Precision medicine and the cursed dimensions

Abstract

Our intuition regarding “average” is rooted in one-dimensional thinking, such as the distribution of height across a population. This intuition breaks down in higher dimensions when multiple measurements are combined: fewer individuals are close to average for many measurements simultaneously than for any single measurement alone. This phenomenon is known as the curse of dimensionality. In medicine, diagnostic sophistication generally increases through the addition of more predictive factors. Disease classes themselves become more dissimilar as a result, increasing the difficulty of incorporating (i.e., averaging) multiple patients into a single class for guiding treatment of new patients. Failure to consider the curse of dimensionality will ultimately lead to inherent limits on the degree to which precision medicine can extend the advances of evidence-based medicine for selecting suitable treatments. One strategy to compensate for the curse of dimensionality involves incorporating predictive observation models into the patient workup.