title: Analysis of aggregate surgically induced refractive change, prediction error, and intraocular astigmatism.
abstract: OBJECTIVE
  To demonstrate analytical methods for evaluating the results of keratorefractive surgical procedures and emphasize the importance of intraocular astigmatism.
  
  
  METHODS
  University of Texas Medical School, Houston, Texas, USA.
  
  
  METHODS
  A standard data set, provided by an editor of this journal, comprising the preoperative and postoperative keratometric and refractive measurements of 100 eyes that had keratorefractive surgery was evaluated by 2 methods, vector and spheroequivalent (SEQ) analysis. The individual and aggregate surgically induced refractive changes (SIRCs) and prediction errors were determined from the refractive and keratometric measurements using both methods and then compared. The refraction vertex distance, keratometric index of refraction, and corneal asphericity were used to make the results calculated from refractive data directly comparable to those derived from keratometric data. Doubled-angle and equivalency plots as well as frequency and cumulative histograms were used to display the data. Standard descriptive statistics were used to determine the mean and standard deviation of the aggregate induced astigmatism after converting the polar values (cylinder and axis) to Cartesian (x and y) values.
  
  
  RESULTS
  The preoperative SEQ refractive errors were undercorrected by at least 0.25 diopter (D) in most cases (78%). Six percent were corrected within +/- 0.24 D, and 16% were overcorrected by at least 0.25 D SEQ. The mean SEQ was -6.68 D +/- 2.49 (SD) before and -0.61 +/- 0.82 D after surgery, reflecting a SIRC SEQ of -6.07 +/- 2.40 D. The defocus equivalent (DEQ) was 7.41 +/- 2.53 D before and 0.96 +/- 0.74 D after surgery; for a nominal 3.0 mm pupil, this corresponded to an estimated improvement in uncorrected visual acuity (UCVA) from worse than 20/200 to better than 20/25, respectively. The predictability of the treatment decreased as the attempted refractive correction increased. The average magnitude of the refractive astigmatism was 1.46 +/- 0.61 D before and 0.40 +/- 0.38 D after surgery. The centroid of the refractive astigmatism was +0.96 x 87.9 +/- 0.85 D, rho = 0.43 before and +0.11 x 83.1 +/- 0.37, rho = 0.49 after surgery. The decrease in the square root of the centroid standard deviation shape factor (rho1/2) indicated an 8% increase in the amount of oblique astigmatism in the population. The prevalence of preoperative keratometric irregular astigmatism in excess of 0.5 D in this group of patients was 13%. The correlation between keratometric and refractive astigmatism was extremely poor before (r2 = 0.26) and especially after surgery (r2 = 0.02), demonstrating the presence of intraocular astigmatism and the limitations of manual keratometry. The centroid of intraocular astigmatism at the corneal plane was +0.48 x 178 +/- 0.49 D, rho = 0.59, and was compensatory.
  
  
  CONCLUSIONS
  The 2 analytical methods are complimentary and permit thorough and quantitative evaluation of SIRCs and allow valid statistical comparisons within and between data sets. The DEQ allows comparison of refractive and visual results. The decrease in refractive predictability with higher corrections is well demonstrated by the SEQ and doubled-angle plots of the SIRC. Doubled-angle plots were particularly useful in interpreting errors of cylinder treatment amount and errors in alignment. The correlation between refractive and keratometric astigmatism was poor for preoperative, postoperative, and SIRC data, indicating the presence of astigmatic elements beyond the corneal surface (ie, intraocular astigmatism). Sources of error in refractive outcome statistics include the use of multiple lens systems in the phoropter, errors in vertex calculations, difficulty in accurately defining the axis of astigmatism, and failure to consider measurement errors when working with keratometric data. The analysis of this particular data set demonstrates the significant clinical benefits of refractive surgery: an 8-fold increase in UCVA, an 11-fold decrease in SEQ refractive error, as well as a 9-fold and nearly a 2 1/2-fold decrease in the magnitude and distribution of astigmatism, respectively.
authors.affiliation: University of Texas Medical School, Houston, Texas, USA. holladay@DocHolladay.com
authors.forename: J T
authors.initials: JT
authors.lastname: Holladay
authors.forename: J R
authors.initials: JR
authors.lastname: Moran
authors.forename: G M
authors.initials: GM
authors.lastname: Kezirian
mesh_terms: D000328:Adult; D001251:Astigmatism / Q000175:diagnosis* / Q000209:etiology; D002387:Cataract Extraction / Q000009:adverse effects*; D003315:Cornea / Q000473:pathology*; D003941:Diagnostic Techniques, Ophthalmological; D005260:Female; D006801:Humans; D008297:Male; D008433:Mathematics; D008962:Models, Theoretical; D011237:Predictive Value of Tests; D012029:Refraction, Ocular; D014792:Visual Acuity