## 2 Methods
### Blackpattern Impact Analysis  
To calculate a blackpattern impact score (BIS), we combine four components: frequency of the BP \((\text{F}(\text{BP},\text{D}))\), the statistical association between the BP and severe causalities (measured by \(\left(\text{P}_{\text{Fisher}}(\text{BP})\right)\), the strength of this association (measured by the phi coefficient \(\phi(\text{BP})\)), and the logistic regression coefficients \(\beta_{i}\) corresponding to the variables in BP. These components are integrated into a comprehensive BIS to prioritize the identified BPs. This approach enables a precise assessment of the BPs concerning severe accidents by considering both their frequency and the strength of their association with severe casualties, thereby identifying BPs that are both frequent and impactful.  
\[\text{BIS}(\text{BP})=\text{F}(\text{BP},\text{D})\times\epsilon^{|\phi(\text {BP})|}\times\left(-\text{log}\big{(}\text{P}_{\text{Fisher}}(\text{BP}) \big{)}\right)\times\left(\prod_{i=1}^{\text{k}}\epsilon^{\beta_{i}}\right) \tag{8}\]  
where  
\(\beta_{i}\) represents the logistic regression coefficient for each variable \(\text{V}_{i}\) in the BP,  
\(\text{F}(\text{BP},\text{D})\) is the frequency of the BP,  
\(\phi(\text{BP})\) is the phi coefficient, which measures the strength of the association between the BP and the outcome,  
\(\text{P}_{\text{Fisher}}(\text{BP})\) is the _p_-value from [PERSON]'s exact test, indicating the statistical significance of the association between the BP and the outcome.  
To amplify the influence of highly significant BPs (with very small _p_-values), the negative logarithm of \(\text{P}_{\text{Fisher}}(\text{BP})\) is used. The transformation \(\left(-\text{log}\big{(}\text{P}_{\text{Fisher}}(\text{BP})\big{)}\right)\) converts very small _p_-values into larger positive numbers. This ensures that BPs with strong statistical significance have a greater impact on the BIS. Both the logistic regression coefficients \(\beta_{i}\) and the phi coefficient \(\phi(\text{BP})\) represent the strength of association. Small coefficients or \(\phi\)-values might otherwise have a minimal effect on the BIS. The exponential transformation \(\epsilon^{\beta_{i}}\) and \(\epsilon^{|\phi(\text{P})|}\) magnifies these values, particularly when they are small. This emphasizes the contribution of BPs where the variables have a stronger association with the outcome.  
The blackpattern impact analysis allows to identify BPs that are not only common and impactful but also statistically significant in their relationship with severe casualties. This approach provides a comprehensive and nuanced prioritization of BPs, ensuring that our analysis highlights the most relevant and meaningful BPs for further investigation or intervention. Table 2 illustrates the features of the blackpattern impact analysis that must be considered when interpreting the retrieved BIS.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**BIS Features** & **Description** \\ \hline High Frequency & Blackpatterns that occur frequently in the dataset are prioritized. \\ \hline High Impact & Blackpatterns with variables that have a strong influence on severe casualties are emphasized. \\ \hline Strong Association & Blackpatterns that are statistically significant in their association with severe casualties are given higher priority. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Features of the blackpattern impact score (BIS).