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Bayes Linear Bayes Networks with an Application to Prognostic Indices

Lookup NU author(s): Wael Al-Taie, Dr Malcolm Farrow

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

Abstract

© 2023 International Society for Bayesian Analysis. Bayes linear kinematics and Bayes linear Bayes graphical models provide an extension of Bayes linear methods so that full conditional updates may be combined with Bayes linear belief adjustment. The use of Bayes linear kinematics eliminates the problem of non-commutativity which was observed in earlier work involving moment-based belief updates. In this paper we describe this approach and investigate its application to the rapid computation of prognostic index values in survival when a patient’s values may only be available for a subset of covariates. We consider the use of covariates of various kinds and introduce the use of non-conjugate marginal updates. We apply the technique to an example concerning patients with non-Hodgkin’s lymphoma, in which we treat the linear predictor of the lifetime distribution as a latent variable and use its expectation, given whatever covariates are available, as a prognostic index.

Publication metadata

Author(s): Al-Taie WAJ, Farrow M

Publication type: Article

Publication status: Published

Journal: Bayesian Analysis

Year: 2023

Volume: 18

Issue: 2

Pages: 437-463

Print publication date: 01/06/2023

Online publication date: 02/05/2023

Acceptance date: 02/04/2018

Date deposited: 11/05/2023

ISSN (print): 1936-0975

ISSN (electronic): 1931-6690

Publisher: International Society for Bayesian Analysis

URL: https://doi.org/10.1214/22-BA1314

DOI: 10.1214/22-BA1314

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