Effects of peripheral redeepening on radial keratotomy surgery

Effects of peripheral redeepeoiog Stanley C. Grandon, M.D. Dearborn, Michigan

00

radial keratotomy surgery

Gary M. Grandon , Ph.D. Greensboro, North Carolina

ABSTRACT In recent years , considerable attention has been given to the longand short-term effects of radial keratotomy. These effects vary according to a number of key surgical parameters , including optical clear zone size , number of incisions, depth of incisions , and placement of incisions. This paper examines the effect of peripheral redeepening on standard eight-incision radial keratotomy. By comparing a series of cases with 3-mm clear zones ,we found that, on average , an additional 0.47 diopters of correction could be directly attributed to peripheral redeepening after controlling for the effects of preoperative myopia, age, and other related measures. This additional correction could be beneficial to patients in whom maximum effects are desired . Key Words: peripheral r edeepening, radial k eratotomy

Radial keratotomy (RK) surgery has proven to be a satisfactory technique for treating myopia in a large class of patients.l- 7 It has been shown that the technique is effective and yields appropriate amounts of refractive correction when patients are within certain physiological bounds. These include the degree of preoperative myopia, the age of the patient , and other less important measures (G.M. Grandon , s.C. Grandon, Computer predictability analysis: Radial keratotomy data, KeratoRefractive Society, San Francisco, 1985; Causal modeling of RK, a computer analysis, International KeratoRefractive Surgery Socie ty, New Orleans , 1986).4,8 This study examines the effect of peripheral redeepening procedures used to increase the refractive correction of RK surgery. Radial keratotomy surgeons have debated whether redeepening the incision at surgery improves the overall result. The rationale for redeepening seems obvious. The periphery of the cornea is always thicker than the center. By advancing the diamond blade and reentering the incisions and deepening them in the

periphery, it would seem that greater peripheral weakening would be achieved, thus allowing for greater peripheral deformation and greater central flattening. Schachar's quantitative RK theory9 suggests that the effect of redeepening is due to the relative lengthening of incisions. According to his tables, we should expect approximately 0.33 diopters (D) of effect by lengthening an incision from 3.0 mm to 4.5 mm. The current study atte mpts to determine the amount of refractive correction that can be attributed to peripheral redeepening. To determine this, we must control for other concomitant influences. Unfortunately, many surgical studies do not lend themselves to pure experimental tests . Few physicians will withhold optimal treatment procedures from patients for the sake of experiment, particularly when theory and clinical judgment indicate otherwise. For situations in which prospective assignment of patients to treatment groups is not appropriate, a battery of powerful statistical techniques have been developed.l°.l l These

From the Eye Surgery Institute, Dearborn, Michigan , and the University of North Carolina , Greensboro. Reprint requests to Gary M. Grandon , Ph .D., Academic Computer C enter, 235 Business and Economics, University of North Carolina , Greensboro, North Carolina 27412. 268

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techniques are able to adjust "statistically" for group differences before testing specific hypotheses about group outcomes. In this study, the analysis of covariance was used to examine the differences in the preoperative/postoperative change in spherical equivalent, while statistically controlling for variations in preoperative myopia, patient age, weeks on steroids, and other known or suspected determinants of surgical outcome. We also examined cases with preoperative spherical equivalents between - 4.75 D and - 5.25 D to control for preoperative concomitant influences. We limited our investigation to eyes that had had only spherical procedures performed on them (preoperative cylinder of less than 1 D), maximal attempted corrections, and three months or longer follow-up. From this group, we compared cases with redeepening and those without.

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Fig. 1.

MATERIALS AND METHODS Patients had complete eye examinations with cycloplegic refraction using 1 % cyclopentolate hydrochloride (Cyclogyl®). Keratometry was performed using the Bausch & Lomb keratometer. Using ARK study nomograms 8 and later the Grandon predictability software 12 (based on multiple regression analysis ofSCG's cases), the clear zone size was determined using predictive parameters of age, sex, axial length, keratometry, and corneal diameter. Peripheral redeepening was performed at surgery if the patient's myopia was at least 1.5 D greater than a 3-mm optical zone without redeepening would, by prediction, correct. All cases used for this study had eight incisions. Pachymetry using the Storz cornea scan CS 1000 was performed preoperatively using central, four paracentral, and four peripheral readings (paracentral readings were in a circle with a diameter of 3 mm to 4 mm from the central reading). The pachymeter was set at 1,630 meters per second. The RK procedure was performed using the standard American technique, making incisions from the optical zone toward the periphery. Eyes were anesthetized using 4% lidocaine (Xylocaine®) topical anesthesia. The clear zone was marked in the visual axis. An eight-incision radial marker was used to mark the radial incisions. A K.O.I. diamond knife was used in all cases. The knife setting was determined by adding 0.03 mm to the thinnest paracentral ultrasound pachymeter reading. The diamond knife was checked using the Bores blade block and later the Myocure glass blade block. The eight incisions were then made using moderate pressure from the optical zone mark to just short of the perilimbal capillaries. If redeepening was performed, after the initial eight incisions a 5-mm radial marker was placed in the visual axis. The diamond knife setting was then increased 0.03 mm. At the 5-mm mark, the original incisions

