## 6 Discussion  
Compared to using only the mean ADC value, the quantitative statistical histogram features and the proposed classification system tremendously improved the accuracy from 29.4% to 69.41% (Az increased from 0.33 to 0.70). The statistical analysis indicates that all three classifiers are significantly different from the conventional mean ADC method with our dataset. Compared to general statistical histogram features, the classification with GMM features using random forest technique slightly improved the accuracy from 65.88% to 69.41%, while adaBoost and RF classifiers generated the same accuracy no matter whether GMM features were included. There is no significant difference between the three machine-learned classifiers. The conventional mean ADC method performs worse than a random classifier (Az \(<\) 0.5). The reason is that conventionally researchers hypothesized that mean ADC increases because the tumor cell density decrease after an effective treatment. This assumption may not be valid for our dataset, because it involves in an anti-angiogenesis drug, which suppresses the cancer cell growth without necessary killing tumor cells (decreasing their density) at an early stage (5-7 weeks). Another possible reason is that in our dataset many of the GBM tumors are recurrent GBM tumors that are usually necrotic. The treatment tends to reduce necrosis and edema, which will diminish ADC. Essentially there are two competing processes at work: cell density, edema and necrosis [25]. Another state-of-art study included features that capture spatial information in tumor heterogeneity features. Functional diffusion map (fDM) [22, 23] is a popular technique studying the ADC value increase or decrease voxel-by-voxel. [PERSON] et al. applied fDM to 20 patients, classified patients into \begin{table}
\begin{tabular}{l l l l l} \hline
**Classifier** & **Sensitivity** & **Specificity** & **Accuracy** & **Az** \\ \hline AdaBoost & 39.39\% & 80.77\% & 64.7\%\({}^{*}\) & 0.60 \\ Random forest & 51.52\% & 80.77\% & 69.41\%\({}^{*}\) & 0.70 \\ SVM & 27.27\% & 92.3\% & 67.06\%\({}^{*}\) & 0.60 \\ \hline \end{tabular}
\end{table} 
Table 6: Performance comparison among three classifiers with GMM features. Figure 5: ROC curve for three classifiers with GMM features. the three categories: PR, SD and PD, and reported 100% accuracy [22]. However, the threshold they used for classification was determined from a single dataset of 20 patients used for both training and testing, while in our experiments, a cross validation analysis was performed. In [PERSON] et al's study, they explored the assessment of fractionated radiation therapy for different types of brain tumors with 20 patients scanned on the same scanner [22]. However, in our study, we focused on the GBM brain tumors treated by anti-angiogenesis drugs, which suppress the blood supply for the tumor cells and may not directly decrease the tumor cellularity. The difference in accuracy may come from the different mechanism of treatment. Additionally, our dataset is from GBM drug trials across multiple sites, thus our preliminary study is an important contribution for exploring DWI as an early imaging biomarker in a real pharmaceutical drug trial. In future work, we will extract texture feature to include spatial information, and shape features will be extracted as well. By introducing a new richer feature set indicating more useful tumor information, we aim to include more information about tumors and further improve the performance of the classification system. One limitation of this study is that we classified CR, PR and SD as responders for the ground truth to achieve a binary classification. Since SD and PR may have different patterns in terms of their ADC histogram change, a multi-category classification system will be explored in future work. Another limitation of the study is that we used the Macdonald criteria at the eighth or tenth week after treatment for determining treatment response.