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Proper statistical methods required to compare clinical measurements
LETTERS
surgery. On the other hand, our patients showed hypertropia that increased with up gaze and ipsilateral gaze and no marked restriction on forced duction test; inspection of the muscle at surgery did not disclose fibrosis (except in the same case), thus satisfying the criteria of overactive strabismus pattern.11,12 Besides, most of our patients typically reported they saw double on patch removal, which might be more compatible with paresis by anesthetics. Capo´ et al.6 demonstrated how the tip of a needle can touch the superior rectus muscle in cadaveric dissection. Because only the tip of the needle touches the superior rectus muscle, limited segmental damage might cause an overaction, whereas diffuse contracture from more extensive muscle damage produces restrictive patterns.6,7 In fact, overaction is more common when the superior rectus muscle is involved, and restriction is more common when the inferior rectus muscle is involved.3,6 The affected muscle in local anesthesia depends to some extent on the type of anesthesia. The muscle struck during a peribulbar block is usually the inferior rather than the superior rectus muscle, but for a retrobulbar injection, the 2 muscles are equally likely to be struck.6 Because most reports of diplopia after local anesthesia enrolled mixed populations with retrobulbar and peribulbar anesthesia and none of our patients had peribulbar anesthesia, we found a lower incidence of inferior rectus muscle involvement with retrobulbar anesthesia only. Grimmett and Lambert13 also identified 4 patients with superior rectus muscle overaction after retrobulbar injection among 7 cases with strabismus that developed after cataract extraction. Mun˜oz and coauthors3 found 11 cases of superior rectus overaction or paresis, and 10 cases of inferior rectus fibrosis or overaction, but did not describe the type of anesthesia used. As we mentioned in the Discussion,11 the smaller anatomical orbit dimensions in Asians, especially the shorter vertical diameter,14–16 might contribute to the remarkable frequency of superior rectus involvement in our study compared with the frequency in previous studies of white patients. We believe that the predominance of superior rectus involvement in our study may be attributed to the application of retrobulbar anesthesia and an anatomical difference of orbit. We appreciate that Chan and coauthors gave us the opportunity to clarify 1 of the points in our article.dSoo
Kyung Han, MD, Jeong Hun Kim, MD, Jeong-Min Hwang, MD
References 1. Catalano RA, Nelson SB, Calhoun JH, et al. Persistent strabismus presenting after cataract surgery. Ophthalmology 1987; 94:491–494 2. Rainin EA, Carlson BM. Postoperative diplopia and ptosis; a clinical hypothesis based on the myotoxicity of local anesthetics. Arch Ophthalmol 1985; 103:1337–1339
3. Mun˜oz M, Capo´ H, Siatkowski RM. Results of surgery for vertical strabismus following cataract extraction performed under local anesthesia. Binocul Vis Strabismus Q 1996; 11:275–280 4. Esswein MB, von Noorden GK. Paresis of a vertical rectus muscle after cataract extraction. Am J Ophthalmol 1993; 116:424–430 5. Carlson BM, Emerick S, Komorowski TE, et al. Extraocular muscle regeneration in primates; local anestheticinduced lesions. Ophthalmology 1992; 99:582–589 6. Capo´ H, Roth E, Johnson T, et al. Vertical strabismus after cataract surgery. Ophthalmology 1996; 103:918– 921; discussion by DL Guyton, 921 7. Capo´ H, Guyton DL. Ipsilateral hypertropia after cataract surgery. Ophthalmology 1996; 103:721–730 8. Pearce IA, McCready PM, Watson MP, Taylor RH. Vertical diplopia following local anaesthetic cataract surgery: predominantly a left eye problem? Eye 2000; 14: 180–184 9. Hamed LM, Helveston EM, Ellis FD. Persistent binocular diplopia after cataract surgery. Am J Ophthalmol 1987; 103:741–744 10. Hamed LM. Strabismus presenting after cataract surgery. Ophthalmology 1991; 98:247–252 11. Han SK, Kim JH, Hwang JM. Persistent diplopia after retrobulbar anesthesia. J Cataract Refract Surg 2004; 30: 1248–1253 12. Han SK, Hwang JM. Thyroid disease and vertical rectus muscle overaction after retrobulbar anesthesia. J Cataract Refract Surg 2003; 29:78–84 13. Grimmett MR, Lambert SR. Superior rectus muscle overaction after cataract extraction. Am J Ophthalmol 1992; 114:72–80 14. Hwang K, Baik SH. Surgical anatomy of the orbit of Korean adults. J Craniofac Surg 1999; 10:129–134 ¯ . Morphometric mea15. Karakas P, Bozkir MG, Oguz O surements from various reference points in the orbit of male Caucasians. Surg Radiol Anat 2003; 24:358–362 16. Danko I, Haug RH. An experimental investigation of the safe distance for internal orbital dissection. J Oral Maxillofac Surg 1998; 56:749–752