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(Grandon) Diagram of RK incisions with and without redeepening.

were reentered and, with moderate pressure, were retraced to the perilimbal area again (Figure 1). After the incisions were made, they were irrigated with balanced salt solution. The eye was irrigated with gentamicin, 5% homatropine was instilled, and the eye was patched. After surgery, gentamicin eye drops were used for 12 days (four times daily) and steroid drops were used after reepithelialization (usually two to three days) for two to six weeks in decreasing doses depending on refraction. Radial keratotomy surgery has been performed over the past several years on over 2,000 eyes (SCC). A range of appropriate surgical techniques have been used for these patients, including peripheral redeepening techniques when indicated. The preoperative, surgical, and postoperative patient data have been collected and maintained using techniques similar to those used by the ARK study. 8 The database consists of over 133 variables for over 4,100 visits. The computerized data reside in an SAS13 database. All data processing and analyses are performed using this software at the University of North Carolina at Greensboro's Academic Computer Center. Of these cases, 231 qualified for inclusion in this study; that is, they had had surgery using spherical procedures, 3-mm clear zones, eight incisions, maximal incision depth, and had follow-ups of three months or longer. Patients with eight-incision surgeries were chosen for this study to control for the known effects of number of incisions on degree of refractive correction. Change variables (i.e., change in spherical equivalent) were calculated as differences from the most recent follow-up visit and the corresponding measurement during the preoperative visit. Other follow-up data were also taken from the most recent follow-up visit (i.e., postoperative spherical equivalent). One hun-

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Table 1. Preoperative overview of patients with maximum RK eight incision surgeries, with and without peripheral redeepening. Without Redeepening (N = 79)

With Redeepening (N = 152)

Variable

Mean

SD

Minimum

Maximum

Mean

Preoperative spherical equivalent

-5.29 D

0.95 D

-3.25 D

-7.7.5 D

-7.03 D

SD

Minimum

Maximum

-3.75 D

-13.13 D

1.58 D

Average keratometry

43.93

1.58

40.50

47.82

44.38

1.49

39.94

47.44

Corneal diameter

11.94

0.44

11.00

13.00

11.91

0.59

10.50

13.00

Axial length

25.46

0.78

23.40

27.30

25.71

1.00

23.40

28.70

Intraocular pressure

18.26

2.14

12.00

22.00

18.38

2.54

11.00

24.00

Patient age

31.68

9.73

17.00

63.00

33.22

9.76

18.00

60.00

Patient sex

57% male; 43% female

46% male; 54% female

Steroids

37% <4 weeks; 63% ?4 weeks

26% <4 weeks; 74% ?4 weeks

dred fifty two of these cases-66%-were redeepened, while 79 cases-34%-were not.

variable is simultaneously predicted by a number of predictor variables. Depending on various statistical assumptions and the relationship among the predictor variables, differentially stable prediction formulas are produced. A related technique appropriate for determining mean differences between groups when a number of other variables also influence that mean is the analysis of covariance.l O,ll,17 As mentioned earlier, this technique is particularly important because it can control nonrandom assignment of patients to treatment groups, which is a common problem of postscriptive studies. The analysis of covariance allows for removal of the variation caused by a number of concomitant variables from a predicted variable. lO ,ll,17 Means of this residual variable are contrasted for a specific grouping variable. In this instance, our grouping variable is redeepening, our predicted or dependent variable is change in spherical equivalent, and our preoperative covariates or concomitant variables, which also influence the value of postoperative spherical equivalent, are preoperative spherical equivalent, age, corneal diameter, axial length, intraocular pressure, patient sex, average keratometry, and weeks on steroids. This analysis was performed using the SAS18 CLM (general linear models procedure) on the maximal surgery cases described earlier. The statistical summary is presented in Table 3. Table 3 shows that redeepening has achieved a significance level of 0.0268. vVe must remember,

