# Statistical and Clustering Analysis of Safety Profiles of FDA-Approved Protein Kinase Inhibitors
## 3 Results
### Cluster Analysis of the Spectrum of AEs for the Approved Protein Kinase Inhibitors  
To minimize noise and improve the robustness of the clustering analysis, we excluded AE PTs reported in only three or fewer drugs (below 5% of the total drugs analyzed). This filtering step reduced dataset dimensionality while retaining the most relevant AE PTs. Hierarchical clustering was performed using the complete linkage clustering, chosen because it is less sensitive to outliers and noise compared to methods such as nearest neighbor (single linkage) and ensures that clusters are compact and well separated [32]. We utilized the Manhattan distance metric due to its suitability for handling high-dimensional data containing numerous zero entries. In previous research, it yielded the best results for grouping patterns between subjects that showed similar structure in the variation of IL-1\(\beta\) gene expression over time [33]. The PKI drugs were categorized into six distinct clusters, which are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
Cluster 1 has the highest number of elements, with 23 drugs, followed closely by Cluster 2 with 22 drugs, and Cluster 4 with 14 drugs. Clusters 3, 5, and 6 have a small number of drugs, indicating a specific profile of AEs. The shape of each cluster is presented in Figure 3.  
Considering the proximity matrix, the smallest distance between a drug pair was 0.000042, found between gefitinib and selmetinib, while the highest distance was 0.248, observed for the pair of neratinib and pexidartinib. The average values for Cluster 2 (0.010) were smaller than those of Cluster 1 (0.015) and Cluster 4 (0.014), indicating a higher degree of similarity among the effects of the compounds in Cluster 2. Based on the proximity matrix, we prepared a heat map illustrating the distances between each drug's safety profile across the various clusters, as presented in Figure 4. \begin{table}
\begin{tabular}{c c c c c} \hline
**Cluster 1** & **Cluster 2** & **Cluster 3** & **Cluster 4** & **Cluster 5** & **Cluster 6** \\ \hline Gefitinib & Imatinib & Lapatinib & & \\ \hline Gilteritinib & Lenvatinib & Midostaurin & & \\ \hline Ibrutinib & Nilotinib & Pazopanib & & \\ \hline Idelalisib & Palbociclib & Ribociclib & & \\ \hline Larotrecitinib & Ponatinib & Ripretinib & & \\ \hline Lorlatinib & Regorafenib & & & \\ \hline Netarsudil & Sorafenib & & & \\ \hline Osimertinib & Sunitinib & & & \\ \hline Pemigatinib & Tepotinib & & & \\ \hline Pexidartinib & Trametinib & & & \\ \hline Ruxolitinib & Vandetanib & & & \\ \hline Selumetinib & Vemurafenib & & & \\ \hline Tofacitinib & Zanubrutinib & & & \\ \hline Upadicitinib & & & & \\ \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
Figure 3: Dendrogram of drug clustering based on their adverse event (AE) frequency profile, using the Manhattan distance metric and complete linkage method. A Kruskal-Wallis analysis was performed on each pair of clusters to assess if there were significant differences in the frequency of the top 10 most frequent AEs. A _p_-value of less than 0.05 was considered indicative of statistical significance. The results are presented in Table 5.  
There were no significant differences in the frequency of death across any clusters, indicating that death as an AE occurs consistently in each PKI group. Nevertheless, for four drugs, all from Cluster 1 (acalabrutinib, dacomitinib, erlotinib, and osimertinib), the death frequency represented a high outlier. Similar to the frequency of death, pain, rash, off-label use, and drug ineffective showed no significant frequency differences among clusters. Cluster 1 generally exhibited fewer AEs in terms of diarrhea, fatigue, nausea, and vomiting compared to the other clusters. Cluster 2 also had lower frequencies of these AEs compared to Clusters 3, 4, and 5. Conversely, Cluster 3 showed higher frequencies of several key AEs, particularly gastrointestinal issues like diarrhea, nausea, and vomiting.