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Reply: Intraocular lens power after refractive surgery: Haigis-L formula
LETTERS
Intraocular lens power after refractive surgery: Haigis-L formula Intraocular lens (IOL) power calculation after refractive surgery is a major concern for many ophthalmic surgeons as the number of cataract cases in patients with histories of keratorefractive procedures is increasing. We have used the Haigis-L formula in our post-refractive cataract cases with adequate success and appreciate Haigis’ work.1 The basis of corneal power correction in the Haigis-L formula is the correlation between the incorrectly measured corneal radii and the effective corneal power after refractive surgery. A linear regression equation with good correlation coefficient derives from a scatterplot correlating effective equivalent corneal power from the history method with the actually measured corneal radius after refractive surgery. A basic theoretical problem in the rationale behind the correlation between effective corneal power and the measured radius exists. Naturally, the dioptric corneal power is derived from the radius by inverse correlation (ie, the parameters are inversely proportional) according to the paraxial approximation in geometrical optics (power Z difference in refractive index/radius). Therefore, the graph of this reciprocal function would be a hyperbola. Assumption of a simple linear correlation between power and radius with presence of the confounding change made by refractive surgery may not be complete and exact. We think the Haigis-L regression formula will work in most cases, but the error of nonlinear relation is still present. This type of error is very similar to the error of the earlier generation of IOL calculation formulas such as the SRK/1, with the linear assumption of a nonlinear relation that worked well at the time of introduction but was later replaced by sophisticated generations of calculation methods. We have shown that factors other than radii may help to predict the error in calculations2 and taking into account all available data in their place may result in improved outcome.
REPLY: Peyman and Peyman are, of course, right in pointing out that corneal power and radius should basically follow a 1/radius relation rather than a linear dependence on radius. This can readily be derived from elementary optics. In fact, a 1/radius fit to our original data (Figure 1) yields a slightly better correlation coefficient (0.961) than the linear fit (0.957) used in the paper. Results obtained with the 2 fits, however, do not differ significantly (P Z .48) from each other. The ‘‘exact’’ analytical dependence of the effective corneal power on measured radius is not known since the measurement situation is difficult (performed on an aspheric surface off center), with measurement results additionally influenced by hardware-specific evaluation algorithms. Also, the refractive contribution of the posterior corneal surface is not known exactly. Therefore, with the database in Figure 1, which stems from measurements earlier than 2003, it seemed appropriate to apply a simple linear regression model (W. Haigis, PhD, et al., ‘‘Messung von Hornhautradien bei normalen Augen und Augen nach LASIK,’’ presented at the 16th Kongress der Deutschen Ophthalmochirurgen, Nu¨rnberg, Germany, August 2003). This may not be justified for corneas treated with more modern equipment with larger optical zones and customized ablations. We derived different correction curves for different instruments and different types of ablation.1 Although linear corrections still promise good results on an average, nonlinear functions may help to increase the predictability of refractive surgery outcomes. I agree with the conclusions of Peyman and Peyman: Corneal radius is but one factor, and today’s simple approaches will be replaced by tomorrow’s more sophisticated solutions. The future may well hold a biometry/ keratometry device that offers different correction curves according to optical zone diameter and ablation type. However, today’s patients have to be treated with today’s methods.dWolfgang Haigis, MS, PhD
Alireza Peyman, MD Mohammadreza Peyman, MD Isfahan, Iran REFERENCES 1. Haigis W. Intraocular lens calculation after refractive surgery for myopia: Haigis-L formula. J Cataract Refract Surg 2008; 34:1658–1663 2. Razmjoo H, Peyman A, Kashfi A, Peyman M, Dehghani A. A regression model for correcting intraocular lens power after refractive surgery independent of preoperative data. Eur J Ophthalmol 2006; 16:525–529
1650
Q 2009 ASCRS and ESCRS Published by Elsevier Inc.
