A new data-driven model for post-transplant antibody dynamics in high risk kidney transplantation

The dynamics of donor specific human leukocyte antigen antibodies during early stage after kidney transplantation are of great clinical interest as these antibodies are considered to be associated with short and long term clinical outcomes. The limited number of antibody time series and their diverse patterns have made the task of modelling difficult. Focusing on one typical post-transplant dynamic pattern with rapid falls and stable settling levels, a novel data-driven model has been developed for the first time. A variational Bayesian inference method has been applied to select the best model and learn its parameters for 39 time series from two groups of graft recipients, i.e. patients with and without acute antibody-mediated rejection (AMR) episodes. Linear and nonlinear dynamic models of different order were attempted to fit the time series, and the third order linear model provided the best description of the common features in both groups. Both deterministic and stochastic parameters are found to be significantly different in the AMR and no-AMR groups showing that the time series in the AMR group have significantly higher frequency of oscillations and faster dissipation rates. This research may potentially lead to better understanding of the immunological mechanisms involved in kidney transplantation.