# A Novel Non-Parametric Spatiotemporal Scan Statistic: An Application to Detect Disease Outbreaks
## 3 Experimental Results
### A Comparison Study  
We thirdly conducted a comparison study on the simulated datasets mentioned in Section 3.1 to assess and compare the performance of the novel Spatiotemporal Mann-Whitney Scan Statistics with the existing widely used Space Time Scan Statistic and Space Time Permutation Scan Statistic. A novel performance measure is introduced for the purpose of comparing the performance due to the unavailability of a common measure which can be used for both parametric and non-parametric scan statistics. This novel performance measure is introduced as a Total Score which integrates four sub-scores concerned with the following four major aspects in identifying disease outbreak areas. * Score 1: Ability to detect smaller areas of outbreak  
As stated in Section 3.1, the data are simulated assuming that outbreak occurred in the five zip codes of Williamsburg, Roosevelt Island, Bulls Head, La Guardia and West Farms of the five major boroughs Brooklyn (A), Manhattan (B), Staten Island (C), Queens (D) and the Bronx (E), respectively. Among these five major boroughs, Manhattan (B) and the Bronx (E) are relatively small areas. In the occurrence of an outbreak in a zip code, it is highly likely that the disease spreads quickly across smaller areas and that cases are reported from several parts of that area. Thus, such a small area can be quickly detected when assessing the number of incidents. Therefore, if a scan statistic can identify at least one zip code belonging to either B or E areas, Score 1 is equal to 1, whereas if it was able to identify at least one zip code belonging to both areas B and E, Score 1 is equal to 2. Hence, Score 1 can take values 0, 1 or 2. * Score 2: Ability to detect larger areas of outbreak  
As opposed to the circumstances in Score 1, Score 2 is used to assess the ability of scan statistics to detect larger areas given that outbreak occurred in a particular zip code. Unlike the above scenario, when an outbreak occurs in a zip code of a larger area, it is unlikely to spread to the entire region and that cases are reported from the entire region. Thus, large areas such as A, C and D will not be quickly identifiable. Therefore, if a scan statistic can identify at least one zip code belonging to either A, C or D, Score 2 is equal to 2. Thus, Score 2 can take the values 0, 2, 4 or 6. * Score 3: Ability to detect neighborhoods of the outbreak location  
Irrespective of the area of the outbreak zip code being small or large, if a scan statistic can identify surrounding zip codes of the outbreak zip code, it should be rewarded. Identification of the surrounding zip codes of the exact outbreak zip codes helps to narrow down the region in which health officials should take action. Thus, Score 3 is defined to assess the ability of scan statistics in detecting adjacent zip codes of the exact outbreak zip code. Accordingly, the standard adjacent zip codes of each outbreak zip code were identified, and if a scan statistic can identify at least one adjacent zip code of an outbreak zip code, Score 3 is equal to 0.1. Since there are five outbreak zip codes, score 3 can take the values 0, 0.1, 0.2, 0.3, 0.4 or 0.5. * Score 4: Ability to detect the exact location of outbreak  
Score 4 serves to assess the ability of the scan statistic to detect the exact zip codes in which the outbreak occurred. If a scan statistic can identify the exact zip code in one of its significant clusters, it should be given extra points. Accordingly, for the identification of each exact zip code 0.3 marks are given. Hence, Score 4 can take the values 0, 0.3, 0.6, 0.9, 1.2 or 1.5. The total score can be used to assess the overall performance of the scan statistics in detecting disease outbreak areas, which is an aggregation of the four above-mentioned sub-scores. Accordingly, the total score can take any value between 0 and 10. In the presence of a single data sample, the total score obtained for each technique can be compared. Accordingly, the **higher the total score, the better the performance of the scan statistic.