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Back calculation of prediction error compared with controlled trial prediction error of Goggin nomogram for toric intraocular lens cylinders
LETTERS
We have further examined the data collected for our study and compared surgical and postoperative complications for patients with and without DR after either laser-assisted cataract surgery or conventional phacoemulsification. The analysis yielded the following results: Surgical complications during laser-assisted cataract surgery occurred in 8.6% of cases with DR and in 2.8% of cases without DR. Surgical complications after conventional phacoemulsification cataract surgery occurred in 1.6% of cases and 1.5% of cases, respectively. Surgical complications in the European Registry of Quality Outcomes for Cataract and Refractive Surgery (EUREQUO) database include torn posterior capsule, vitreous loss, iris damage, dropped nucleus, and “other” (including anterior capsule tears). Postoperative complications after laser-assisted cataract surgery occurred in 2.9% of cases with DR and in 3.4% of cases without DR. Postoperative complications after conventional phacoemulsification cataract surgery occurred in 10.4% of cases and in 2.1% of cases, respectively. Postoperative complications in the EUREQUO database include posterior capsule opacification, uncontrolled intraocular pressure, intraocular lens explantation, and “other” (including postoperative CME). In other words, in our study, patients with DR had more surgical complications if they had laser-assisted cataract surgery but more postoperative complications if they had conventional phacoemulsification. These results motivate further studies in patients with diabetes having cataract surgery.dSonia Manning, MD, FRCSI(Ophth), Ype Henry, MD, FEBO, Paul Rosen, FRCS, FRCOphth, Ulf Stenevi, MD, PhD, Mats Lundstr€om, MD, PhD
REFERENCES
1. Chee S-P, Yang Y, Ti S-E. Clinical outcomes in the first two years of femtosecond laser–assisted cataract surgery. Am J Ophthalmol 2015; 159: 714–719 2. Schultz T, Joachim SC, Kuehn M, Dick HB. Changes in prostaglandin levels in patients undergoing femtosecond laser-assisted cataract surgery. J Refract Surg 2013; 29:742–747 3. Conrad-Hengerer I, Hengerer FH, Al Juburi M, Schultz T, Dick HB. Femtosecond laser-induced macular changes and anterior segment inflammation in cataract surgery. J Refract Surg 2014; 30:222–226
Back calculation of prediction error compared with controlled trial prediction error of Goggin nomogram for toric intraocular lens cylinders Ferreira et al.1 examined the prediction error of refractive astigmatism outcomes with toric intraocular lens (IOL) calculation using a number of calculation methods. In common with many publications on this subject, they used an historic calculation method. They examined the refractive outcomes in a group of eyes in which the toric IOL cylinder power implanted was calculated by 1 method and, using the actual refractive outcome recorded postoperatively, they asked the question whether other methods would have
863
predicted this outcome more accurately. This is a common method of assessing toric IOL cylinder calculation in the current literature and has some validity. However, it assumes that the postoperative refraction and the various methods of corneal power measurement would remain the same from test to test, a patently erroneous assumption.2 The comparison of the effectiveness of medical techniques has always rested on randomized controlled trials or, at least, on nonrandomized controlled trials, to avoid such confounding variables. Using their method, the authors examined a toric IOL cylinder power calculation technique I and my coauthors introduced.3 It is not stated clearly in their Method section but is implied in their Discussion section that they used my method correctly in terms of IOL cylinder power. It appears they applied the corrections I suggest in eyes requiring IOL cylinder powers of 2.0 diopters (D) or less. I have presented evidence that errors based on anterior corneal “rule” do not occur to any significant degree in eyes requiring correction above this value. However, throughout their article, they refer to use of the “Goggin coefficient” (implying 1 coefficient), whereas I describe 2 coefficients of adjustment, 1 for with-the-rule anterior corneal astigmatism and 1 for against-the-rule.3 I would be grateful if they could clarify their use of these published values. Using their back-calculation technique and by whatever way they have used my adjustment for the probable effect of posterior corneal astigmatism, they report mean absolute prediction errors of 0.65 D G 0.38 (SD) and 0.63 G 0.36 D and prediction error centroids of 0.42 @ 166 and 0.38 @ 170 when using my technique. By contrast, we have reported, in a controlled trial of my method of calculation and actual surgical implantation, a median absolute error of 0.23 D (95% confidence interval [CI], 0.13-0.35) (decreased from a median of 0.45 D [95% CI, 0.33-0.58] in control eyes; P Z .004) and a centroid of 0.15 D at 146 (the centroid for control eyes was 0.49 D at 175 degrees).4 These are lower for Goggin nomogram–adjusted values than any produced by Ferreira et al.1 using their back-calculation methods. To my knowledge, ours is the only publication of actual