A Survival Tree Partition Model Using Latent Gaussian Processes and Laplace Approximations

• Activity Number: 347 - Computationally Intensive Bayesian Methodology
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Richard Payne* and Bani Mallick
• Companies: Eli Lilly & Company and Texas A&M University
• Keywords: Bayesian Statistics; Bayesian Computation; Laplace Approximation; Partition Modeling; Reversible Jump MCMC; Survival Analysis

Abstract

Survival analysis plays an important role in medical research. Proportional hazard models are widely used but the proportional hazards assumption is not always appropriate. Traditional nonparametric estimates, including Kaplan-Meier curves, require the user to specify comparison groups of interest, possibly missing important response-covariate relationships. Utilizing a Bayesian tree partition model, important changes in survival across the covariate space are inferred from the data. The piecewise-constant hazard function in each partition element is modeled using a latent exponentiated Gaussian process. An efficient reversible jump Markov chain Monte Carlo algorithm is accomplished by marginalizing the parameters in each partition element via a Laplace approximation. The method can be used to help determine subgroups in time-to-event data, and is applied to simulated data and a lung cancer dataset.