Fig. 3.

Data analysis flowchart. (1) Data processing—measured quantities at all spatial points and all $n$ subjects across the first three timepoints are first divided into tumor and normal (healthy) regions (see Fig. 1). All tumor points are then $z$-score normalized to their respective normal (healthy) regions [see Eq. (1)], and the mean is taken for a given subject and timepoint. Finally, one-, two-, or three-model parameters are chosen from among the combinations of measured quantities and timepoints as model inputs. (2) Leave-one-out logistic regression—a set of $n$ logistic regression algorithms are performed, each of which leaves out a single subject from the training data and produces a ${\overrightarrow{\beta }}^i$ weight vector. Each ${\overrightarrow{\beta }}^i$ is then used to calculate the probability of response for the subject left out of the given training set [see Eqs. (2) and (4)]. (3) Model evaluation—ROC analysis is performed using the calculated $P_{\mathcal{R}}^i$ values to determine the AUC and a median weight vector $⟨\overrightarrow{\beta }⟩$ is calculated from the $n$ resulting ${\overrightarrow{\beta }}^i$ vectors.