Robust prediction of failure time through unified Bayesian analysis of nonparametric transformation models

Nonparametric transformation models (NTMs) have sparked much interest in survival prediction owing to their flexibility with both transformations and error distributions unspecified. However, fitting these models has been hampered because they are unidentified. Existing approaches typically constrain the parameter space to ensure identifiablity, but they incur intractable computation and cannot scale up to complex data; other approaches address the identifiablity issue by making strong \textit{a priori} assumptions on either of the nonparametric components, and thus are subject to misspecifications. Utilizing a Bayesian workflow, we address the challenge by constructing new weakly informative nonparametric priors for infinite-dimensional parameters so as to remedy flat likelihoods associated with unidentified models. To facilitate applicability of these new priors, we subtly impose an exponential transformation on top of NTMs, which compresses the space of infinite-dimensional parameters to positive quadrants while maintaining interpretability. We further develop a cutting-edge posterior modification technique for estimating the fully identified parametric component. Simulations reveal that our method is robust and outperforms the competing methods, and an application to a Veterans lung cancer dataset suggests that our method can predict survival time well and help develop clinically meaningful risk scores, based on patients' demographic and clinical predictors.