Bayesian calibration of a natural history model with application to a population model for colorectal cancer

Abstract:
Background. Cancer natural history models are essential whenevaluating screening/preventative interventions or changes todiagnostic pathways. Natural history models commonly use a statetransition structure, but it is often not possible to observe thestate transition probabilities required for parameterization. Aim. Thework aimed to accurately represent the uncertainty in the parametersof a state transition model for the natural history of colorectalcancer by embedding the problem in the framework of Bayesianinference.

Methods. The Metropolis-Hastings algorithm was used to estimatenatural history parameters and screening test characteristics bygenerating multiple sets of parameters from the posteriordistribution, which is the probability distribution that is compatiblewith the observed data. Observed data included colorectal cancerincidence categorized by age and stage, autopsy data on polypprevalence, and cancer and polyp detection rates from the first roundof screening with the fecal occult blood test in England. The approachwas implemented using Visual Basic.

Results. The results were subsequently examined for convergence usingthe package CODA in R 2.8.0. Outputs from fitting were samples fromthe joint posterior distribution of the natural history parametersgiven the epidemiological data. The parameter sets obtained are shownto have a good fit to all the observed data sets. These parameter setsare used when running probabilistic sensitivity analysis.

Conclusion. The advantages of this strategy are that it drawsefficiently from a high-dimensional correlated parameter space. Thealgorithm is simple to code and runs overnight on a standard desktopPC. Using this method, the parameter sets are drawn according to theirposterior probability given calibration data, and thus they correctlysummarize the residual uncertainty in the parameter space.