing 50 per cent of the total at-risk population, and we use this definition here. Kulldorff11 refers to the collection of tracts having their centroid contained within each circle as a zone, The scan statistic considers each zone as a potential cluster, and z. identifies the zones least consistent with the null hypothesis. We note that for data consisting of regional counts, while the centroids are contained within a circle, zones actually reflect an irregular area defined by the union of polygonal regions associated with the tracts. Let and be the population size and case count, respectively, in zone nz cz Define and as the probability of being a case inside and outside zone respectively. z. z, Based on the null hypothesis the alternative Kulldorff11 defines a H0:=versus HA:>, likelihood ratio statistic proportional to ,
where i = (4)  = RR – 1 for i = 1,…,I, and RR is the relative risk of disease within the cluster6. For unknown λ we consider the conditional alternative hypothesis H1: C1,…,CI  c+ ~ multinomial(c+, 1,…,I) (5) where i = , i = 1,…, (6) 2.3 Kulldorff’s spatial scan statistic Kulldorff11 defines a spatial scan statistic to detect the most likely cluster based on locally observed likelihood ratio test statistics. The scan statistic is constructed based on circles of increasing radii centered at each tract centroid until a maximum radius, selected a priori, is attained. Kulldorff and Nagarwalla7 suggest a largest circle containing 50 per cent of the total at-risk population, and we use this definition here. Kulldorff11 refers to the collection of tracts having their centroid contained within each circle as a zone, z. The scan statistic considers each zone as a potential cluster, and identifies the zones least consistent with the null hypothesis. We note that for data consisting of regional counts, while the centroids are contained within a circle, zones actually reflect an irregular area defined by the union of polygonal regions associated with the tracts. Let nz and cz be the population size and case count, respectively, in zone z. Define and as the probability of being a case inside and outside zone z, respectively. Based on the null hypothesis H0:=versus the alternative HA:>, Kulldorff11 defines a likelihood ratio statistic proportional to ,
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