Stochastic differential equation for modelling health related quality of life

Abstract

In this work we propose a stochastic differential equation (SDE) for modelling health related quality of life (HRQoL) over a lifespan. HRQoL is assumed to be bounded between 0 and 1, equivalent to death and perfect health, respectively. Drift and diffusion parameters of the SDE are chosen to mimic decreasing HRQoL over life and ensuring epidemiological meaningfulness. The Euler-Maruyama method is used to simulate trajectories of individuals in a population of n = 1000 people. Age of death of an individual is simulated as a stopping time with Weibull distribution conditioning the current value of HRQoL as time-varying covariate. The life expectancy and health adjusted life years are compared to the corresponding values for German women.