Incorporating additional evidence as prior information to resolve non-identifiability in Bayesian disease model calibration

Abstract

Background: Statisticians evaluating the impact of policy interventions such as screening or vaccination will need to make use of mathematical and computational models of disease progression and spread. Calibration is the process of identifying the parameters of these models, with a Bayesian framework providing a natural way in which to do this in a probabilistic fashion. Markov Chain Monte Carlo (MCMC) is one of a number of computational tools that is useful in carrying out this calibration. Objective: In the context of complex models in particular, a key problem that arises is one of non-identifiability. In this setting, one approach which can be used is to consider and ensure that appropriately informative priors are specified on the joint parameter space. We give examples of how this arises and may be addressed in practice. Methods: Using a basic SIS model the calibration process and the associated challenge of non-identifiability is discussed. How this problem arises in the context of a larger model for HPV and cervical cancer is also illustrated. Results: The conditions which allow the problem of non-identifiability to be resolved are demonstrated for the SIS model. For the larger HPV model, how this impacts on the calibration process is also discussed.