title: Improving Cox survival analysis with a neural-Bayesian approach.
abstract: In this article we show that traditional Cox survival analysis can be improved upon when supplemented with sensible priors and analysed within a neural Bayesian framework. We demonstrate that the Bayesian method gives more reliable predictions, in particular for relatively small data sets. The obtained posterior (the probability distribution of network parameters given the data) which in itself is intractable, can be made accessible by several approximations. We review approximations by Hybrid Markov Chain Monte Carlo sampling, a variational method and the Laplace approximation. We argue that although each Bayesian approach circumvents the shortcomings of the original Cox analysis, and therefore yields better predictive results, in practice the use of variational methods or Laplace is preferable. Since Cox survival analysis is infamous for its poor results with (too) many inputs, we use the Bayesian posterior to estimate p-values on the inputs and to formulate an algorithm for backward elimination. We show that after removal of irrelevant inputs Bayesian methods still achieve significantly better results than classical Cox.
authors.affiliation: Theoretical Foundation SNN Laboratory, University of Nijmegen, Geert Grooteplein 21, 6525 EZ Nijmegen, The Netherlands. bart.bakker@philips.com
authors.forename: Bart
authors.initials: B
authors.lastname: Bakker
authors.forename: Tom
authors.initials: T
authors.lastname: Heskes
authors.forename: Jan
authors.initials: J
authors.lastname: Neijt
authors.forename: Bert
authors.initials: B
authors.lastname: Kappen
mesh_terms: D000970:Antineoplastic Agents / Q000627:therapeutic use; D001499:Bayes Theorem; D003198:Computer Simulation; D005260:Female; D006801:Humans; D008390:Markov Chains; D009010:Monte Carlo Method; D009426:Netherlands / Q000453:epidemiology; D016571:Neural Networks, Computer; D010051:Ovarian Neoplasms / Q000188:drug therapy / Q000401:mortality; D016016:Proportional Hazards Models; D016019:Survival Analysis
chemical_list: D000970:Antineoplastic Agents