## 4 Discussion
This quantitative comparison demonstrated that the proposed machine learning approach generally achieves much better accuracy of parameter estimation and slightly lower accuracy of state response prediction than obtained by the conventional methodologies that minimize the model response error. Therefore, it can be concluded that the proposed approach provides more accurate parameter estimation, which enhances the general validity of the resulting models, even if it does not achieve the closest fit to the observed state responses. In contrast, although the prediction error methods yield a good fit between the model response and the data, its general validity is limited due to inaccuracies in parameter estimation. Another important section of the results addresses a detailed case study focused on experimenting with a single particular patient. First, an in silico subject was randomly generated following the considered statistical distribution of the model parameters within the population. Then, the state responses to the suboptimal leading dose were obtained for the duration of one dosing period by simulating the model defined by (1) for the given initial conditions. A comparison of these state responses with their approximations obtained by the proposed parametrization technique is given in Figure 4. It is evident that the state responses can be approximated very accurately by the function of an exponential nature and an absolute (constant) term. Nevertheless, it is important to remember that the aim of parametric approximation is not to achieve a perfect fit but rather to extract the features of the responses and thus describe them with a small set of parameters. Another important result of the personalization accuracy analysis is the comparison between the actual instance of vector \(\xi\) given by (38) and its estimate \(\hat{\xi}\) given by (41). This is also visualized in Figure 5. for the parameter vector \(\hat{\theta}\). The results demonstrated that the parameters estimated from the finite sequence of state responses to the leading dose were of good accuracy, with all estimates falling within the confidence intervals. The relative (percentual) width of the confidence interval \(\pm\frac{\Delta\hat{\theta}_{i}}{\hat{\theta}_{i}}\) is visibly different for each parameter depending on the diagonal entries of the covariance matrix \(\hat{P}\) following (38). The conventional least squares minimization of the model simulation error yielded the estimates given by (43) and visualized in Figure 7. Based on these results, it can be claimed that the error of personalization is higher than, but still acceptable. Another important part of the results analysis is the personalization of the steady states, which is ultimately required for the optimal chemotherapy design. Since the steady states are derived from the model parameters, their accuracy results from the accuracy of model personalization. The actual coexisting state is defined by (39), and the personalized models resulted in the estimated coexisting states as given by (42) and (44). We can claim that the most accurate estimate of the coexisting steady state was obtained by the proposed approach. The remaining results addressed the problem of personalized optimization of the chemotherapy dosing protocol. Based on the model personalized from the patient's response to the suboptimal leading dose, the sequence of six optimal chemotherapy doses was determined by numeric optimization, and this dosing protocol was applied to the virtual subject, resulting in the state responses plotted in Figure 9. These state responses demonstrate effective and relatively fast stabilization of all three variables to the target coexisting state representing cancer in remission. However, significant fluctuations are present at the beginning of the treatment, which are difficult to manage due to the fixed suboptimal leading dose and adverse initial conditions. It is also important to notice that the tumor responses showed periodic behavior.