Proper statistical methods required to compare clinical measurements
O
strin and Glasser1 compare 4 techniques of the standard clinical ‘‘push-up’’ method for measuring the amplitude of accommodation. The assessment of their data is based on the statistical method of regression analysis. The inappropriate selection and use of this analysis can and does result in misleading
J CATARACT REFRACT SURG—VOL 31, MAY 2005
865
LETTERS
Table 1. The coefficient of variation of the amplitude of accommodation for each method used by Ostrin and Glasser1 (calculated using the data given in Table 1). Coefficient of Variation (%) Age Group (Y) Method of Measurement Push up
31–35
36–40
41–45
46–50
51–55
24.6
15.2
18.2
38.2
45.2
Mean of All Age Groups 28.3
Minus to blur
36.6
31.9
31.0
46.8
31.3
35.5
Focometer
38.4
26.1
14.2
29.0
29.2
27.4
HCR with trial lenses
49.4
47.8
34.8
51.6
52.5
47.2
HCR with plocarpine
21.1
58.2
14.4
41.8
86.1
44.3
HCR Z Hartinger coincidence refractometer
conclusions.2 The appropriate statistical method for comparing clinical measurement techniques was well described in the classic paper by Bland and Altman2 in 1986. We are unable to correctly reanalyze their data since the authors do not provide sufficient data for our independent evaluation by the Bland-Altman method. However, a comparison of the precision of the authors’ techniques can be evaluated from their data. This is achieved by determining the coefficient of variation expressed as a percentage (%CV):3
Standard Deviation 100 %CV ¼ Mean
The smaller the %CV, the better the precision. Calculation of the %CV of each of the techniques by using the mean and standard deviation of the measurements provided by Ostrin and Glasser1 demonstrates that, contrary to the authors’ conclusions, the Hartinger measurements are the least precise (Table 1). In brief, inadequate sample size within each subgroup and inappropriate selection and application of statistical methods can lead to incorrect conclusions. Ostrin and Glasser have not addressed these issues in their methodology and analysis, leaving their conclusions without scientific merit. RONALD A. SCHACHAR, MD, PHD Dallas, Texas, USA
References 1. Ostrin LA, Glasser A. Accommodation measurements in a prepresbyopic and presbyopic population. J Cataract and Refract Surg 2004; 30:1435–1444 866
2. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986; 1:307–310 3. Indrayan A, Sarmukaddam SB. Medical Biostatistics. New York, Marcel Dekker, Inc. 2001; 125–127
Reply: We are pleased to see that Schachar has read our recent article on accommodation measurements in a prepresbyopic and presbyopic population.1 The purpose of the paper was to identify appropriate methods to do objective accommodation measurements in the target population of accommodation restoration procedures and to show that subjective measurements of accommodation overestimate the true objectively measured accommodative amplitude. Regression analysis was simply used to illustrate the differences between methods, not to perform a statistical analysis. We are, of course, aware of the Bland-Altman analysis as a statistical procedure to compare methods.2 In our paper, we clearly demonstrate and describe that there are individual variations in accommodative amplitude due to interindividual differences in response to pilocarpine and trial lens-induced blur. The coefficient of variation that Schachar used simply expresses this interindividual variation and does not, as he suggests, evaluate the precision of the measurement methods. A Bland-Altman analysis of the data would also simply express the interindividual variations and not evaluate the precision of the measurement methods. We made no claims about the precision of the Hartinger measurements based on the results in our study. It is Schachar’s attempt to evaluate the precision of the Hartinger measurements with our data rather than the conclusions we reached that is without scientific merit. The point of our paper, and indeed the very reason we undertook the study, was to demonstrate that objective tests exist for accommodation measurement. It is the use of such objective accommodation measurements that demonstrates the absence of accommodation restoration in scleral expansion patients.3,4 A statistical analysis is not required to identify
