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Case Studies in Bayesian Statistical Modelling and Analysis by Anthony N. Pettitt, Kerrie L. Mengersen, Clair L. Alston

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10

Bayesian Weibull Survival Model for Gene Expression Data

Sri Astuti Thamrin1, 2, James M. McGree1 and Kerrie L. Mengersen1

1Queensland University of Technology, Brisbane, Australia

2Hasanuddin University, Indonesia

10.1 Introduction

In many fields of applied studies, there has been increasing interest in developing and implementing Bayesian statistical methods for modelling and data analysis. In medical studies, one problem of current interest is the analysis of survival times of patients, with the main aim of modelling the distribution of failure times and the relationship with variables of interest.

Gene expression data can be used to explain some variability in patient survival times. Making the best use of current DNA microarray technology in biomedical research allows us to study patterns of gene expression in given cell types, at given times, and under given set of conditions (Segal 2006). Estimation of patient survival times can be based on a number of statistical models. For example, a straightforward approach is a proportional hazards (PH) regression model (Nguyen and Rocke 2002). This model can be used to study the relationship between the time to event and a set of covariates (gene expressions) in the presence of censoring (Park and Kohane 2002).

In a microarray setting, there may be other information available about the regression parameters that represent the gene expressions. The traditional (frequentist) PH regression model uses present data as a basis to estimate ...

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