A discrete-time split-state framework for multi-state modeling with application to describing the course of heart disease.

In chronic disease epidemiology, the investigation of disease etiology has largely focused on an endpoint, while the course of chronic disease is understudied, representing a knowledge gap. Multi-state models can be used to describe the course of chronic disease, such as Markov models which assume that the future state depends only on the present state, and semi-Markov models which allow transition rates to depend on the duration in the current state. However, these models are unsuitable for chronic diseases that are largely non-memoryless. We propose a Discrete-Time Split-State Framework that generates a process of substates by conditioning on past disease history and estimates discrete-time transition rates between substates as a function of duration in a (sub)state. Specifically, as the substates are created by conditioning on past history, they satisfy the Markov assumption, regardless of whether the original disease process is Markovian; and the transition rates are approximated by competing risks in a short time interval estimated from cause-specific Cox models. In the simulation study, we simulated a Markov process with an exponential distribution, a semi-Markov process with a Weibull distribution, and a non-Markov process with an exponential distribution. The coverage rate of transition rates estimated using our framework was 94% for the Markov process and 93% for the non-Markov process. However, the estimated transition rates were under coverage (72%) for the semi-Markov process, which is likely due to the approximation of transition rates in discrete time. In the application, we applied the framework to describe the course of heart disease in a large cohort study. In summary, the framework we proposed can be applied to both Markov and non-Markov processes and has potential to be applied to semi-Markov processes. For future research, as substates created using our framework track past disease history, the transition rates between substates have the potential to be used to derive summary estimates that characterize the disease course.