  Kidney transplantation is the preferred treatment for people suffering from
end-stage renal disease. Successful kidney transplants still fail over time,
known as graft failure; however, the time to graft failure, or graft survival
time, can vary significantly between different recipients. A significant
biological factor affecting graft survival times is the compatibility between
the human leukocyte antigens (HLAs) of the donor and recipient. We propose to
model HLA compatibility using a network, where the nodes denote different HLAs
of the donor and recipient, and edge weights denote compatibilities of the
HLAs, which can be positive or negative. The network is indirectly observed, as
the edge weights are estimated from transplant outcomes rather than directly
observed. We propose a latent space model for such indirectly-observed weighted
and signed networks. We demonstrate that our latent space model can not only
result in more accurate estimates of HLA compatibilities, but can also be
incorporated into survival analysis models to improve accuracy for the
downstream task of predicting graft survival times.
