# A Game-Theoretical Approach to Clinical Decision Making with Immersive Visualisation
## 4 Results and Discussion
### Use Case Study  
This section illustrates how game theory helped the analyst find possible linkages between patients' genomic similarities, treatment profiles, and survivability. We discuss the feature of VROOM and how game theory can help to improve efficiency and provide more options in interrogating the data. VROOM's full functionalities and objectives are published in the paper by [PERSON] and [PERSON] [15]. This paper only discusses the immersive visualisation features relevant to game theory applications. Comparisons are made between the two to showcase how game theory can help make discoveries. The \"OHSC Three Risk\" data set and the dimensionality reduction algorithm are chosen for the discussion. The visualisation shows the entire TARGET data set patient cohort in an immersive 3D environment, as shown in Figure 1. The patients are roughly clustered in the three segments to indicate the patient risk level. The red, yellow, and cyan colours indicate high, medium, and low risk, respectively. Same-risk patients are located closely together thanks to the computational analytics, as shown in groups a, b, and c in the figures. In Figure 1, the selected patient is represented by the larger sphere with a blue halo around it. Notice that the white lines connecting the POI are its neighbours determined by the game theory engine. Figure 2 shows the immersive visualisation running in a VR environment. Its functionality is similar to the one shown in Figure 1. The significant difference is that the neighbours in this figure are based on their Euclidean distances from the selected patient, POI. Before we discuss the difference it made, we shall share the relevant VROOM capabilities for the user to analyse the data. From overview visualisation as shown in Figure 1 or Figure 2, the analyst can select a patient of interest (hereafter referred to as POI) to conduct detailed studies. As shown in Figure 3a, the analyst selects the patient using the select command by gazing and air-clicking on the patient. The analysts can grab the sphere representing the patient and put it onto the virtual tablet shown in Figure 3b. The virtual tablet shows the metadata of the patient, such as age, gender, and ethnicity. It also provides statistical information such as boxplots and bar charts. The boxplot (Figure 3c) shows the patient gene value compared to the sample population of the currently displayed data, which is helpful to indicate if the POI gene value is an outlier or within the interquartile range (IQR). At the same time, the bar chart displays the value of each of the 17 genes. These tools provide an overview and detailed visual analytics capabilities to the analyst. As this feature only deals with the POI, there are no differences between the two systems. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & \multicolumn{4}{c}{**Doctor B**} \\ \hline  & & LSC17 & DNMT3B\_ZBTB4 & CD34 & DNMT3B\_ZBTB4 & DNMT3B\_ZBTB46\_MMRN1 \\ \hline \multirow{4}{*}{**VROOM**} & t-SNE & 0.9 & 0.6 & 0.8 & **1.1** & 0.3 \\ \cline{2-6}  & PCA & 0.7 & 0.8 & 0.8 & 1.0 & 0.4 \\ \cline{2-6}  & NMF & 0.4 & 1.0 & 0.8 & 0.8 & 0.5 \\ \cline{2-6}  & UMAP & 0.5 & 0.7 & 0.8 & 0.8 & 0.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The Social Optimality payoff matrix. In this case, the numerical values in the tables are the total payoff for Doctor A and Doctor B. The highlighted red cell has the highest value; hence, it is the Social Optimality selection. Figure 1: VROOM, our immersive visualisation in an AR headset. It shows a 3D similarity space of patient cohorts. In this case, the OHSC three-risk data set is used. The red, yellow, and cyan indicate the patient risk factors, high, medium, and low risk, respectively, labelled by a, b, c. The white line connecting the selected patient, which has a blue hue, to the rest of its neighbours is determined by game theory using the method discussed in Section 3. The black line indicates the separation of the clusters.