Bayesian hidden Markov model with time-to-event emissions for risk-prediction in cancer screening

Biphasic testing protocols with a sub-100% sensitive primary test to detect asymptomatic disease are widely used in decision-making and testing scenarios. In this setting, a positive primary test cannot confirm the presence of the disease but triggers a confirmatory sequence that accelerates detection. In our cancer screening scenario, these latent states may be detected at some later stage, without any primary testing. We propose a model using eventual detection times of cancer to predict the prevalence of the latent state of interest. We begin by describing a model for predicting latent state prevalence in the initial screening round. The model takes into account the accelerated detection due to screening. Then, we generalize the approach into a sequence of screening rounds using a discrete-time hidden Markov model, where the emission is multivariate with time-to-event component. The model is fitted within the Bayesian framework and provides a foundation for developing risk-based targeted protocols for decision-makers. We assess estimation performance through a simulation study using two different estimation algorithms. Finally, the model is fitted to the data from a Finnish colorectal cancer screening pilot study to generate metrics for improving screening programmes.