How much information can metabolic syndrome provide? An application of information theory

The purpose of this article is to show, using principles from Shannon's information theory, that it is possible to estimate the amount of information loss that occurs, in relative terms, when multiple continuous biological traits are dichotomized and aggregated, as is the case with many diagnostic definitions. We use metabolic syndrome as a case in point. It is our position that this type of information loss can impede the progress of medical research. This argument will first be made on theoretical grounds and then be supplemented using data from a clinical trial involving 252 women enrolled in cardiac rehabilitation. After laying out relevant principles, we conduct analyses to show how such information loss occurs during data transformation. Our analyses demonstrate that transforming the multiple traits that comprise metabolic syndrome into a single binary indicator discarded over 98% of the potential information contained in the original measurements. We go on to illustrate how such information loss impedes the establishment of meaningful statistical relationships with an indicator of cardiovascular health, time on an exercise tolerance test.