Flexible transition timing in discrete-time multistate life tables using Markov chains with rewards

Discrete-time multistate life tables are attractive because they are easier to understand and apply in comparison to their continuous-time counterparts. While such models are based on a discrete time grid, it is often useful to calculate derived magnitudes, like state occupation times, under assumptions that posit that transitions take place at other times, such as mid-period. Unfortunately, currently available models allow only a very limited set of choices about transition timing. We propose to utilize Markov chains with rewards as an intuitive and general way of modelling the timing of transitions. Combining existing discrete-time models with the rewards methodology results in an estimation strategy that features easy parameter estimation, flexible transition timing, and little theoretical overhead. We illustrate the usefulness of rewards- based multistate life tables with SHARE data for the estimation of working life expectancy using different retirement transition timings. We also demonstrate that, for the single-state case, the rewards-based multistate life tables match traditional life table methods exactly. We provide code to replicate all results of the paper, as well as R and Stata packages for general use of the method proposed.