Transfer entropy as a tool for inferring causality from observational studies in epidemiology

Abstract

Recently Wieners causality theorem, which states that one variable could be regarded as the cause of another if the ability to predict the future of the second variable is enhanced by implementing information about the preceding values of the first variable, was linked to information theory through the development of a novel metric called transfer entropy. Intuitively, transfer entropy can be conceptualized as a model-free measure of directed information flow from one variable to another. In contrast, directionality of information flow is not reflected in traditional measures of association which are completely symmetric by design. Although information theoretic approaches have been applied before in epidemiology, their value for inferring causality from observational studies is still unknown. Therefore, in the present study we use a set of simulation experiments, reflecting the most classical and widely used epidemiological observational study design, to validate the application of transfer entropy in epidemiological research. Moreover, we illustrate the practical applicability of this information theoretic approach to real-world epidemiological data by demonstrating that transfer entropy is able to extract the correct direction of information flow from longitudinal data concerning two well-known associations, i.e. that between smoking and lung cancer and that between obesity and diabetes risk. In conclusion, our results provide proof-of-concept that the recently developed transfer entropy method could be a welcome addition to the epidemiological armamentarium, especially to dissect those situations in which there is a well-described association between two variables but no clear-cut inclination as to the directionality of the association.