Bayesian Calibration of a Natural History Model with Application to a Population Model for Colorectal Cancer

Background. Cancer natural history models are essential when evaluating screening/preventative interventions or changes to diagnostic pathways. Natural history models commonly use a state transition structure, but it is often not possible to observe the state transition probabilities required for parameterization. Aim. The work aimed to accurately represent the uncertainty in the parameters of a state transition model for the natural history of colorectal cancer by embedding the problem in the framework of Bayesian inference. Methods. The Metropolis-Hastings algorithm was used to estimate natural history parameters and screening test characteristics by generating multiple sets of parameters from the posterior distribution, which is the probability distribution that is compatible with the observed data. Observed data included colorectal cancer incidence categorized by age and stage, autopsy data on polyp prevalence, and cancer and polyp detection rates from the first round of screening with the fecal occult blood test in England. The approach was implemented using Visual Basic. Results. The results were subsequently examined for convergence using the package CODA in R 2.8.0. Outputs from fitting were samples from the joint posterior distribution of the natural history parameters given the epidemiological data. The parameter sets obtained are shown to have a good fit to all the observed data sets. These parameter sets are used when running probabilistic sensitivity analysis. Conclusion. The advantages of this strategy are that it draws efficiently from a high-dimensional correlated parameter space. The algorithm is simple to code and runs overnight on a standard desktop PC. Using this method, the parameter sets are drawn according to their posterior probability given calibration data, and thus they correctly summarize the residual uncertainty in the parameter space.