### Tumor Growth Patterns Found in the Data

This page is an extension of Section 4.2 of the paper and describes tumor growth patterns found in the data - based on statistical computations we performed on the training set (a total of approximately 1/2 million voxels).

Here, we present the probabilities of a voxel with a particular property or has an attribute a, given the voxel is tumor, i.e., P(att(voxel) = a | +t) or given it is non-tumor, i.e. P(att(voxel) = a | -t) .

Probability that a voxel is tumor P(+t) vs. non-tumor P(-t):
P(+t) = 0.625
P(-t) = 0.375

Probability that a voxel is edema given it is tumor vs. it is non-tumor:
P(e | +t) = 0.449
P(e | -t) = 0.251

Probabilities of a voxel having at least one edema-neighbor:
P(eNei | +t) = 0.522
P(eNei | -t) = 0.314

Probabilities of a voxel with a T1 image intensity below 0.5:
P(t1 | +t) = 0.417
P(t1 | -t) = 0.508

Probabilities of a voxel with a T1-contrast image intensity below 0.5:
P(t1c | +t) = 0.409
P(t1c | -t) = 0.472

Probabilities of a voxel with a T2 image intensity above 0.75:
P(t2 | +t) = 0.226
P(t2 | -t) = 0.148

Probabilities of a voxel that has at least one neighbor with a T2 image intensity above 0.75:
P(t2Nei | +t) = 0.376
P(t2Nei | -t) = 0.275

Probabilities of a voxel being white matter:
P(wm | +t) = 0.321
P(wm | -t) = 0.237

Probabilities of a voxel that has at least one white matter neighbor:
P(wmNei | +t) = 0.497
P(wmNei | -t) = 0.381

Probabilities of a voxel being grey matter:
P(gm | +t) = 0.449
P(gm | -t) = 0.392

Probabilities of a voxel that has at least one grey matter neighbor:
P(gmNei | +t) = 0.722
P(gmNei | -t) = 0.646

Probability that a voxel is tumorous given this voxel is edema, has T2 intensity above 0.75 and is white matter:
P(+t | e, t2, wm) = 0.860
Probability that a voxel is tumorous given this voxel is edema, has T2 intensity above 0.75 and is grey matter:
P(+t | e, t2, gm) = 0.839

Probability that a voxel is tumorous given this voxel is edema, has at least one edema neighbor, has T2 intensity above 0.75, has at least one neighbor with T2 intensity above 0.75, is white matter, and has at least one white matter neighbor:
P(+t | e, eNei, t2, t2Nei, wm, wmNei) = 0.948

Probability that a voxel is tumorous given this voxel is edema, has at least one edema neighbor, has T2 intensity above 0.75, has at least one neighbor with T2 intensity above 0.75, is grey matter, and has at least one grey matter neighbor:
P(+t | e, eNei, t2, t2Nei, gm, gmNei) = 0.929