  Cancer stage is a large determinant of patient prognosis and management in
many cancer types, and is often assessed using medical imaging modalities, such
as CT and MRI. These medical images contain rich information that can be
explored to stratify patients within each stage group to further improve
prognostic algorithms. Although the majority of cancer deaths result from
metastatic and multifocal disease, building imaging biomarkers for patients
with multiple tumors has been a challenging task due to the lack of annotated
datasets and standard study framework. In this paper, we process two public
datasets to set up a benchmark cohort of 341 patient in total for studying
outcome prediction of multifocal metastatic cancer. We identify the lack of
expressiveness in common multiple instance classification networks and propose
two injective multiple instance pooling functions that are better suited to
outcome prediction. Our results show that multiple instance learning with
injective pooling functions can achieve state-of-the-art performance in the
non-small-cell lung cancer CT and head and neck CT outcome prediction
benchmarking tasks. We will release the processed multifocal datasets, our code
and the intermediate files i.e. extracted radiomic features to support further
transparent and reproducible research.
