A Bayesian framework to quantify survival uncertainty

Abstract

Abstract Background Existing survival models do not model uncertainty in personalized (per-patient) prediction of survival, which is useful for treatment planning of cancers. Moreover, their restrictive modeling assumptions limit their accuracy of personalized survival estimation. For example, the Cox proportional hazard (CPH) model assumes a constant effect of each input feature on survival rate over time along with a linear combination of features. The multi-task logistic regression (MTLR) allows a smooth time-varying impact of each feature without relaxing the linearity assumption. Recently, neural-MTLR (N-MTLR) was proposed to relax the linearity assumption as well. We propose Bayesian (B-MTLR) and Bayesian neural network (BN-MTLR) frameworks for predicting survival that are more accurate than the previous methods and compute uncertainty for each personalized prediction. We demonstrate that including more granular information, such as PAM50 gene expressions instead of the PAM50 labels, both increases accuracy and decreases uncertainty in personalized survival prediction. Methods Using four-fold cross validation on the TCGA-BRCA we compared the accuracy of personalized prediction (C-index and IBS) for CPH, MTLR, N-MTLR, B-MTLR, and BN-MTLR using PAM50 labels and clinical variables. We also compared BN-MTLR models trained on PAM50 gene-set and clinical variables for decrease in uncertainty due to more granular inputs. Results The table below shows that for PAM50 labels and clinical variables the C-index is higher and the IBS is lower for B-MTLR and BN-MTLR compared to the existing techniques. Additionally, BN-MTLR gave a mean uncertainty of 0.12 using PAM50 gene expression as opposed to 0.22 using PAM50 labels across all patients. Table: 112P . Comparison of models Methods C-index mean (std. dev.) IBS mean (std. dev.) CPH 0.67 (0.10) 0.20 (0.07) MTLR 0.68 (0.06) 0.21 (0.06) N-MTLR 0.68 (0.02) 0.16 (0.04) B-MTLR 0.69 (0.05) 0.14 (0.02) BN-MTLR 0.70 (0.05) 0.10 (0.01) Conclusions The proposed Bayesian extensions of survival models give better mean personalized accuracy and allow computation of personalized uncertainty scores, which will pave the way for more informative models for treatment planning of cancers. Legal entity responsible for the study The authors. Funding Has not received any funding. Disclosure All authors have declared no conflicts of interest.