*3.2. Logistic Regression Modeling*

Given the overall lack of consensus for features that consistently discriminated between treatment groups, we evaluated the ROI image intensities on the voxel-level (Figure 3A,B) to the presence of Tumor (Figure 3C,D) using logistic regression. The regression coefficients provide an estimate of the explained variance each image modality has on the likelihood of the presence of Tumor. Models incorporating all eight image features were created for each treatment and the resulting regression coefficients were calculated (Figure 3C). The significant features consistent in both models were T1ce, FLAIR, QA, and GFA (Student's t test, corrected for multiple comparisons using False Discovery Rate (FDR), *p* < 0.05). However, T1ce, FLAIR, and GFA express inverted information between the models: T1ce shows that for the RT group, higher intensities indicated the presence of Tumor tissue, whereas for the No RT group, higher intensities indicated the presence of Abnormal tissue. The converse is true for FLAIR and GFA: for the RT group, higher intensities indicated the presence of Abnormal tissue, and for the No RT group, higher intensities indicated the presence of Tumor tissue. Therefore, the same approach for differentiating Abnormal and Tumor tissue for patients in the No RT group is not wholly applicable to patients in the RT group (only for QA). Figure 3D illustrates how the No RT and RT models—built using the T1ce, FLAIR, QA, and GFA features—perform similarly (area under curve (AUC) = 0.84 and AUC = 0.75, respectively) when accounting for treatment. However, the aggregate model ("All patients", Figure 3D) performed the worst (AUC = 0.60)—showing that the conflicting information (demonstrated in Figures 2 and 3C) degraded the model's ability to differentiate Abnormal and Tumor tissue using multi-modal MRI.

**Figure 3.** Differentiating the histopathology classifications Abnormal and Tumor on the voxel-level accounting for prior chemoradiation treatment regime. Voxel intensity histograms from the (**A**) No RT and (**B**) RT groups. Solid lines indicate median, dashed lines indicate the lower and upper interquartile interval. (**C**) Logistic regression coefficients: filled circles indicate significant features in the model, open circles indicate non-significant features. Error bars show standard deviation. (**D**) Logistic regression model performance using only the features deemed significant in (**C**). ROC denotes "receiver operator characteristics", AUC denotes "area under curve", and the "All patients" model (built only using features significant in both models) is an aggregate of the treatment groups.
