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