Cardiovascular
A Multi-state Non-Markov Regression Model to Estimate Progression of Coronary Heart Disease (CHD) Ming Ding* Ming Ding Haiyi Chen Feng-Chang Lin
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, which assumes that current state is independent of past states, and thus are unsuitable to estimate progression of chronic diseases that is largely non-memoryless. In this paper, we propose a new non-Markov regression model that allows past states to affect transition rates of current states. The key innovation is that by conditioning on past disease history, we divide disease states into substates to convert non-Markov to Markov process to estimate transition parameters. Specifically, we apply cause-specific Cox models (CSC) including past states as covariates to obtain transition rates (TR) of substates, as well as transition probability (TP) and state occupational probability (SOP) of substates. The transition parameters of disease states are calculated as weighted average of transition parameters of substates, where the weight is estimated based on distribution of past disease history. The significance of our model is that the division into substates allow to gain new mechanistic insight of chronic disease, and the transition parameters of disease states is highly suitable to describe progression of chronic diseases that exhibit non-Markov properties. We applied our model to describe progression of coronary heart disease (CHD) in the ARIC study, where CHD progression is modeled in five states: healthy, high risk (development of hypertension, hyperlipidemia, or type 2 diabetes), CHD, heart failure, and mortality. We obtained TR, TP, and SOP for each substate transition at each age (Figure). Our method has potential of wide application in chronic disease epidemiology.
