Research
A latent space model for HLA compatibility networks in kidney transplantation
Abstract
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.
Contributions
We introduce the notion of an HLA compatibility network between donor and recipient HLAs, a noisy signed and weighted network estimated from outcomes of kidney transplants involving those HLAs.
We propose a latent space model for the HLA compatibility network to capture the underlying structure between HLAs and better predict their compatibilities.
We demonstrate that applying our latent space model to the HLA compatibility network results in more accurate predictions of the compatibilities.
We find that the predicted compatibilities from our latent space model can further improve accuracy for the downstream task (see Figure 1) of predicting outcomes of kidney transplants, namely the graft survival times.
Results
Prediction Accuracy
Baseline models:
Cox proportional hazards (CoxPH): Directly uses the estimated CoxPH coefficients without any further processing.
Non-negative matrix tri-factorization (NMTF) : A technique for learning low-dimensional feature representation of relational data that decomposes the given matrix into three smaller matrices rather than two matrices as in standard non-negative matrix factorization.
Principal component analysis (PCA): A classical linear dimensionality reduction technique that projects the given matrix into a lower dimensional space. We reconstruct the compatibilities from the first d principal components.
Table 1: Evaluation metrics for HLA compatibility and graft survival time prediction. Our proposed LSM performs competitively on HLA compatibility prediction on all 3 loci and achieves the best C-index for graft survival time prediction.
From Table 1, note that the predicted weights using other models to refine the estimated compatibilities are more accurate for each of the 4 metrics and 3 loci compared to directly using the CoxPH coefficients. Among the refinement methods, the LSM and NMTF have similar prediction accuracy, and both significantly outperform PCA. While the NMTF is competitive to our LSM in prediction accuracy, the LSM can also provide useful interpretations through the latent space, as shown in figure 2.
Looking at the C-indices, notice that our proposed latent space model improves the C-index by about 0.011 compared to directly using the CoxPH coefficients. The NMTF and PCA provide smaller improvements of 0.009 and 0.007, respectively. We note that an improvement of 0.011 in the C-index for graft survival prediction in kidney transplantation is a large improvement! For comparison, using the same dataset and inclusion criteria, Nemati et al. evaluated C-indices using 6 different HLA representations across 3 different survival prediction algorithms and found achieved a maximum improvement of 0.007. Similarly, using the same dataset but slightly different inclusion criteria, Luck et al. achieved a maximum improvement of 0.005. The appreciable improvement in Cindex demonstrates the utility of our latent space modeling approach not only for interpreting HLA compatibilities, but also for graft survival prediction
Fig. 1 End-to-end evaluation of HLA compatibility estimates using downstream task of survival prediction. The HLA compatibility estimates from the Cox PH model (red line) are compared against the updated estimates from the latent space model (blue line) for survival prediction accuracy.
Model-based Exploratory Analysis
From examining the latent positions in figure 2, we find that pairs of nodes with higher edge weights tend to appear closer together in the latent space and vice versa. For example, in the HLAA plot, donor A74 and recipient a29 have a high weight of 0.349 and tend to be placed close together in the 2-D plot. Conversely, donor A28 and recipient a33 have a low weight of −0.257 and are placed on opposite sides of the latent space. We draw cyan dashed lines indicating the top 3 highest weight pairs and magenta dashed lines indicating the top 3 lowest weight pairs in all three 2-D HLA latent space plots.
Fig. 2 The 2-D latent space plot for HLA networks for loci A. Red x: donor node; green circle: recipient node. The 3 highest and lowest edge weights are shown with dashed cyan and magenta lines, respectively. Donor-recipient pairs with the highest edge weights tend to be placed closer together in the latent space compared to those with the lowest edge weights.