Analysis of aggregate surgically induced refractive change, prediction error, and intraocular astigmatism

Purpose: To demonstrate analytical methods for evaluating the results of ke ratorefractive surgical procedures and emphasize the importance of intraocu lar astigmatism. Setting: University of Texas Medical School, Houston, Texas, USA. Methods: A standard data set, provided by an editor of this journal, compri sing the preoperative and postoperative keratometric and refractive measure ments of 100 eyes that had keratorefractive surgery was evaluated by 2 meth ods, vector and sphero-equivalent (SEQ) analysis. The individual and aggreg ate surgically induced refractive changes (SIRCs) and prediction errors wer e determined from the refractive and keratometric measurements using both m ethods and then compared. The refraction vertex distance, keratometric inde x of refraction, and corneal asphericity were used to make the results calc ulated from refractive data directly comparable to those derived from kerat ometric data. Doubled-angle and equivalency plots as well as frequency and cumulative histograms were used to display the data. Standard descriptive s tatistics were used to determine the mean and standard deviation of the agg regate 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 l east 0.25 diopter (D) in most cases (78%). Six percent were corrected withi n +/- 0.24 D, and 16% were overcorrected by at least 0.25 D SEQ. The mean S EQ was -6.68 D +/- 2.49 (SD) before and -0.61 +/- 0.82 D after surgery, ref lecting 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 m m pupil, this corresponded to an estimated improvement in uncorrected visua l acuity (UCVA) from worse than 20/200 to better than 20/25, respectively. The predictability of the treatment decreased as the attempted refractive c orrection increased. The average magnitude of the refractive astigmatism wa s 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 sq uare root of the centroid standard deviation shape factor (rho (1/2)) indic ated an 8% increase in the amount of oblique astigmatism in the population. The prevalence of preoperative keratometric irregular astigmatism in exces s of 0.5 D in this group of patients was 13%. The correlation between kerat ometric and refractive astigmatism was extremely poor before (r(2) = 0.26) and especially after surgery (r(2) = 0.02), demonstrating the presence of i ntraocular astigmatism and the limitation of manual keratometry. The centro id 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 compariso ns within and between data sets. The DEQ allows comparison of refractive an d visual results. The decrease in refractive predictability with higher cor rections is well demonstrated by the SEQ and doubled-angle plots of the SIR C. Doubled-angle plots were particularly useful in interpreting errors of c ylinder treatment amount and errors in alignment. The correlation between r efractive and keratometric astigmatism was poor for preoperative, postopera tive, and SIRC data, indicating the presence of astigmatic elements beyond the corneal surface (ie, intraocular astigmatism). Sources of error in refr active outcome statistics include the use of multiple lens systems in the p horopter, errors in vertex calculations, difficulty in accurately defining the axis of astigmatism, and failure to consider measurement errors when wo rking with keratometric data. The analysis of this particular data set demo nstrates 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.