Ordinal Privileged Distillation for Histopathology-Only Survival Prediction

Multimodal learning can improve cancer survival prediction, but some modalities may be unavailable at deployment. Existing approaches often address this limitation through molecular reconstruction or representation matching, which can require learning variation beyond the survival task. We instead use a teacher trained on the auxiliary modality alone and take its survival outputs as the sole source of supervision from that modality. Transferring these outputs raises a further challenge. Existing survival distillation objectives typically encourage numerical agreement, although teachers and students observing different modalities need not share the same optimal predictions. We prove that matching the teacher’s event probabilities at each time interval can shift the student’s optimal predictions. We therefore introduce Ordinal Privileged Distillation (OPD), which transfers pairwise risk ordering derived from the teacher’s survival curves without matching its absolute score scale or pairwise score gaps. A pairwise logistic loss supplies ordinal supervision alongside a survival loss that accounts for right censoring, leaving the student’s inference architecture unchanged. We evaluate OPD using transcriptome data as the training-only modality and whole-slide images (WSIs) as the student’s input. Extensive experiments on eight cancer benchmark datasets and four WSI backbones demonstrated our superiority over other methods.