A Multi-state Non-Markov Framework to Estimate Progression of Chronic Disease

In chronic disease epidemiology, the investigation of disease etiology has largely focused on one endpoint, and the progression of chronic disease as a multi-state process is understudied, representing a knowledge gap. Most existing multi-state regression models require Markov assumption and are unsuitable to describe the course of chronic disease progression that is largely non-memoryless. We propose a new non-Markov framework that allows past states to affect the transition rates of current states, and the key innovation is the conversion of a non-Markov to Markov process by conditioning on past disease history to divide disease states into substates. Specifically, we apply cause-specific Cox models, including past states as covariates, to obtain transition rates of substates, which were used to estimate transition probabilities using the discrete-time Aalen-Johansen estimator. In simulation study, the non-Markov model generated higher coverage rates of transition rates compared to Markov models, particularly for non-Markov process (By applying non-Markov and Markov models, coverage rates were 91% and 88% for Markov process with exponential distribution, 52% and 43% for Markov process with Weibull distribution, 92% and 49% for non-Markov process with exponential distribution, and 59% and 23% for non-Markov process with Weibull distribution). We applied our model to describe the course of coronary heart disease (CHD) progression, where CHD was modeled in healthy, at-risk, CHD, heart failure, and mortality states. In summary, the significance of our framework lies in the fact that transition parameters between disease sub-states may provide a more accurate description of disease course than Markov regression models and shed light on new mechanistic insight into chronic disease. Our method has the potential for wide application in chronic disease epidemiology.