RESULTS A preoperative overview of patients is presented in Table 1. The patients exhibited differences in spherical equivalents and sex, but differences in other areas were less obvious. Table 2 shows there were significant differences between spherical equivalents in redeepened and nonredeepened cases. The mean difference between change in spherical equivalent for cases that were redeepened and those that were not was 1.63 D. It would be inappropriate to assume that redeepening was the only cause for this change in spherical equivalent. We must look more carefully at causes of differential outcomes in RK surgery. At present, a number of computer programs predict the outcome ofRK surgery. 12,14-16 More formal reports of predictive formulas are few (C.M. Crandon, s.c. Crandon: Causal modeling ofRK, a computer analysis, International Kerato-Refractive Surgery Society, New Orleans, 1986).4,16 Most programs and authors agree that some combination of the measures in Table 1 account for between 30% and 80% of the variation in patient outcome. The amount of explained variance depends on the degree of preoperative myopia and other factors. Multiple regression analysis 17 is the most common technique used for this type of statistical modeling. With multiple regression, one outcome

Table 2. Mean changes in spherical equivalent and average keratometry, with and without redeepening, three months or more after surgery. Without Redeepening (N = 79) Variable

Mean

SD

Change in spherical equivalent

4 ..51 D

1.34 D

Change in keratometry

270

-3.44

1.08

Minimum

Maximum

0.63 D -0.32

7.75 D -5.44

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With Redeepening (N = 152) Mean

SD

6.14 D

1.89 D

-4.29

SURG- VOL 13, MAY 1987

1.50

Minimum 2.38 D -1.07

Maximum 13.00 D -9.00

Table 3. Analysis of covariance for maximal surgery cases to determine the effect of redeepening on change in spherical equivalent. The magnitude of the effect of each variable is indicated by its "unique" sum of squares indicated by "Type III SS." DF

Source

Type III SS

F-Ratio

Significance

Redeepening

1

7.67

4.97

0.0268

Preoperative spherical equivalent

1

64.81

41.94

0.0001

Age

1

5.24

3.39

0.0668

Corneal diameter

1

6.87

4.44

0.0361

Axial length

1

9.90

6.41

0.0120

Intraocular pressure

1

2.29

1.49

0.2239

Sex

1

0.37

0.24

0.6248

Preoperative keratometry

1

4.18

2.70

0.1016

Steroids

1

12.7,5

8.2,5

0.0045

Error

221

341.45

Total

230

818.70

however, that we have a directed hypothesis that the mean of the redeepened cases will be larger than the mean of those which have not been redeepened. It is therefore appropriate to judge the contrast between the two residual mean scores by use of a standard onetail t-test. The F-ratio is intrinsically two-tailed and in this case tests the hypothesis that the mean of redeepened cases is the same as nonredeepened cases. In Table 4 we can see that the adjusted mean difference between the two groups of surgeries is 0.47 D and that this difference is statistically significant at the 0.0134 level. To examine the issue of nonproscriptive assignment of cases to surgical treatment groups further, we can look at a group of cases in which the nonredeepened cases are not statistically different from the redeepened ones. We focus on cases with preoperative spherical equivalents between - 4.75 D and - 5.25 D. Our reasoning is as follows: If we select a group of cases in which there are no statistical differences on concomitant measures (spherical equivalent, axial length, time

on steroids, etc.), we can assume that the only influence affecting the change in spherical equivalent is the redeepening procedure. There were 43 cases in this - 4.75 D to - 5.25 D range of preoperative spherical equivalents. Eighteen were redeepened, the remaining 25 were not. A multiple analysis of variance 17 was performed between the two groups (redeepened and nonredeepened). The dependent measures were age, preoperative spherical equivalent, spherical equivalent change, number of weeks on steroids, axial length, intraocular pressure, corneal diameter, preoperative keratometry, and patient sex. None of the univariate contrasts were statistically significant and the multiple F-ratio was 1.4 (df=9.33; p= .2277, nonsignificant), Having been unable to demonstrate group differences in concomitant variables, we repeated the analysis of covariance performed on the whole population of cases. This analysis yielded very similar results. The analysis showed an average group difference of 0.589 D (significant at P = .042) even after again controlling for the same set of concomitant variables. DISCUSSION The overall effect of redeepening in this series of surgeries was 0.47 D when other likelv concomitant effects were filtered out. This is both statistically significant and clinically important. An examination of postoperative visual acuity for the two groups showed that this additional correction contributed significantly to patient satisfaction (Figures 2 through 6). Figures 2 and 5 show postoperative visual acuity for all cases with and without redeepening. Although the percentage of cases achieving 20/40 or better with redeepening was only 69% as opposed to 73% for those without redeepening, some of the patients qualifying for redeepening had considerably worse acuity preoperatively. When we look at Figures 3 and 6 with cases less than - 6 D of preoperative myopia, we see that the 20/40 success rate was actually greater for those with

