Material & Methods

A trend line is, in statistics, a linear regression this is to say an approach to modeling the relationship between two variables X&Y. In fact we selected to use a second order polynomial regression because it fits more to illustrate the effects of a treatment according to the pre treatment vision or the evolution of the improvement according to the follow up than a strict linear regression or a order 3 polynomial regression (we cannot imagine a vision going up and then and then up again after a single treatment.I will try to explain you why a polynomial regression presentation is more exact in our study than a histogram presentation.

If you consider this population A of 80 cases, with the pre treatment visual acuity here and the post treatment here, this is to say if you consider the improvement or loss according to the pre treatment vision, we can see that there is an homogenous distribution of results which are mostly positive in the upper zone of this iso-acuity line.

The representative histogram will be negative and will not represent the general trend. The characteristic of the trend line is that, even if it takes into consideration all the cases including the exotic ones, it also considers the entire number of cases, so that the aberrant results effect will be diluted. But, of course, you can tell me «this is absurd to analyze 80 cases with 15 columns, you should regroup the columns!» But then how to regroup them. If we decide to regroup 3 by 3, the second column regrouping 1.4 , 1.3 and 1.2 will not fit as well. So we can decide to regroup 4 by 4 and then we begin to trick according to what we would like to appear. Regression line is more exact and impossible to forge.

Here, the interrupted black line represents the gain obtained whatever the treatment for the 2159 studied cases according to the pre treatment vision. I do not understand how people can still present the percentage of improvement superior to 3 lines without considering the initial vision. You easily understand that it is easier to obtain 4 lines improvement when the pretreatment vision is count finger than when it is 20/40; this would lead the patient to see more than 20/20. The true evaluation of results should rely on classification of results according to pre treatment VA.