Factors Affecting Predictability of Radial Keratotomy DONALD R. SANDERS, MD, PhD,* MICHAEL R. DEITZ, MD,t DIANNE GALLAGHER*

Abstract: A major criticism of radial keratotomy (RK) has been its lack of predictability, a lack due in large measure to the use of simple correlational statistics assessing the relationship between refractive result and each predictor­variable being evaluated separately. This report utilizes multivariate analysis in an attempt to account for the effects of a number of predictor-variables simul­taneously. Variables studied are patient age, optical zone size, number of in­cisions, mean incision depth, preoperative average keratometry, preoperative average applanation tension, patient sex, and age-sex interrelationship. The area of the optical clear zone selected by the surgeon was found to be the most important factor determining refractive change as a result of RK, explaining one-quarter to one-half of the variability of the procedure. The effects of the other factors and the limitations of the method are discussed. Although this method cannot produce a fully predictive equation, we believe this analysis can serve as a good starting point for beginning RK surgeons and a method by which experienced RK surgeons can improve their techniques. [Key words: multivariate analysis, predictor-variable, radial keratotomy, refractive result, regression analysis.] Ophthalmology 92: 1237 -1243, 1985

Radial keratotomy (RK) is currently being performed in virtually every major city in the United States. Ap­proximately 150,000 RK procedures have been performed in this country since its introducti"on here in 1978 by Bo­res, based on the work of Fyodorov in Russia.! This rapid growth has been stimulated by a number of reported series documenting reasonable safety and efficacy.2-7

One major criticism ofRK, however, has been that the results were unpredictable.8 Much of this criticism has been based on analysis of data using simple correlational statistics assessing the relationship between outcome and each individual predictor-variable being evaluated sepa­rately.

Clearly, a better approach would be to use multivariate analysis, attempting to account for the effects of a number of predictor-variables simultaneously. Such an analysis, using stepwise and best subset regression analysis, was performed in an experimental setting by Jester et al.9 who

From the Departments of Ophthalmology, University of Illinois at Chicago: and Bethany Medical Center, Kansas City, Kansas.t

Presented at the Eighty·ninth Annual Meeting of the American Academy of Ophthalmology, Atlanta, Georgia, November 11-15,1984.

Reprint requests to Donald R. Sanders, M.D., Ph.D., 1855 w. Taylor St., Chicago, IL 60612.

looked at effects ofRK in human cadaver eyes. This report documents the application of a similar method in a clinical setting.

PATIENTS AND METHODS

Factors affecting the predictability of radial keratotomy were studied in two separate series of cases, both operated upon by the same surgeon (MRD). The first 290 consec­utive RK procedures (series 1) were operated upon be­tween November 16, 1979, and January 4, 1982.7 A car­bon steel blade was used for performing the incisions in this series. In series 2, a diamond knife was used in 189 consecutive radial keratotomies performed between De­cember 1, 1982, and August 1, 1983. For purposes of analysis only cases with preoperative myopia of7.5 D or less were used (series 1, N = 265; series 2, N = 170).

Data from the one-year postoperative visit were used for the first series since it was the latest visit that was reasonably complete. Since the follow-up was much shorter in the second series, three-month data were the latest reasonably complete measurement. We have pre­viously reported relative refractive stability of the surgeon's results between 3 months and 12 months,7 and analysis of 12-month data available for the second series corrob­orated this finding.

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OPHTHALMOLOGY • SEPTEMBER 1985 • VOLUME 92 • NUMBER 9

Table 1. Descriptive Characteristics of Study Population

Number of patients Age Sex (% male) Number of Eyes Preoperative

Spherical equivalent Average keratometry Optical zone size

Mean incision depth Intraocular pressure Number of incisions (% 16 cuts) Change in spherical equivalent (D) Postoperative spherical equivalent (D)

* 12 months. t3 months.