surgical use of any method of toric IOL calculation that includes the posterior corneal astigmatism effect and the only publication to include a control group. Finally, I would like to point out that my method will not greatly improve the prediction error of what the authors term the “original Alcon calculator” (as they found). My method simply allows for the likely effect of posterior corneal astigmatism. The original Alcon calculator contained other errors that I and my coauthors pointed out in 20115 that far exceed the error induced by the failure to include posterior corneal astigmatism. That calculator has now largely been superseded.5 Any calculator similarly affected by other sources of error will not be ameliorated by the Goggin nomogram. Michael Goggin, FRCSI(Ophth), FRCOphth, FRANZCO, MS Adelaide, South Australia Volume 43 Issue 6 June 2017
864
LETTERS
REFERENCES
1. Ferreira TB, Ribeiro P, Ribeiro FJ, O’Neill JG. Comparison of astigmatic prediction errors associated with new calculation methods for toric intraocular lenses. J Cataract Refract Surg 2017; 43:340–347 2. Goggin M, Patel I, Billing K, Esterman A. Variation in surgically induced astigmatism estimation due to test-to-test variations in keratometry. J Cataract Refract Surg 2010; 36:1792–1793 3. Goggin M, Zamora-Alejo K, Esterman A, van Zyl L. Adjustment of anterior corneal astigmatism values to incorporate the likely effect of posterior corneal curvature for toric intraocular lens calculation. J Refract Surg 2015; 31:98–102 4. Goggin M, van Zyl L, Caputo S, Esterman A. Outcome of adjustment for posterior corneal curvature in toric intraocular lens calculation and selection. J Cataract Refract Surg 2016; 42:1441–1448. Available at: http://www. jcrsjournal.org/article/S0886-3350(16)30397-2/pdf. Accessed May 10, 2017 5. Goggin M, Moore S, Esterman A. Outcome of toric intraocular lens implantation after adjusting for anterior chamber depth and intraocular lens sphere equivalent power effects. Arch Ophthalmol 2011; 129:998–1003. Correction, 1494. Available at: http://jamanetwork.com/journals/jamaophthalmology/ fullarticle/1106787. Correction Available at: http://jamanetwork.com/journals/ jamaophthalmology/fullarticle/1106484. Accessed May 10, 2017
Reply: We thank Dr. Goggin for his interest in our article and his observations. We agree that the backcalculation method has some limitations, namely that it is intrinsically retrospective in nature, as we highlighted in the Discussion section of our paper. We compared 11 methods to improve toric IOL calculation. Although the gold standard in science is the prospective randomized trial, such trials would only be possible in studies similar to ours after reducing the number of groups by knowing the methods with a smaller prediction error. To compare the 11 methods in a prospective trial, in a powersample calculation (analysis of variance model with a significance level 5% and a power of 80%) to detect differences as small as 0.01 D in the centroid prediction error as we found in our study, 47 536 eyes would be required, rendering the study very difficult in clinical practice. We encourage future prospective randomized trials comparing methods with a lower prediction error given that scientific knowledge is a continuous process. Although we referred to Goggin’s method as the “Goggin coefficient,” we applied the 2 different coefficients for
Volume 43 Issue 6 June 2017
with-the-rule and against-the-rule (ATR) eyes exactly as published in the article by Goggin et al.1 We apologize for not being clear about this. We acknowledge the importance of the controlled trial Goggin et al. recently published,2 showing the advantage of the method he initially described, as a valuable addition to the literature. We did not include this study in the Discussion and References sections of our article because it had not been published at the time of the initial submission of our study. As we state in the Discussion section, the reduction in sample size resulting from the low number of eyes requiring less than 2.0 D of cylindrical power and the lower number of eyes with ATR astigmatism in our study, in which Goggin’s coefficients performed better, might have limited our results with these coefficients. We agree that the original Alcon calculator has numerous limitations, which we point out in our article. However, it has been used for many years and it is still available online to this date, hence the importance of thinking about strategies for reducing all its sources of error and ultimately improve clinical results with toric IOLs. Finally, we would like to thank Dr. Goggin for his important contributions on this subject. We encourage future studies on this important topic, namely answering the questions we left open in our study.dTiago B. Ferreira, MD, Paulo Ribeiro, PhD, Filomena J. Ribeiro, MD, PhD, FEBO, Jo~ao G. O’Neill, MD, PhD REFERENCES
1. Goggin M, Zamora-Alejo K, Esterman A, van Zyl L. Adjustment of anterior corneal astigmatism values to incorporate the likely effect of posterior corneal curvature for toric intraocular lens calculation. J Refract Surg 2015; 31: 98–102 2. Goggin M, van Zyl L, Caputo S, Esterman A. Outcome of adjustment for posterior corneal curvature in toric intraocular lens calculation and selection. J Cataract Refract Surg 2016; 42:1441–1448. Available at: http://www. jcrsjournal.org/article/S0886-3350(16)30397-2/pdf. Accessed May 12, 2017
