Use of the Metropolis-Hastings Algorithm in the Calibration of a Patient Level Simulation of Prostate Cancer Screening

Designing cancer screening programmes requires an understanding of epidemiology, disease natural history and screening test characteristics. Many of these aspects of the decision problem are unobservable and data can only tell us about their joint uncertainty. A Metropolis-Hastings algorithm was used to calibrate a patient level simulation model of the natural history of prostate cancer to national cancer registry and international trial data. This method correctly represents the joint uncertainty amongst the model parameters by drawing efficiently from a high dimensional correlated parameter space. The calibration approach estimates the probability of developing prostate cancer, the rate of disease progression and sensitivity of the screening test. This is then used to estimate the impact of prostate cancer screening in the UK. This case study demonstrates that the Metropolis-Hastings approach to calibration can be used to appropriately characterise the uncertainty alongside computationally expensive simulation models.