I read with interest the paper by Carifi and associates regarding formula accuracy in small eyes. I was pleased that the Hoffer Q performed well in these eyes, as expected. Unfortunately there are several crucial errors in the design and reporting of their study.

The first error is not zeroing out the mean error (ME) of each formula by changing the lens factor individually for each formula until the ME reaches zero. This eliminates the bias of the lens factor chosen and is the only proper way to do this so you are comparing apples with apples. This can easily be done using the Excel software’s Data/What If Analysis/Goal Seek function. It is then appropriate to compare the median absolute error (MedAE) of each formula.

The second error is basing conclusions on the comparison of the mean absolute error (MAE.) It is inappropriate to report this, since the absolute errors are not a Gaussian distribution. Only the MedAEs should be compared. This can be confirmed by any statistician. There are methods that allow legitimate statistical comparison of MAE, such as “bootstrapping,” but no such method is mentioned in this article. In the past, many authors, including myself, have made this mistake. The authors do report MedAEs but completely ignore them in their conclusions, discussion, and recommendations. Comparing MEs says nothing about formula accuracy but only about the lens factors used by the authors—that is, if different from zero, they used a lens factor too high or too low for that patient group.

Unfortunately, the above 2 errors compound to make the study’s conclusions invalid. If you carefully look at the MedAE reported in their Table 3, it can be seen that their conclusions are not valid. The authors state “…the Holladay 2 formula showed the most accurate ME and MAE…” but fail to mention that the MedAE of the Hoffer Q (0.76) was the smallest and was lower than the Holladay 2 (0.8), Holladay 1 (0.89), Haigis (1.01), and SRK/T (1.2.) Since the MEs should have been zeroed out before analysis, one cannot even trust this comparison, since it is dependent upon the lens factors the authors used. Also, it is stated that “…the Holladay 2 performing the best in terms of either ME…,MAE…, or percentage of eyes within 1 diopter of target…,” totally ignoring the appropriate comparison of MedAE. The ME being the lowest merely means the lens factor chosen for the Holladay 2 was more accurate than the others for this group of eyes.

In their final recommendation, the authors state “…a practical suggestion could be to calculate the required IOL power with the Hoffer Q, Haigis, and Holladay 2 formulas and choose the most sensible option.” They do not suggest what parameters would lead one to the option being “ sensible .” The most sensible recommendation would be to follow the suggestions of the huge study that proved statistically which formulas perform best in which eyes (Ref 19,) first recommended by this author in 1993.