## 3 Results  
Figure 1 shows a bar plot of the patients' clinical variables importance score. The figure shows that dose per fraction and weight have a higher correlation with tumor volume change than other clinical variables. However, this bar plot does not reflect the relationship between variables and whether any combination of variables may have a higher correlation with the volume change. Partial dependence plot (PDP) and individual conditional expectation (ICE) analysis: partial dependence plots (PDP) and individual conditional expectation (ICE) plots, as seen in Figure 2, can be used to visualize and analyze the interaction between the tumor volume reduction rate and a set of input predictors. The partial dependency map (also known as the PDP or PD plot) illustrates the marginal effect of one or two features on the predicted outcome of a machine learning algorithm. A partial dependency plot can demonstrate whether the relationship between a percentage volume change and variable is linear, monotonic, or more complex. Individual conditional expectation (ICE) plots demonstrate how the prediction of an instance varies when an attribute changes. Since it focuses on a general average rather than particular cases, the partial dependency plot for the average influence of a feature is a global technique. Figure 2 plots the corresponding PD line in red overlaid on ICE lines in grey. A scatter plot of the selected predictor and predicted responses is also included for all patients. The figure shows that gender, number of treatment fractions and dose per fraction do not affect volume change within the patient group studied. However, dose per fraction, age, and weight appear to correlate with percentage volume change within this patient group. Figure 1: A bar plot of the patients’ clinical variables importance score. While PDPs figures are useful for displaying the average influence of the individual target features, they may mask a connection caused by interactions between target features. Figure 3 visualizes the partial dependence of predicted responses (percentage volume change) on the predictor variables dose per fraction and age. The figure shows that the volume change % was at its lowest range at a younger age and higher dose per fraction. Figure 4 visualizes the partial dependence of predicted responses (percentage volume change) on the predictor variables weight and age. Figure 5 shows the partial dependence of predicted responses (percentage volume change) on the predictor variables' dose per fraction and weight. Figure 4 again reflects the positive impact of the younger age and lower weight. Figures 3-5 show that younger age and low weight with a higher dose per fraction reflect better treatment outcome in terms of the volume change %, further investigation of this is required. Figure 3: A PDP that visualizes partial dependence of predicted responses (volume change %) on the predictor variables dose per fraction and age. Figure 2: A PDP plot (red line) and ICE plots (grey lines) for each predictor. A scatter plot (circle markers) of the selected predictor and predicted responses is also included. The result shown in Table 3 demonstrate that age provides the main interest after the first iteration. In the next step additional predictors are added to age and the \(p\)-value of each additional predictor calculated again. The steps described above are repeated until adding an additional predictor does not yield a better \(t\)-test and \(p\)-value. The stepwise regression model showed that age, dose per fraction and weight are best predictors for tumour volume reduction rate and the relationship can be summarized in the following equation, where \(c_{1}\), \(c_{2}\), and \(c_{3}\) are constants:  
\[\text{TVRR}\sim 1+c_{1}\text{ Age}+c_{2}\text{ Dose Per Fraction}+c_{3}\text{ Weight} \tag{3}\]  
Using the result obtained one may fit a stepwise linear regression model to the data to determine how well the model fits the data. The root mean squared error (RMSE) of the linear regression is 0.164.