We have further examined the data collected for our study and compared surgical and postoperative complications for patients with and without DR after either laser-assisted cataract surgery or conventional phacoemulsification. The analysis yielded the following results: Surgical complications during laser-assisted cataract surgery occurred in 8.6% of cases with DR and in 2.8% of cases without DR. Surgical complications after conventional phacoemulsification cataract surgery occurred in 1.6% of cases and 1.5% of cases, respectively. Surgical complications in the European Registry of Quality Outcomes for Cataract and Refractive Surgery (EUREQUO) database include torn posterior capsule, vitreous loss, iris damage, dropped nucleus, and “other” (including anterior capsule tears). Postoperative complications after laser-assisted cataract surgery occurred in 2.9% of cases with DR and in 3.4% of cases without DR. Postoperative complications after conventional phacoemulsification cataract surgery occurred in 10.4% of cases and in 2.1% of cases, respectively. Postoperative complications in the EUREQUO database include posterior capsule opacification, uncontrolled intraocular pressure, intraocular lens explantation, and “other” (including postoperative CME). In other words, in our study, patients with DR had more surgical complications if they had laser-assisted cataract surgery but more postoperative complications if they had conventional phacoemulsification. These results motivate further studies in patients with diabetes having cataract surgery.dSonia Manning, MD, FRCSI(Ophth), Ype Henry, MD, FEBO, Paul Rosen, FRCS, FRCOphth, Ulf Stenevi, MD, PhD, Mats Lundstr€om, MD, PhD
REFERENCES
1. Chee S-P, Yang Y, Ti S-E. Clinical outcomes in the first two years of femtosecond laser–assisted cataract surgery. Am J Ophthalmol 2015; 159: 714–719 2. Schultz T, Joachim SC, Kuehn M, Dick HB. Changes in prostaglandin levels in patients undergoing femtosecond laser-assisted cataract surgery. J Refract Surg 2013; 29:742–747 3. Conrad-Hengerer I, Hengerer FH, Al Juburi M, Schultz T, Dick HB. Femtosecond laser-induced macular changes and anterior segment inflammation in cataract surgery. J Refract Surg 2014; 30:222–226
Back calculation of prediction error compared with controlled trial prediction error of Goggin nomogram for toric intraocular lens cylinders Ferreira et al.1 examined the prediction error of refractive astigmatism outcomes with toric intraocular lens (IOL) calculation using a number of calculation methods. In common with many publications on this subject, they used an historic calculation method. They examined the refractive outcomes in a group of eyes in which the toric IOL cylinder power implanted was calculated by 1 method and, using the actual refractive outcome recorded postoperatively, they asked the question whether other methods would have
863
predicted this outcome more accurately. This is a common method of assessing toric IOL cylinder calculation in the current literature and has some validity. However, it assumes that the postoperative refraction and the various methods of corneal power measurement would remain the same from test to test, a patently erroneous assumption.2 The comparison of the effectiveness of medical techniques has always rested on randomized controlled trials or, at least, on nonrandomized controlled trials, to avoid such confounding variables. Using their method, the authors examined a toric IOL cylinder power calculation technique I and my coauthors introduced.3 It is not stated clearly in their Method section but is implied in their Discussion section that they used my method correctly in terms of IOL cylinder power. It appears they applied the corrections I suggest in eyes requiring IOL cylinder powers of 2.0 diopters (D) or less. I have presented evidence that errors based on anterior corneal “rule” do not occur to any significant degree in eyes requiring correction above this value. However, throughout their article, they refer to use of the “Goggin coefficient” (implying 1 coefficient), whereas I describe 2 coefficients of adjustment, 1 for with-the-rule anterior corneal astigmatism and 1 for against-the-rule.3 I would be grateful if they could clarify their use of these published values. Using their back-calculation technique and by whatever way they have used my adjustment for the probable effect of posterior corneal astigmatism, they report mean absolute prediction errors of 0.65 D G 0.38 (SD) and 0.63 G 0.36 D and prediction error centroids of 0.42 @ 166 and 0.38 @ 170 when using my technique. By contrast, we have reported, in a controlled trial of my method of calculation and actual surgical implantation, a median absolute error of 0.23 D (95% confidence interval [CI], 0.13-0.35) (decreased from a median of 0.45 D [95% CI, 0.33-0.58] in control eyes; P Z .004) and a centroid of 0.15 D at 146 (the centroid for control eyes was 0.49 D at 175 degrees).4 These are lower for Goggin nomogram–adjusted values than any produced by Ferreira et al.1 using their back-calculation methods. To my knowledge, ours is the only publication of actual surgical use of any method of toric IOL calculation that includes the posterior corneal astigmatism effect and the only publication to include a control group. Finally, I would like to point out that my method will not greatly improve the prediction error of what the authors term the “original Alcon calculator” (as they found). My method simply allows for the likely effect of posterior corneal astigmatism. The original Alcon calculator contained other errors that I and my coauthors pointed out in 20115 that far exceed the error induced by the failure to include posterior corneal astigmatism. That calculator has now largely been superseded.5 Any calculator similarly affected by other sources of error will not be ameliorated by the Goggin nomogram. Michael Goggin, FRCSI(Ophth), FRCOphth, FRANZCO, MS Adelaide, South Australia Volume 43 Issue 6 June 2017