Series 1 *

152 31.5 ± 8.3 40%

232

-4.5 ± 1.4 44.4±1.3 3.4 ± 0.5

89.9 ± 6.3 15.4 ± 3.1 32% 4.8 ± 1.6* 0.3 ± 1.3*

Series 2t

106 32.7 ± 8.4 44%

124

-4.0 ± 1.6 44.1 ± 1.5

3.6 ± 0.7 87.7 ± 5.4 15.3 ± 3.2 7% 4.1 ± 1.7t 0.0 ± 0.8t

Complete preoperative and 12 month follow-up data were available for 232/265 (87.5%) of the eyes in series 1; complete preoperative and three-month follow-up data were available for 124/170 (73%) of the eyes in series 2. Table I presents descriptive statistics for the variables studied for the two series. Patient, preoperative, and sur­gical characteristics of the two groups were similar except that the second series had more milder cases, thus the average preoperative myopia was less, the average optical zone size used was larger, and there were fewer 16-incision cases.

The preoperative and surgical variables studied in­cluded patient age, patient sex, optical clear zone area, number of incisions, average keratometry, intraocular pressure, corneal diameter, paracentral corneal thickness, and Maklakov tonometry measurements.

At the time of the three-month examination, the Haag­Streit optical pachymeter was used to measure the depth of each radial incision within a millimeter of the optical clear zone. The technique consisted of measuring the

depth, or "thickness," of scar and immediately measuring the apparent corneal thickness with the same positioning of the device. Dividing the first measurement by the sec­ond produced the ratio of radial incision depth to corneal thickness at that point. The result can be expressed as a percentage of radial depth.

Using this percentage eliminates error due to nonper­pendicularity because any foreshortening or oblique lengthening affects both measurements proportionately. The mean of the 8 deepest incisions was used for all cal­culations, including 16 incision cases.

The technique for determining which factors signifi­cantly affected refractive outcome was multiple regression analysis. This method analyzes the relationship between a dependent or criterion variable (in this case, change in spherical equivalent due to RK surgery) and a set of in­dependent or predictor-variables (patient age, optical zone size, achieved incision depth, and the like).

We "screened" variables for effect by seeing if a linear form of the variable entered into a stepwise multiple regression equation, requiring P = 0.15 for inclusion, us­ing the first RK series. A number of interactive terms that made sense clinically were also added. A series of regres­sion models using subsets of the predictor-variables were then fitted to the data and coefficients of determination (~) calculated in order to determine the best subset model for prediction.

A subset of variables, which accounted for the largest proportion of the variability in change in spheric~l equiv­alent and made sense from a clinical standpoint, were determined and incorporated into the final regression equation for the first series. Nonlinear forms of the vari­ables studied were tested but none provided a significantly better description of the relationship than the linear forms.

For the second series studied, we determined the "best fit" coefficients using the exact variable forms, as in the final regression equation for series 1. The final regression equations for series 1 and 2 were tested against both series 1 and series 2 for goodness of fit. It was expected that the

Table 2. Fitted Regression Coefficients for Final Prediction Model

Series 1 Series 2

% Order of % Order of Increase in Entry into Increase in Entry into

Coefficient Cumulative r2 Predictability Model Coefficient Cumulative r2 Predictability Model

Clear zone area -0.2998 0.26 1 -0.2891 0.52 1 Mean incision depth 0.1015 0.42 16 2 0.0771 0.59 7 2 Age 0.0550 0.48 6 3 0.044 0.61 2 5 Sex* 1.627 0.50 2 4 1.261 0.61 0* Number of

Incisionst 0.0654 0.52 2 5 0.189 0.68 7 3 lOP 0.0707 0.53 1 6 0.0339 0.68 0* Preoperative

Average K 0.1552 0.55 2 7 0.2347 0.72 4 4 Sex x age -0.0358 0.56 1 8 -0.0330 0.73 1*

* Female = 0, Male = 1. t <16 cuts = 0 16 cuts = 1. * did not meet 0.15 significance level for entry into stepwise model.

