Transition Intensities for Critical Illness: A Study on Canadian Health Data

Abstract

Multiple state model is a mathematical model which is characterised by two important elements, transition intensity and transition probability. Critical illness has increased rapidly which is alarmed by the healthcare experts, and becoming an important concern in society. In this paper, by using the Canadian health data, we provide an estimation of transition intensities from the healthy state to the critical illness state with the application of prevalence rate. We provide a discrete calculation of transition intensities with some mathematical formula discussed by some previous studies. Next, we assume that the transition intensities of critical illnesses and death due to other causes are modelled by Gompertz and Makeham mortality models. We also compare and estimate the transition intensities of critical illnesses and dead due to other causes between these two models using a model selection method. We observe the sensitivity of the Gompertz and Makeham models with the different values of extra mortality . Lastly, we obtain and present the numerical results of the transition intensities of healthy lives to critical illness with the Canadian health data.