Penalized Bayesian forward continuation ratio model with application to high-dimensional data with discrete survival outcomes

While time-to-event data are often continuous, there are several instances where discrete survival data, which are inherently ordinal, may be available or are more appropriate or useful. Several discrete survival models exist, but the forward continuation ratio model with a complementary log-log link has a survival interpretation and is closely related to the Cox proportional hazards model, despite being an ordinal model. This model has previously been implemented in the high-dimensional setting using the ordinal generalized monotone incremental forward stagewise algorithm. Here, we propose a Bayesian penalized forward continuation ratio model with a complementary log-log link and explore different priors to perform variable selection and regularization. Through simulations, we show that our Bayesian model outperformed the existing frequentist method in terms of variable selection performance, and that a 10% prior inclusion probability performed better than 1% or 50%. We also illustrate our model on a publicly available acute myeloid leukemia dataset to identify genomic features associated with discrete survival. We identified nine features that map to ten unique genes, five of which have been previously associated with leukemia in the literature. In conclusion, our proposed Bayesian model is flexible, allows simultaneous variable selection and uncertainty quantification, and performed well in simulation studies and application to real data.