J CATARACT REFRACT SURG—VOL 31, MAY 2005
surgery. On the other hand, our patients showed hypertropia that increased with up gaze and ipsilateral gaze and no marked restriction on forced duction test; inspection of the muscle at surgery did not disclose fibrosis (except in the same case), thus satisfying the criteria of overactive strabismus pattern.11,12 Besides, most of our patients typically reported they saw double on patch removal, which might be more compatible with paresis by anesthetics. Capo´ et al.6 demonstrated how the tip of a needle can touch the superior rectus muscle in cadaveric dissection. Because only the tip of the needle touches the superior rectus muscle, limited segmental damage might cause an overaction, whereas diffuse contracture from more extensive muscle damage produces restrictive patterns.6,7 In fact, overaction is more common when the superior rectus muscle is involved, and restriction is more common when the inferior rectus muscle is involved.3,6 The affected muscle in local anesthesia depends to some extent on the type of anesthesia. The muscle struck during a peribulbar block is usually the inferior rather than the superior rectus muscle, but for a retrobulbar injection, the 2 muscles are equally likely to be struck.6 Because most reports of diplopia after local anesthesia enrolled mixed populations with retrobulbar and peribulbar anesthesia and none of our patients had peribulbar anesthesia, we found a lower incidence of inferior rectus muscle involvement with retrobulbar anesthesia only. Grimmett and Lambert13 also identified 4 patients with superior rectus muscle overaction after retrobulbar injection among 7 cases with strabismus that developed after cataract extraction. Mun˜oz and coauthors3 found 11 cases of superior rectus overaction or paresis, and 10 cases of inferior rectus fibrosis or overaction, but did not describe the type of anesthesia used. As we mentioned in the Discussion,11 the smaller anatomical orbit dimensions in Asians, especially the shorter vertical diameter,14–16 might contribute to the remarkable frequency of superior rectus involvement in our study compared with the frequency in previous studies of white patients. We believe that the predominance of superior rectus involvement in our study may be attributed to the application of retrobulbar anesthesia and an anatomical difference of orbit. We appreciate that Chan and coauthors gave us the opportunity to clarify 1 of the points in our article.dSoo
Kyung Han, MD, Jeong Hun Kim, MD, Jeong-Min Hwang, MD
References 1. Catalano RA, Nelson SB, Calhoun JH, et al. Persistent strabismus presenting after cataract surgery. Ophthalmology 1987; 94:491–494 2. Rainin EA, Carlson BM. Postoperative diplopia and ptosis; a clinical hypothesis based on the myotoxicity of local anesthetics. Arch Ophthalmol 1985; 103:1337–1339
3. Mun˜oz M, Capo´ H, Siatkowski RM. Results of surgery for vertical strabismus following cataract extraction performed under local anesthesia. Binocul Vis Strabismus Q 1996; 11:275–280 4. Esswein MB, von Noorden GK. Paresis of a vertical rectus muscle after cataract extraction. Am J Ophthalmol 1993; 116:424–430 5. Carlson BM, Emerick S, Komorowski TE, et al. Extraocular muscle regeneration in primates; local anestheticinduced lesions. Ophthalmology 1992; 99:582–589 6. Capo´ H, Roth E, Johnson T, et al. Vertical strabismus after cataract surgery. Ophthalmology 1996; 103:918– 921; discussion by DL Guyton, 921 7. Capo´ H, Guyton DL. Ipsilateral hypertropia after cataract surgery. Ophthalmology 1996; 103:721–730 8. Pearce IA, McCready PM, Watson MP, Taylor RH. Vertical diplopia following local anaesthetic cataract surgery: predominantly a left eye problem? Eye 2000; 14: 180–184 9. Hamed LM, Helveston EM, Ellis FD. Persistent binocular diplopia after cataract surgery. Am J Ophthalmol 1987; 103:741–744 10. Hamed LM. Strabismus presenting after cataract surgery. Ophthalmology 1991; 98:247–252 11. Han SK, Kim JH, Hwang JM. Persistent diplopia after retrobulbar anesthesia. J Cataract Refract Surg 2004; 30: 1248–1253 12. Han SK, Hwang JM. Thyroid disease and vertical rectus muscle overaction after retrobulbar anesthesia. J Cataract Refract Surg 2003; 29:78–84 13. Grimmett MR, Lambert SR. Superior rectus muscle overaction after cataract extraction. Am J Ophthalmol 1992; 114:72–80 14. Hwang K, Baik SH. Surgical anatomy of the orbit of Korean adults. J Craniofac Surg 1999; 10:129–134 ¯ . Morphometric mea15. Karakas P, Bozkir MG, Oguz O surements from various reference points in the orbit of male Caucasians. Surg Radiol Anat 2003; 24:358–362 16. Danko I, Haug RH. An experimental investigation of the safe distance for internal orbital dissection. J Oral Maxillofac Surg 1998; 56:749–752