Figure 1. Correction curves (proportional to radius (red) and to 1/radius (black) for the IOLMaster (Carl Zeiss Meditec): effective (equivalent) corneal power from the refractive history method as a function of corneal radius measured with the IOLMaster after laser in situ keratomileusis for myopia. 0886-3350/09/$dsee front matter doi:10.1016/j.jcrs.2009.04.040
LETTERS
REFERENCE 1. Haigis W, Lege BAM, Neuhann TF. Korrekturkurven zur Hornhautbrechkraftbestimmung nach myoper LASIK. In: Kohnen T, Auffarth GU, Pham DT, eds, 20. Kongress der Deutschsprachigen Gesellschaft fu¨r Intraokularlinsen-Implantation und refraktive Chirurgie. Heidelberg, 3, und 4. Ma¨rz 2006. Biermann Verlag, Ko¨ln, Germany, 2006; 415–419
10-point analog scale not equivalent to a 10-point questionnaire In their study of depressive personality symptoms and satisfaction with vision following laser in situ keratomileusis (LASIK),1 Morse et al. found that patients with higher preoperative depressive symptom scores on the Armstrong Laboratory Personality Survey (ALPS) were more likely to be dissatisfied 1 and 6 months after surgery. I have several concerns regarding the methodology and conclusions. First, the ‘‘Patients and Methods’’ section reports that the Navy Refractive Surgery Survey (NRSS) was administered to patients preoperatively and 1 and 6 months postoperatively. The NRSS was first described in 20032; to my knowledge, neither the survey development and validation process3 nor the full survey has been published. For analysis, the authors extracted a single question that asked patients to rate their satisfaction on a 10-point analog scale and the results of only the 2 postoperative evaluations were reported. The data from the remainder of the NRSS were not provided, leading readers to wonder whether the full survey was actually performed. If yes, why not provide all the results? If no, then a global and nonspecific measure of patient satisfaction (the ‘‘smiley-face’’ scale) was the only assessment and this fact should not be disguised behind mention of the NRSS. Second, refractive surgery represents a change (delta) in the patient’s visual physiology. Its effect should be measured using a delta function, in this case the difference in analog scale vision satisfaction before and after surgery. Perhaps more depressed patients were also on average more satisfied with their baseline vision. In this case, LASIK may have been ‘‘satisfaction neutral.’’ The authors have implicitly assumed no correlation between preoperative depressive symptoms and preoperative vision satisfaction when this correlation could be easily investigated using their preoperative data. In fact, it may have been negative (less depressed patients being less satisfied). Third, the results as presented do not allow identification of informative outlier patients. Although the depressive symptom survey scores ranged from 0 to 16 and the vision satisfaction scores could range from 1 to 10, making the raw data ideal for presentation as simple X/Y correlation plots, patients were clustered
1651
into 3 satisfaction categories and 3 depression categories for an odds-ratio analysis. If a preoperatively nondepressed patient was very dissatisfied with the post-LASIK vision, perhaps he or she had a poor result. If the uncorrected visual acuity was excellent, the patient may have experienced a decline in other visual psychometrics that was worth investigating.4,5 Finally, the connection between a poor LASIK outcome and postoperative depression has much anecdotal support, some of which was presented at the U.S. Food and Drug Administration Ophthalmic Devices Panel meeting in April 2008. To better investigate the relationship between LASIK and depressive symptoms, the ALPS could have been performed at the 6-month postoperative visit (again providing a delta), at least to those patients in the ‘‘satisfied’’ and ‘‘less satisfied’’ categories. In the current article, the take-home message to refractive surgeons is that screening out depressed candidates will likely result in a happier group of post-LASIK patients in the waiting room. This is the surgeon’s perspective. As part of the informed consent process, perhaps patients should be advised that LASIK which results in reduced vision quality or chronic ocular surface pain might also precipitate major organic depression. The more profound question is whether individuals at greater risk for this complication can be identified before surgery. Due to its limited scope, the study by Morse et al. has not addressed this serious issue. Sandra Brown, MD Concord, North Carolina, USA
REFERENCES 1. Morse JS, Schallhorn SC, Hettinger K, Tanzer D. Role of depressive symptoms in patient satisfaction with visual quality after laser in situ keratomileusis. J Cataract Refract Surg 2009; 35:341–346 2. Schallhorn SC, Kaupp SE, Tanzer DJ, Tidwell J, Laurent J, Bourque LB. Pupil size and quality of vision after LASIK. Ophthalmology 2003; 110:1606–1614 3. Fraenkel G, Comaish IF, Lawless MA, Kelly MR, Dunn SM, Byth K, Webber SK, Sutton GL, Rogers CM. Development of a questionnaire to assess subjective vision score in myopes seeking refractive surgery. J Refract Surg 2004; 20:10–19 4. Lackner B, Pieh S, Schmidinger G, Hanselmayer G, Simadere C, Reitner A, Skorpik C. Glare and halo phenomena after laser in situ keratomileusis. J Cataract Refract Surg 2003; 29:444–450 5. Brown SM, Bradley JC, Xu KT, Chadwick AA, McCartney DL. Visual field changes after laser in situ keratomileusis. J Cataract Refract Surg 2005; 31:687–693
REPLY: In addition to addressing Brown’s concerns about our methodology, we are happy to discuss her assumptions about the study and her opinions about the take-home message of the article.
