Lexis diagram and illness-death model: simulating populations in chronic disease epidemiology

Chronic diseases impose a tremendous global health problem of the 21st century. Epidemiological and public health models help to gain insight into the distribution and burden of chronic diseases. Moreover, the models may help to plan appropriate interventions against risk factors. To provide accurate results, models often need to take into account three different time-scales: calendar time, age, and duration since the onset of the disease. Incidence and mortality often change with age and calendar time. In many diseases such as, for example, diabetes and dementia, the mortality of the diseased persons additionally depends on the duration of the disease. The aim of this work is to describe an algorithm and a flexible software framework for the simulation of populations moving in an illness-death model that describes the epidemiology of a chronic disease in the face of the different times-scales. We set up a discrete event simulation in continuous time involving competing risks using the freely available statistical software R. Relevant events are birth, the onset (or diagnosis) of the disease and death with or without the disease. The Lexis diagram keeps track of the different time-scales. Input data are birth rates, incidence and mortality rates, which can be given as numerical values on a grid. The algorithm manages the complex interplay between the rates and the different time-scales. As a result, for each subject in the simulated population, the algorithm provides the calendar time of birth, the age of onset of the disease (if the subject contracts the disease) and the age at death. By this means, the impact of interventions may be estimated and compared.