Spatial autoregressive models for scan statistic

A Shared‐Frailty Spatial Scan Statistic Model for Time‐to‐Event Data

“…Therefore, the $$\varphi _k$$ must be estimated under the true hypothesis among $$\mathcal {H}_0$$ and the set of alternative hypotheses $$\mathcal {H}_1^{(w)}$$, that is, the hypothesis under which the observations have been generated. In line with the approach developed by Ahmed, Cucala, and Genin (2021), we need to determine the “best model” among the candidate hypotheses ($$\mathcal {H}_0$$ and $$\mathcal {H}_1^{(w)}$$). To this end, for each potential cluster $$w \in \mathcal {W}$$, we considered the Bayes factor $$\text{BF}^{(w)}$$, defined as the marginal likelihood ratio between the model under $$\mathcal {H}_1^{(w)}$$ ($$\mathcal {M}_1^{(w)}$$) and the model under $$\mathcal {H}_0$$ ($$\mathcal {M}_0$$): …”

“…1 , that is, the hypothesis under which the observations have been generated. In line with the approach developed by Ahmed, Cucala, and Genin (2021), we need to determine the "best model" among the candidate hypotheses ( 0 and  (𝑤) 1 ). To this end, for each potential cluster 𝑤 ∈ , we considered the Bayes factor BF (𝑤) , defined as the marginal likelihood ratio between the model under…”

“…Furthermore, it has been shown that ignoring spatial dependence when using spatial scan statistics leads to a significant increase in the type I error (Loh and Zhu 2007). Since then, several researchers have developed methods that take spatial dependence into account (Ahmed, Cucala, and Genin 2021; Lee, Sun, and Chang 2020; Lin 2014; Loh and Zhu 2007). However, none of these methods were designed for time‐to‐event data and the adjustment for intraspatial unit correlations.…”