J CATARACT REFRACT SURG - VOL 35, SEPTEMBER 2009
Intraocular lens power after refractive surgery: Haigis-L formula Intraocular lens (IOL) power calculation after refractive surgery is a major concern for many ophthalmic surgeons as the number of cataract cases in patients with histories of keratorefractive procedures is increasing. We have used the Haigis-L formula in our post-refractive cataract cases with adequate success and appreciate Haigis’ work.1 The basis of corneal power correction in the Haigis-L formula is the correlation between the incorrectly measured corneal radii and the effective corneal power after refractive surgery. A linear regression equation with good correlation coefficient derives from a scatterplot correlating effective equivalent corneal power from the history method with the actually measured corneal radius after refractive surgery. A basic theoretical problem in the rationale behind the correlation between effective corneal power and the measured radius exists. Naturally, the dioptric corneal power is derived from the radius by inverse correlation (ie, the parameters are inversely proportional) according to the paraxial approximation in geometrical optics (power Z difference in refractive index/radius). Therefore, the graph of this reciprocal function would be a hyperbola. Assumption of a simple linear correlation between power and radius with presence of the confounding change made by refractive surgery may not be complete and exact. We think the Haigis-L regression formula will work in most cases, but the error of nonlinear relation is still present. This type of error is very similar to the error of the earlier generation of IOL calculation formulas such as the SRK/1, with the linear assumption of a nonlinear relation that worked well at the time of introduction but was later replaced by sophisticated generations of calculation methods. We have shown that factors other than radii may help to predict the error in calculations2 and taking into account all available data in their place may result in improved outcome.
REPLY: Peyman and Peyman are, of course, right in pointing out that corneal power and radius should basically follow a 1/radius relation rather than a linear dependence on radius. This can readily be derived from elementary optics. In fact, a 1/radius fit to our original data (Figure 1) yields a slightly better correlation coefficient (0.961) than the linear fit (0.957) used in the paper. Results obtained with the 2 fits, however, do not differ significantly (P Z .48) from each other. The ‘‘exact’’ analytical dependence of the effective corneal power on measured radius is not known since the measurement situation is difficult (performed on an aspheric surface off center), with measurement results additionally influenced by hardware-specific evaluation algorithms. Also, the refractive contribution of the posterior corneal surface is not known exactly. Therefore, with the database in Figure 1, which stems from measurements earlier than 2003, it seemed appropriate to apply a simple linear regression model (W. Haigis, PhD, et al., ‘‘Messung von Hornhautradien bei normalen Augen und Augen nach LASIK,’’ presented at the 16th Kongress der Deutschen Ophthalmochirurgen, Nu¨rnberg, Germany, August 2003). This may not be justified for corneas treated with more modern equipment with larger optical zones and customized ablations. We derived different correction curves for different instruments and different types of ablation.1 Although linear corrections still promise good results on an average, nonlinear functions may help to increase the predictability of refractive surgery outcomes. I agree with the conclusions of Peyman and Peyman: Corneal radius is but one factor, and today’s simple approaches will be replaced by tomorrow’s more sophisticated solutions. The future may well hold a biometry/ keratometry device that offers different correction curves according to optical zone diameter and ablation type. However, today’s patients have to be treated with today’s methods.dWolfgang Haigis, MS, PhD
Alireza Peyman, MD Mohammadreza Peyman, MD Isfahan, Iran REFERENCES 1. Haigis W. Intraocular lens calculation after refractive surgery for myopia: Haigis-L formula. J Cataract Refract Surg 2008; 34:1658–1663 2. Razmjoo H, Peyman A, Kashfi A, Peyman M, Dehghani A. A regression model for correcting intraocular lens power after refractive surgery independent of preoperative data. Eur J Ophthalmol 2006; 16:525–529
1650
Q 2009 ASCRS and ESCRS Published by Elsevier Inc.
