A hidden Markov model for disease trend analysis with joinpoints

Abstract The joinpoint model assumes piece-wise linear curves joined at multiple unknown joinpoints where the slope changes and has been widely used for disease surveillance. There are 2 analytical challenges that cannot be addressed with standard joinpoint methods. First, computation becomes infeasible as the number of potential joinpoints become large. Second, assessing the uncertainty that a joinpoint occurs at a particular time or window of time. We propose a hidden Markov model (HMM) that provides a computationally feasible approach to deal with these challenges. We show that it is natural to formulate the joinpoint model by modelling successive differences in observations as an HMM with the Markov chain being specified as a birth-process where each state change reflects the occurrence of a subsequent joinpoint. An extension of the forward–backward algorithm, developed for maximum-likelihood estimation of HMMs, easily accommodates long disease sequences with a large number of joinpoints. Further, we show how functions of the posterior distribution of state occupancy can be used to access joinpoint uncertainty. We show simulations with various settings and an application study of COVID-19 incidence data.