## Pythagoras theorem could improve patient care

Triangles, few of us have ever thought of a relationship between healthcare and triangles. Most of us will remember Pythagoras theorem from our school days, but rarely have a reason to use it in day-to-day life. Well for Doctors that might change, a team of medical researchers has found the 2,500-year-old Pythagoras theorem could be the most effective way to identify the point at which a patient’s health begins to improve.

The team of Doctors set out to find a way to better determine when a patient had “turned the corner” or started to improve. After several false starts, they made the unlikely discovery after looking at data from Receiver Operating Characteristic (ROC) curves.

These curves were initially developed during World War II for the analysis of signals to help operators decide whether a blip on the screen was an enemy target, an allied forces ship, or an aircraft. After the war, during the 1980s, the curves were adopted by epidemiologists to help them decide at what point an individual has recovered from an illness.

## “It all comes down to choosing a point on a curve to determine when recovery has occurred. For many chronic conditions, epidemiologists agree that the correct point to choose is that which is closest to the top-left corner of the plot containing the curve,” Dr Froud, from Warwick Medical School at the University of Warwick, said.

## “As we stopped to think about it, it struck us as obvious that the way to choose this point was by using Pythagoras theorem.”

Pythagoras theorem states that in a right-angled triangle, the sum of the squares of the two right-angled sides is equal to the square of the hypotenuse (i.e the longer diagonal that joins the two right angled sides). This means that one can determine the length of the hypotenuse given the length of the other two sides.

## “We set about exploring the implications of this and how it might change conclusions in research. We conducted several experiments using real trial data and it seems using Pythagoras’ theorem makes a material difference. It helps to identify the point at which a patient has improved with more consistency and accuracy than other methods commonly used,”said Dr Froud.

## “The moral of the story is that before you throw out the old stuff in the attic – just go through it one last time – as there may be something in there that is still relevant and useful,” he added.

Physicists often call math the language of the universe, so it shouldn’t be too surprising that we could use math in this situation. The real surprise, if any, was how simple the equation could be in determining when a patient’s health was improving. This discovery could help reduce the ever increasing costs of healthcare in a time where a record number of people need care. Triangles, who would’ve thought?

**Sources****:**

Froud, R., & Abel, G. (2014). Using ROC Curves to Choose Minimally Important Change Thresholds when Sensitivity and Specificity Are Valued Equally: The Forgotten Lesson of Pythagoras. Theoretical Considerations and an Example Application of Change in Health Status PLoS ONE, 9 (12) DOI: 10.1371/journal.pone.0114468

## But enough about us, what about you?