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Improving Cox survival analysis with a neural‐Bayesian approach
Author(s) -
Bakker Bart,
Heskes Tom,
Neijt Jan,
Kappen Bert
Publication year - 2004
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1904
Subject(s) - bayesian probability , markov chain monte carlo , laplace's method , prior probability , computer science , laplace transform , posterior probability , bayesian average , mathematics , bayesian inference , algorithm , variable order bayesian network , mathematical optimization , artificial intelligence , machine learning , mathematical analysis
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. Copyright © 2004 John Wiley & Sons, Ltd.