# A Novel Non-Parametric Spatiotemporal Scan Statistic: An Application to Detect Disease Outbreaks
## 4 Discussion and Conclusions  
We specifically focused on improving the existing MW Scan Statistic, incorporating the time component and using it to detect disease outbreak areas. Following the suggestion in [5], the Spatiotemporal MW Scan Statistic was improved in this study by using the spatiotemporal distance defined in [11]. The performance of this improved scan statistic was then evaluated.  
Based on the obtained results, the Spatiotemporal MW Scan Statistic performs significantly well in detecting the area of disease outbreak in a larger geographical region. Moreover, it can effectively detect the exact disease outbreak area in the majority of cases. Even if the exact outbreak area was not detected in the most likely cluster, it was detected in one of the secondary clusters by this scan statistic.  
It is important to acknowledge several limitations of the current study, which restrict the generality of the conclusions that can be drawn from these experiments. Only a limited number of samples were evaluated in assessing the performance of the newly developed Spatiotemporal MW Scan Statistic due to higher computational time (approx. 10 h/sample). Moreover, the issue of the ties in ranking the response variable in calculating the Spatiotemporal MW Scan Statistic might cause distortions of the results. Furthermore, no population adjustments were considered in calculating the Spatiotemporal MW Scan Statistic. Due to the unavailability of a common measure which can be used to evaluate the performance of both parametric and non-parametric scan statistics, we applied only a basic performance measure. A more appropriate probabilistic performance measure will be developed to conduct future experiments.  
The improvement of the Spatiotemporal MW Scan Statistic will be a promising alternative in the field of scan statistics as it can be applied to different scenarios without making any assumptions of the distribution of the response variable and can still detect significant spatiotemporal clusters. Even though the response variable of the applications used in this study is a count variable, this improved scan statistic can be applied to continuous data with the same framework provided. We aimed to identify the most likely clusters (MLCs) over a specific time period. Thus, based on the results, the identified clusters are the disease hotspots over the whole time period. This work can be further improved by the consideration of clusters across variable time frames and by incorporating population adjustments which will enable the detection of multiple outbreaks simultaneously, along with their precise time characteristics.  
Conceptualization, C.D.T. and K.H.H.; Data curation, K.H.H.; Formal analysis, K.H.H.; Investigation, K.H.H.; Methodology, K.H.H. and C.D.T.; Project administration, C.D.T.; Software, K.H.H.; Supervision, C.D.T.; Validation, K.H.H.; Visualization, K.H.H.; Writing--original draft, K.H.H.; Writing--review & editing, C.D.T. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Publicly available datasets were analyzed in this study. These data can be found at [[http://www.satscan.org/datasets](http://www.satscan.org/datasets)]([http://www.satscan.org/datasets](http://www.satscan.org/datasets)) (accessed on 25 December 2021) (Simulated Datasets) and [[https://github.com/CSSEGISandData/COVID-19](https://github.com/CSSEGISandData/COVID-19)]([https://github.com/CSSEGISandData/COVID-19](https://github.com/CSSEGISandData/COVID-19)) (accessed on 25 December 2021) (COVID-19 Data).  
**Acknowledgments:** The authors thank [PERSON] (University of Montpellier) for providing the basic R programs of the Mann-Whitney Scan Statistic along with his insights and expertise that greatly assisted and improved the research.  
**Conflicts of Interest:** The authors declare no conflict of interest.