DIVIDING BY ZERO IN MEDICINE, INCLUDING OPHTHALMOLOGY
Quite early in any math course at school you learn that you cannot divide by zero. Why not, you ask incredoulusly? Who decided this? God? Probably; answers and explanations given are many and convincing: It is simply a forbidden or impossible or undefined operation. It is actually so bad that you have to be extra careful when you design a complicated mathematical operation not to include, hiddenly or inadvertently, a division by zero. It could easily happen when you invert a division; e g 0/a is allowed, but a/0 is not. It happened to me once in the dissertation calculations but was discovered in time.
One might think that if a mathematical operation is so frowned upon, it never appears as part of a practical problem, nor is one otherwise tempted to use it. Unfortunately it is the other way round in medicine (including ophthalmology). We are all the time running into situations where it is tempting to divide by zero. Like this: We often want to compare the efficiency of different forms of therapy; we want to see if one is better than another, and we want to be able to say how much better, how many times better. Let us say that a study showed that with old medicine A nobody (n1=0) survived a particularly obnoxious form av flu, while with medicine B everybody (n2=a) survived. Assume that the comparison study was otherwise correctly designed (EBM) and carried through, a comparison between the effects of A and B could easily and temptingly involve an element of division by zero, n2/n1 = a/0. In words, how much better is medicine B than medicine A? Much better, no doubt...but how much? How many times better is a then 0?
Let us move to ophthalmology. We often measure and compare visual acuities; we have learned reasonably acceptably to compare situations with “more lines read”. E g when talking effects of Visudyne we are talking about more or less “lines read” two years after treatment. Or when seeing in fog, no swan to the left (unenhanced image), swan to the rigth (enhanced image)? How much better to you see the “right swan”? Go to http://www.lyyn.com for swans.
How would one express this in figures?
We have a tremendous and well deserved respect for numbers, for figures. Because "When you can measure what you are speaking about, and express it in numbers, you know something about it. But when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind." (Lord Kelvin, Popular Lectures and Addresses, 1889). - As far as I can see, Lord Kelvin was not quite correct. There are comparison situations, as such measurable, in real life, critical situations, which we are unable to describe in numbers. But where we can still make logical, clear, statistically irrefutable statements about them.
I well remember a patient who after successful cataract surgery expressed extreme satisfaction: “...now I see infinitely better than before surgery...”. This is literally as close as one can get to a division by zero. And she was very right of course.....division by “almost zero” results in “almost infinity”.
Which finally brings us to Zero as a concept. Is Zero a number or something else totally? How, why is it so special? Go read this or this for further confusion. There are whole books on the subject too; check with http://www.amazon.com
Olle holm
just don´t do it..