In the last post we described with graphics how the patients were before surgery and how they were after it, the simulated data can be found here. In this one we will relate those results to each other. The first graphic can be seen quite a lot in publications, here is the attempted vs achieved spherical equivalent (SE):


pre post1


The black thick diagonal is the attempted = achieved SE and ideally all points should be on it. The blue diagonals are the attempted = achieved +/- 1 D, the points falling in the light blue region achieve a SE within +/- 1 D of the attempted SE. The interesting thing about this graphic is that is independent of the target refraction, it doesn´t matter if we want to end up emmetrope or with -1 D for monovision for example, the target refraction has already been taking into account in the attempted SE.

The second graphic shows the SE preop vs the SE postop:


pre post2


I actually prefer this graphic to the first one, probably because it´s easier to see deviations from a horizontal line than from a diagonal. On the other hand, here ideally the points would be on the thicker horizontal bar crossing the 0 but only if the target refraction is emmetropia, the vertical thick line is for a SE preop of 0 D. To solve the target refraction problem we could separate the points by target. Since the data I am using doesn´t have a target refraction I will assume all men have a target refraction of -0.75 D and all women a target refraction of 0, here is the result:


 pre post3


Now we have a panel per target refraction. From here on we can focus on different aspects and make more subdivisions depending on what we are interested to see and add more elements to the graphic, here is an example:


pre post4



In this graphic we have two panels one for patients under 40 years old and other for patients above 40, within each panel the points are coloured by sex. The black line surrounded by a gray shaded area is the linear regression for all the points in that panel, the shaded area is the 95 % confidence interval for that regression line.

Up to know we haven´t taken the astigmatism into account and we still don´t know what is happening with it, obviously it´s not the same a +0.50 sph. -1.00 cyl. at 180º and a +1.00 sph. -2.00 cyl. at 90º although both SE are 0. In the next post I will make graphics that will show more about the cilinder and the axis.


I am going to start this series of posts about graphics for showing results of refractive surgery with basic descriptive graphics. The data used for all the graphics of the series consists of 100 simulated observations, you can find the table here, it is very basic data, just id, sex, age, eye (right or left) and subjective refraction pre and post-operative. Some graphics will be more suitable for the public while others can be used just for yourself to get a better insight of what is going on.

You might just want to know that the mean age of the patients is 39.96 years with a standard deviation (sd) of 12.48 and a mean spherical equivalent (SE) of -3.13 D with a sd of 3.39 and be happy with it, or you might want to know more, to begin with, their distributions:



The age distribution is quite uniform, the SE distribution too but there is a peak between -6 D and -7 D, that SE doubles the amount of patients approximatly than lower SE and myopes higher that -7 are very few. We can have a look at the distribution for people older or younger than 40:




It seems above 40 patients are less myope in our data. Another way to see this is with a boxplot:




Here the white dot is the mean and the vertical line next to it is the median. We can also see the distributions including the sex of the patient:




The bars are stacked, that means that a whole vertical bar shows the total patients for that SE interval and the color within the bar shows if it is for males or females, in cases where there are both colours it shows the amount of each one, for example above 40 years old for SE between -6 and -7 there are 8 patients, 2 females and 6 males.

We can do the same for the postoperative SE and we will get this:




The range now goes between -1.50 D and +1.50 D and is much more normally distributed around -0.25. We will now look at the cumulative percentage of patiens within a given range:

description6This graphic tells us that 35% of the patients ended with a SE between +0.25 D and -0.25 D, that 58% are within +0.50 D and -0.50 D and so on.

All this descriptive graphics can be done by any factor you are interested in, like surgery type, operation room, discharged patients at 3 months (yes or no?) and also instead of SE you could see the cumulative percentages within a given visus.

Now we know what we have before and after the surgery, in the next post we will relate one to the other in different ways.


In the Functional Outcome and Patient Satisfaction after Laser In Situ Keratomileusis for Correction of Myopia and Myopic Astigmatism paper there are six tables and no graphics. I am going to make two graphics from table 3.

The first one is the distribution of spherical equivalents (SE) preoperative and postoperative:




The second one shows the same results for the cumulative percentages:





The X axis tick marks at 0, -3, -6 and -8 D are not my favourite but is what it can be done with the given data.

With the next article I am going to start a series of posts to show results of refractive surgery from several perspectives and different degrees of detail. I will also simulate the data and show it in a table.