# Making Large Cox’s Proportional Hazard Models Tractable in Bayesian Networks

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Jidapa Kraisangka,
Marek J. Druzdzel
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Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:252-263, 2016.

#### Abstract

Cox’s proportional hazard (CPH) model is a statistical technique that captures the interaction between a set of risk factors and an effect variable. While the CPH model is popular in survival analysis, Bayesian networks offer an attractive alternative that is intuitive, general, theoretically sound, and avoids CPH model’s restrictive assumptions. Existing CPH models are a great source of existing knowledge that can be reused in Bayesian networks. The main problem with applying Bayesian networks to survival analysis is their exponential growth in complexity as the number of risk factors increases. It is not uncommon to see complex CPH models with as many as 20 risk factors. Our paper focuses on making large survival analysis models derived from the CPH model tractable in Bayesian networks. We evaluate the effect of two complexity reduction techniques: (1) parent divorcing, and (2) removing less important risk factors based on the accuracy of the resulting models.

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