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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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9

Ordering of Hierarchies in Hierarchical Models: Bone Mineral Density Estimation

Cathal D. Walsh1 and Kerrie L. Mengersen2

1Trinity College Dublin, Ireland

2Queensland University of Technology, Brisbane, Australia

9.1 Introduction

In combining evidence from multiple sources, the use of hierarchical Bayesian models has become commonplace. There has been a strong growth in the use of such models in meta-analysis and in mixed treatment comparisons.

Where there are study-level properties that change (e.g. the exact outcome measure used or the patient type examined), it is natural to take account of this in the nesting of the hierarchies used in the analysis.

In this chapter we examine the impact that the ordering of hierarchies within such analyses has. In particular the overall conclusions that are drawn depend on the nesting of levels within the analysis, thus emphasizing the importance of careful consideration of model structure when fitting models in this framework.

9.2 Case Study

9.2.1 Measurement of Bone Mineral Density

Fractures are a major contributor to failing health in an ageing population. When an older person fractures a bone it causes an immediate reduction in mobility and this in turn has knock-on effects on their ability to maintain social interactions, to care for themselves and to carry out normal activities of daily living. One major risk factor for fractures is a reduction in bone mineral density (BMD). This is a measure of the quality of the bone, and it is recognized ...

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