Figure 1. Correction curves (proportional to radius (red) and to 1/radius (black) for the IOLMaster (Carl Zeiss Meditec): effective (equivalent) corneal power from the refractive history method as a function of corneal radius measured with the IOLMaster after laser in situ keratomileusis for myopia. 0886-3350/09/$dsee front matter doi:10.1016/j.jcrs.2009.04.040
LETTERS
REFERENCE 1. Haigis W, Lege BAM, Neuhann TF. Korrekturkurven zur Hornhautbrechkraftbestimmung nach myoper LASIK. In: Kohnen T, Auffarth GU, Pham DT, eds, 20. Kongress der Deutschsprachigen Gesellschaft fu¨r Intraokularlinsen-Implantation und refraktive Chirurgie. Heidelberg, 3, und 4. Ma¨rz 2006. Biermann Verlag, Ko¨ln, Germany, 2006; 415–419
10-point analog scale not equivalent to a 10-point questionnaire In their study of depressive personality symptoms and satisfaction with vision following laser in situ keratomileusis (LASIK),1 Morse et al. found that patients with higher preoperative depressive symptom scores on the Armstrong Laboratory Personality Survey (ALPS) were more likely to be dissatisfied 1 and 6 months after surgery. I have several concerns regarding the methodology and conclusions. First, the ‘‘Patients and Methods’’ section reports that the Navy Refractive Surgery Survey (NRSS) was administered to patients preoperatively and 1 and 6 months postoperatively. The NRSS was first described in 20032; to my knowledge, neither the survey development and validation process3 nor the full survey has been published. For analysis, the authors extracted a single question that asked patients to rate their satisfaction on a 10-point analog scale and the results of only the 2 postoperative evaluations were reported. The data from the remainder of the NRSS were not provided, leading readers to wonder whether the full survey was actually performed. If yes, why not provide all the results? If no, then a global and nonspecific measure of patient satisfaction (the ‘‘smiley-face’’ scale) was the only assessment and this fact should not be disguised behind mention of the NRSS. Second, refractive surgery represents a change (delta) in the patient’s visual physiology. Its effect should be measured using a delta function, in this case the difference in analog scale vision satisfaction before and after surgery. Perhaps more depressed patients were also on average more satisfied with their baseline vision. In this case, LASIK may have been ‘‘satisfaction neutral.’’ The authors have implicitly assumed no correlation between preoperative depressive symptoms and preoperative vision satisfaction when this correlation could be easily investigated using their preoperative data. In fact, it may have been negative (less depressed patients being less satisfied). Third, the results as presented do not allow identification of informative outlier patients. Although the depressive symptom survey scores ranged from 0 to 16 and the vision satisfaction scores could range from 1 to 10, making the raw data ideal for presentation as simple X/Y correlation plots, patients were clustered
1651
into 3 satisfaction categories and 3 depression categories for an odds-ratio analysis. If a preoperatively nondepressed patient was very dissatisfied with the post-LASIK vision, perhaps he or she had a poor result. If the uncorrected visual acuity was excellent, the patient may have experienced a decline in other visual psychometrics that was worth investigating.4,5 Finally, the connection between a poor LASIK outcome and postoperative depression has much anecdotal support, some of which was presented at the U.S. Food and Drug Administration Ophthalmic Devices Panel meeting in April 2008. To better investigate the relationship between LASIK and depressive symptoms, the ALPS could have been performed at the 6-month postoperative visit (again providing a delta), at least to those patients in the ‘‘satisfied’’ and ‘‘less satisfied’’ categories. In the current article, the take-home message to refractive surgeons is that screening out depressed candidates will likely result in a happier group of post-LASIK patients in the waiting room. This is the surgeon’s perspective. As part of the informed consent process, perhaps patients should be advised that LASIK which results in reduced vision quality or chronic ocular surface pain might also precipitate major organic depression. The more profound question is whether individuals at greater risk for this complication can be identified before surgery. Due to its limited scope, the study by Morse et al. has not addressed this serious issue. Sandra Brown, MD Concord, North Carolina, USA
REFERENCES 1. Morse JS, Schallhorn SC, Hettinger K, Tanzer D. Role of depressive symptoms in patient satisfaction with visual quality after laser in situ keratomileusis. J Cataract Refract Surg 2009; 35:341–346 2. Schallhorn SC, Kaupp SE, Tanzer DJ, Tidwell J, Laurent J, Bourque LB. Pupil size and quality of vision after LASIK. Ophthalmology 2003; 110:1606–1614 3. Fraenkel G, Comaish IF, Lawless MA, Kelly MR, Dunn SM, Byth K, Webber SK, Sutton GL, Rogers CM. Development of a questionnaire to assess subjective vision score in myopes seeking refractive surgery. J Refract Surg 2004; 20:10–19 4. Lackner B, Pieh S, Schmidinger G, Hanselmayer G, Simadere C, Reitner A, Skorpik C. Glare and halo phenomena after laser in situ keratomileusis. J Cataract Refract Surg 2003; 29:444–450 5. Brown SM, Bradley JC, Xu KT, Chadwick AA, McCartney DL. Visual field changes after laser in situ keratomileusis. J Cataract Refract Surg 2005; 31:687–693
REPLY: In addition to addressing Brown’s concerns about our methodology, we are happy to discuss her assumptions about the study and her opinions about the take-home message of the article.
J CATARACT REFRACT SURG - VOL 35, SEPTEMBER 2009