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Mean

Standard Error

Signif t-.1",o < M",

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5.27 D

0.16

0.0134

With redeepening

5.74 D

0.10

Mean difference 0.47 D

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redeepening-89% versus 77%. Patients with myopia greater than - 6 D who were redeepened again fared slightly better than those who were not; 62% 20/40 or better as opposed to 59% (Figures 4 and 7). Patients represented in Figure 7 were the most extreme of all cases and ideal results were not anticipated. Even so, many of them were successful. 272

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Our finding of 0.47 D change in spherical equivalent due to redeepening is greater (by 0.14 D) than that predicted from Schachar's mathematical RK model,9 This could be expected because of the discrepancy between the model's length of incision effect and what actually happens during the redeepening procedure. The effect is comparable to that predicted by the model. In conclusion, we have been able to demonstrate (1) that approximately 0.5 D of additional refractive correction can be attributed directly to the peripheral redeepening technique described, (2) that this did lead to improved visual acuity for our patients, and (3) that this technique extends the range of patients for whom improved vision is now a possibility. REFERENCES 1. Bores LD, Myers W, Cowden J: Radial keratotomy: An analysis of the American experience. Ann Ophthalmol 13:941-948, 1981 2. Hoffer KJ, Darin JJ, Pettit TH, Hofbauer JD, et al: UCLA clinical trial of radial keratotomy; preliminary report. Ophthalmology 88:729-736, 1981 3. Nirankari VS, Katzen LE, Karesh JW, Richards RD, et al: SURG- VOL 13, MAY 1987

4. 5. 6.

7. 8. 9. lO.

Ongoing prospective clinical study of radial keratotomy. Ophthalmology 90:637-641, 1983 Deitz MR, Sanders DR, Marks RG: Radial keratotomy: An overview of the Kansas City study. Ophthalmology 91 :467-478, 1984 Arrowsmith PN, Marks RG: Visual, refractive, and keratometric results of radial keratotomy; one-year follow-up. Arch Ophthalmol102:1612-1617, 1984 Waring GO III, Lynn MJ, Gelender H, Laibson PR, et al: Results of the prospective evaluation of radial keratotomy (PERK) study one year after surgery. Ophthalmology 92:177-198, 1985 Fyodorov SN, Agranovsky AA: Long-term results of anterior radial keratotomy. JOcular Ther Surg 1:217-223, 1982 Sanders D, ed: Radial Keratotomy; ARK Study Group. Thorofare, NJ, Slack Inc, 1984 Schachar RA, Black TD, Huang T: Understanding Radial Keratotomy. Denison, TX, LAL Publishing, 1981 Blalock HM Jr: Causal Inferences in Nonexperimental Re-

search. Chapel Hill, University of North Carolina Press, 1964 11. Campbell DT, Stanley JC: Experimental and Quasi-Experimental Designs for Research. Chicago, Rand McNally College Publishing Company, 1963 12. Grandon SC, Grandon GM: Kera-Stat 4.0 Radial Keratotomy Prediction System. Greensboro, NC, Rosen Grandon Associates, Inc, 1985 13. SAS: SAS User's Guide: Basics, Version 5 Edition. Cary, NC, SAS Institute, Inc, 1985 14. Salz JJ: A consumers' guide to radial keratotomy predictive software. J Refract Surg 1:60-67, 1985 15. Sanders DR: Computerized radial keratotomy predictability programs. J Refract Surg 1:lO9-117, 1985 16. Sanders DR, Hofmann RF, Salz JJ, eds: Refractive Corneal Surgery. Thorofare, NJ, Slack Inc, 1985 17. Snedecor GW, Cochran WG: Statistical Methods Sixth Edition. Ames, Iowa State University Press, 1967 18. SAS: SAS User's Guide: Statistics, Version 5 Edition. Cary, NC, SAS Institute, Inc, 1985

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