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

Abstract

In chronic disease epidemiology, investigation of disease etiology has largely focused on one single endpoint, and progression of chronic disease as a multi-state process is understudied, representing a knowledge gap. Most of existing multi-state regression models require Markov assumption and are unsuitable to estimate progression of chronic diseases that is largely non-memoryless. We propose a new non-Markov framework that allows past states to affect transition rates of current states. The key innovation is that we convert a non-Markov to Markov process by dividing disease states into substates through conditioning on past disease history. Specifically, we apply cause-specific Cox models (CSC) including past states as covariates to obtain transition rates (TR) of substates, which were used to obtain transition probabilities (TP) and state occupational probabilities (SOP) of substates. We applied our model to describe progression of coronary heart disease (CHD) in the ARIC study, where CHD was modeled in healthy, in risk, CHD, heart failure, and mortality states. We presented transition rates, transition probabilities, and state occupational probabilities between states from age 45 to 95 years. In summary, the significance of our framework lies in that transition parameters between disease substates may shed light on new mechanistic insight of chronic disease and may provide more accurate description of non-Markov process than Markov regression models. Our method has potential of wide application in chronic disease epidemiology.