Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care

We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states: the autonomous state, three dependent states of light, moderate and severe dependence levels and the death state. For a general approach, we allow for non null intensities for all the returns from higher dependence levels to all lesser dependencies in the multi-state model. Using data from the 2015 Portuguese National Network of Continuous Care database, as the main research contribution of this paper, we propose a method to calibrate transition intensities with the one step transition probabilities estimated from data. This allows us to use non-homogeneous continuous time Markov chains for modeling Long-Term Care. We solve numerically the Kolmogorov forward differential equations in order to obtain continuous time transition probabilities. We assess the quality of the calibration using the Portuguese life expectancies. Based on reasonable monthly costs for each dependence state we compute, by Monte Carlo simulation, trajectories of the Markov chain process and derive relevant information for model validation and premium calculation.

Automated summary

A non-homogeneous continuous time Markov chain model for Long-Term Care with five states, calibrated transition intensities based on one step transition probabilities estimated from data, was proposed using data from the 2015 Portuguese National Network of Continuous Care database. Solving numerically Kolmogorov forward differential equations allowed for obtaining continuous time transition probabilities, with assessment of calibration quality using Portuguese life expectancies. Monte Carlo simulation was then used to compute trajectories of the Markov chain process based on reasonable monthly costs for each dependence state, deriving relevant information for model validation and premium calculation.