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Calibration of complex models through Bayesian evidence synthesis: a demonstration and tutorial.

Authors
  • Jackson, Christopher H1
  • Jit, Mark2
  • Sharples, Linda D1
  • De Angelis, Daniela1
  • 1 MRC Biostatistics Unit, Cambridge, UK (CHJ, LDS, DD)
  • 2 Health Protection Agency, London, UK (MJ)
Type
Published Article
Journal
Medical decision making : an international journal of the Society for Medical Decision Making
Publication Date
Feb 01, 2015
Volume
35
Issue
2
Pages
148–161
Identifiers
DOI: 10.1177/0272989X13493143
PMID: 23886677
Source
Medline
Keywords
License
Unknown

Abstract

Decision-analytic models must often be informed using data that are only indirectly related to the main model parameters. The authors outline how to implement a Bayesian synthesis of diverse sources of evidence to calibrate the parameters of a complex model. A graphical model is built to represent how observed data are generated from statistical models with unknown parameters and how those parameters are related to quantities of interest for decision making. This forms the basis of an algorithm to estimate a posterior probability distribution, which represents the updated state of evidence for all unknowns given all data and prior beliefs. This process calibrates the quantities of interest against data and, at the same time, propagates all parameter uncertainties to the results used for decision making. To illustrate these methods, the authors demonstrate how a previously developed Markov model for the progression of human papillomavirus (HPV-16) infection was rebuilt in a Bayesian framework. Transition probabilities between states of disease severity are inferred indirectly from cross-sectional observations of prevalence of HPV-16 and HPV-16-related disease by age, cervical cancer incidence, and other published information. Previously, a discrete collection of plausible scenarios was identified but with no further indication of which of these are more plausible. Instead, the authors derive a Bayesian posterior distribution, in which scenarios are implicitly weighted according to how well they are supported by the data. In particular, we emphasize the appropriate choice of prior distributions and checking and comparison of fitted models.

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