Related Experiment Video
Updated: Dec 12, 2025
Comparison of Agreement and Accuracy using Binocular Wavefront Optometer with Autorefractor and Phoropter
Published on: September 16, 2025
Review and recommendations for univariate statistical analysis of spherical equivalent prediction error for IOL power
Jack T Holladay1, Rand R Wilcox, Douglas D Koch
1From the Department of Ophthalmology, Baylor College of Medicine (Holladay, Koch, Wang), Houston, Texas, and Department of Psychology, University of Southern California, Los Angeles (Wilcox), Los Angeles, California, USA.
Purpose:
To provide a reference for study design comparing intraocular lens (IOL) power calculation formulas, to show that the standard deviation (SD) of the prediction error (PE) is the single most accurate measure of outcomes, and to provide the most recent statistical methods to determine P values for type 1 errors.
Setting:
Baylor College of Medicine, Houston, Texas, and University of Southern California, Los Angeles, California, USA.
Design:
Retrospective consecutive case series.
Methods:
Two datasets comprised of 5200 and 13 301 single eyes were used. The SDs of the PEs for 11 IOL power calculation formulas were calculated for each dataset. The probability density functions of signed and absolute PE were determined.
Results:
None of the probability distributions for any formula in either dataset was normal (Gaussian). All the original signed PE distributions were not normal, but symmetric and leptokurtotic (heavy tailed) and had higher peaks than a normal distribution. The absolute distributions were asymmetric and skewed to the right. The heteroscedastic method was much better at controlling the probability of a type I error than older methods.
Conclusions:
(1) The criteria for patient and data inclusion were outlined; (2) the appropriate sample size was recommended; (3) the requirement that the formulas be optimized to bring the mean error to zero was reinforced; (4) why the SD is the single best parameter to characterize the performance of an IOL power calculation formula was demonstrated; and (5) and using the heteroscedastic statistical method was the preferred method of analysis was shown.
