A0901
Title: From Poisson to Bernoulli: Unlocking the finite sample properties of survival processes
Authors: Benny Ren - Stony Brook University (United States) [presenting]
Abstract: Finite sample inference for Cox models is an important problem in many settings, such as clinical trials. Bayesian procedures allow for finite sample inference and incorporation of prior information if MCMC algorithms and posteriors are well-behaved. In addition, estimation procedures should be straightforwardly able to incorporate multilevel modeling, such as cure models and frailty models. To tackle these modeling challenges, a uniformly ergodic Gibbs sampler is proposed for multilevel Cox models and survival functions. A novel Bayesian computation procedure is outlined that succinctly addresses the difficult problem of monotonically modeling the nonparametric baseline cumulative hazard and regression coefficients. Two key strategies are developed. First, a connection between Cox models and negative binomial processes is exploited through the Poisson process to reduce Bayesian computation to iterative Gaussian sampling. Next, it is appealed to sufficient dimension reduction to address the difficult computation of nonparametric baseline cumulative hazard, allowing for the collapse of the Markov transition operator within the Gibbs sampler based on sufficient statistics. The uniformly ergodic Gibbs sampler guarantees that MCMC draws converge in total variation distance to the posterior distribution, allowing for the constrained inference of baseline hazards in finite sample settings. The approach is demonstrated using open-source data and simulations.