Proper statistical methods required to compare clinical measurements
O
strin and Glasser1 compare 4 techniques of the standard clinical ‘‘push-up’’ method for measuring the amplitude of accommodation. The assessment of their data is based on the statistical method of regression analysis. The inappropriate selection and use of this analysis can and does result in misleading
J CATARACT REFRACT SURG—VOL 31, MAY 2005
865
LETTERS
Table 1. The coefficient of variation of the amplitude of accommodation for each method used by Ostrin and Glasser1 (calculated using the data given in Table 1). Coefficient of Variation (%) Age Group (Y) Method of Measurement Push up
31–35
36–40
41–45
46–50
51–55
24.6
15.2
18.2
38.2
45.2
Mean of All Age Groups 28.3
Minus to blur
36.6
31.9
31.0
46.8
31.3
35.5
Focometer
38.4
26.1
14.2
29.0
29.2
27.4
HCR with trial lenses
49.4
47.8
34.8
51.6
52.5
47.2
HCR with plocarpine
21.1
58.2
14.4
41.8
86.1
44.3
HCR Z Hartinger coincidence refractometer
conclusions.2 The appropriate statistical method for comparing clinical measurement techniques was well described in the classic paper by Bland and Altman2 in 1986. We are unable to correctly reanalyze their data since the authors do not provide sufficient data for our independent evaluation by the Bland-Altman method. However, a comparison of the precision of the authors’ techniques can be evaluated from their data. This is achieved by determining the coefficient of variation expressed as a percentage (%CV):3
Standard Deviation 100 %CV ¼ Mean
The smaller the %CV, the better the precision. Calculation of the %CV of each of the techniques by using the mean and standard deviation of the measurements provided by Ostrin and Glasser1 demonstrates that, contrary to the authors’ conclusions, the Hartinger measurements are the least precise (Table 1). In brief, inadequate sample size within each subgroup and inappropriate selection and application of statistical methods can lead to incorrect conclusions. Ostrin and Glasser have not addressed these issues in their methodology and analysis, leaving their conclusions without scientific merit. RONALD A. SCHACHAR, MD, PHD Dallas, Texas, USA
References 1. Ostrin LA, Glasser A. Accommodation measurements in a prepresbyopic and presbyopic population. J Cataract and Refract Surg 2004; 30:1435–1444 866
2. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986; 1:307–310 3. Indrayan A, Sarmukaddam SB. Medical Biostatistics. New York, Marcel Dekker, Inc. 2001; 125–127
Reply: We are pleased to see that Schachar has read our recent article on accommodation measurements in a prepresbyopic and presbyopic population.1 The purpose of the paper was to identify appropriate methods to do objective accommodation measurements in the target population of accommodation restoration procedures and to show that subjective measurements of accommodation overestimate the true objectively measured accommodative amplitude. Regression analysis was simply used to illustrate the differences between methods, not to perform a statistical analysis. We are, of course, aware of the Bland-Altman analysis as a statistical procedure to compare methods.2 In our paper, we clearly demonstrate and describe that there are individual variations in accommodative amplitude due to interindividual differences in response to pilocarpine and trial lens-induced blur. The coefficient of variation that Schachar used simply expresses this interindividual variation and does not, as he suggests, evaluate the precision of the measurement methods. A Bland-Altman analysis of the data would also simply express the interindividual variations and not evaluate the precision of the measurement methods. We made no claims about the precision of the Hartinger measurements based on the results in our study. It is Schachar’s attempt to evaluate the precision of the Hartinger measurements with our data rather than the conclusions we reached that is without scientific merit. The point of our paper, and indeed the very reason we undertook the study, was to demonstrate that objective tests exist for accommodation measurement. It is the use of such objective accommodation measurements that demonstrates the absence of accommodation restoration in scleral expansion patients.3,4 A statistical analysis is not required to identify
J CATARACT REFRACT SURG—VOL 31, MAY 2005