864
LETTERS
REFERENCES
1. Ferreira TB, Ribeiro P, Ribeiro FJ, O’Neill JG. Comparison of astigmatic prediction errors associated with new calculation methods for toric intraocular lenses. J Cataract Refract Surg 2017; 43:340–347 2. Goggin M, Patel I, Billing K, Esterman A. Variation in surgically induced astigmatism estimation due to test-to-test variations in keratometry. J Cataract Refract Surg 2010; 36:1792–1793 3. Goggin M, Zamora-Alejo K, Esterman A, van Zyl L. Adjustment of anterior corneal astigmatism values to incorporate the likely effect of posterior corneal curvature for toric intraocular lens calculation. J Refract Surg 2015; 31:98–102 4. Goggin M, van Zyl L, Caputo S, Esterman A. Outcome of adjustment for posterior corneal curvature in toric intraocular lens calculation and selection. J Cataract Refract Surg 2016; 42:1441–1448. Available at: http://www. jcrsjournal.org/article/S0886-3350(16)30397-2/pdf. Accessed May 10, 2017 5. Goggin M, Moore S, Esterman A. Outcome of toric intraocular lens implantation after adjusting for anterior chamber depth and intraocular lens sphere equivalent power effects. Arch Ophthalmol 2011; 129:998–1003. Correction, 1494. Available at: http://jamanetwork.com/journals/jamaophthalmology/ fullarticle/1106787. Correction Available at: http://jamanetwork.com/journals/ jamaophthalmology/fullarticle/1106484. Accessed May 10, 2017
Reply: We thank Dr. Goggin for his interest in our article and his observations. We agree that the backcalculation method has some limitations, namely that it is intrinsically retrospective in nature, as we highlighted in the Discussion section of our paper. We compared 11 methods to improve toric IOL calculation. Although the gold standard in science is the prospective randomized trial, such trials would only be possible in studies similar to ours after reducing the number of groups by knowing the methods with a smaller prediction error. To compare the 11 methods in a prospective trial, in a powersample calculation (analysis of variance model with a significance level 5% and a power of 80%) to detect differences as small as 0.01 D in the centroid prediction error as we found in our study, 47 536 eyes would be required, rendering the study very difficult in clinical practice. We encourage future prospective randomized trials comparing methods with a lower prediction error given that scientific knowledge is a continuous process. Although we referred to Goggin’s method as the “Goggin coefficient,” we applied the 2 different coefficients for
Volume 43 Issue 6 June 2017
with-the-rule and against-the-rule (ATR) eyes exactly as published in the article by Goggin et al.1 We apologize for not being clear about this. We acknowledge the importance of the controlled trial Goggin et al. recently published,2 showing the advantage of the method he initially described, as a valuable addition to the literature. We did not include this study in the Discussion and References sections of our article because it had not been published at the time of the initial submission of our study. As we state in the Discussion section, the reduction in sample size resulting from the low number of eyes requiring less than 2.0 D of cylindrical power and the lower number of eyes with ATR astigmatism in our study, in which Goggin’s coefficients performed better, might have limited our results with these coefficients. We agree that the original Alcon calculator has numerous limitations, which we point out in our article. However, it has been used for many years and it is still available online to this date, hence the importance of thinking about strategies for reducing all its sources of error and ultimately improve clinical results with toric IOLs. Finally, we would like to thank Dr. Goggin for his important contributions on this subject. We encourage future studies on this important topic, namely answering the questions we left open in our study.dTiago B. Ferreira, MD, Paulo Ribeiro, PhD, Filomena J. Ribeiro, MD, PhD, FEBO, Jo~ao G. O’Neill, MD, PhD REFERENCES
1. Goggin M, Zamora-Alejo K, Esterman A, van Zyl L. Adjustment of anterior corneal astigmatism values to incorporate the likely effect of posterior corneal curvature for toric intraocular lens calculation. J Refract Surg 2015; 31: 98–102 2. Goggin M, van Zyl L, Caputo S, Esterman A. Outcome of adjustment for posterior corneal curvature in toric intraocular lens calculation and selection. J Cataract Refract Surg 2016; 42:1441–1448. Available at: http://www. jcrsjournal.org/article/S0886-3350(16)30397-2/pdf. Accessed May 12, 2017