Statistical analysis when dealing with astigmatism: assessment of different spherocylindrical notations.

Ophthalmic epidemiological studies frequently deal with ocular refractive errors, which are commonly expressed in the form sphere/cylinder x axis. However, this representation has been shown not to be the most suitable one for performing statistical analysis. Although alternative analytical and graphic methods to represent this kind of data have been developed, these formalisms have often gone unnoticed by researchers, despite their usefulness and versatility. Besides, there has been no discussion of how each of them fits in with a particular type of study. In this paper, several mathematical representations of dioptric power are revisited in a comprehensive way. The aim is to encourage researchers in ophthalmology and optometry to use these formalisms in their epidemiological studies, thus profiting from their exactitude and simplicity. Consequently, the emphasis is not on complicated mathematical derivations but on how to use these representations. Their potential and suitability in different applications is analyzed in detail. In addition, some examples are presented to illustrate the mathematical methods considered.