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SANDERS, et al • RADIAL KERATOTOMY

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Fig l. Scatterplots comparing observed change in spherical equivalents to that predicted by the regression equations. Oblique line represents equivalence

line. Circles indicate individual cases; triangles, two cases; and squares, three cases. Top left, series 1 data tested against series 2 regression equation.

Top right, series I data tested against series 1 regression equation. Bottom left, series 2 data tested against series I regression equation. Bottom right,

series 2 data tested against series 2 regression equation.

prediction accuracy of the fonnulas for the populations

from which the parameters of the fonnula were derived

(ie. series 1 fonnula tested against series 1 data) would be

better than the prediction accuracy for the other popu­

lation (ie. series 1 fonnula tested against series 2 data).

However, it is the latter comparison that gives us confi­

dence as to whether the impact of these predictor-variables

remains constant over time even in the same surgeon's

hands.

RESULTS

The following factors appeared in the stepwise regres­

sion equation for the first series: patient age, optical zone

size, number of incisions, mean incision depth, pre­

operative average keratometry, preoperative average

applanation tension, patient sex, and an age-sex inter­

relationship. This combination of 8 tenns explained

56% of the variability of the procedure in the first series

(Table 2). When these factors were placed into a stepwise regres­

sion model, optical zone area was selected as the predictor­

variable which accounted for the largest proportion of the

variability in refractive outcome (26%). Mean incision

depth explained an additional 16% of the variability; the

selection of age in step 3 improved the predictability of

refractive outcome by 6%. Inclusion of the remaining five

variables (sex, number of incisions, preoperative intra­

ocular pressure, preoperative average keratometry, and

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OPHTHALMOLOGY • SEPTEMBER 1985 • VOLUME 92 • NUMBER 9

OAT A SERIES 1 SERIES 1 SERES 2 SERfES 2

EQUATION SERIES 2 SERIES 1 SERIES 1 SERIES 2

Fig 2. Frequency block chart showing goodness of fit of the regression equations derived from series 1 and 2 to the actual observed outcome. A positive value reflects an overprediction by the model tested; a negative value reflects an underprediction. The data in columns 1 through 4 sum­marizes findings in the various parts of Figure 1, respectively. Numbers given in each block are percent of patients.

sex-age interaction) increased the predictability of the model by an additional 8%. Analysis of residuals indicated that the predicted outcome was within 1.5 D of the ob­served outcome in 84% of the cases and within 1 D in 66% of the cases (Figs 1 top right, 2).

. The same battery of predictors which met the 0.15 sig­~lficance level for entry into the stepwise regression equa­tIon for the first series were incorporated into a regression model for the second series. The combination of these factors accounted for 73% of the variability in refractive outcome. As in the first series, the largest proportion of the va?a~i~ity was explai~ed .by optical zone area (52%); mean InClSlOn depth, WhICh Increased the predictability by 7%, was the second variable included in the stepwise model. Number of incisions, defined as either < 16 cuts or 16 cuts, was selected as the third variable and improved the predictive accuracy by 7%. The remaining five vari­ables ex~lained an additional 7% of the variability (Table 2~. Sex, Intraocular pressure, and the sex-age interaction dId not contribute significantly to the prediction outcome for this series, ie. they did not meet the 0.15 significance level for entry into the model. In this series, the predicted spherical equivalent was within 1.5 D in 94% of the cases and within 1 D in 84% of the cases (Figs 1 bottom right, 2).

When the equation derived from series 1 data was fitted to series 2 data, the predicted outcome was within 1.5 D of the actual value in 93% of the cases and within 1 Din 78% ofth.e cases.(Figs 1 bottom left, 2). Conversely, when the equatIon denved from series 2 data was fitted to series 1 data, 76% of the predicted outcome values were within 1.5 D of the actual value and 63% were within 1 D (Figs 1 top left, 2).

DISCUSSION

Information concerning the patient-related and surgery­related factors which significantly affect the amount of correction obtained with RK have come from original

1240

work by Fyodorov;2 a number of experimental studies on animals and cadaver eyes; 10 and clinical observations by Thornton II and other surgeons in the United States. Sta­tistical analysis of radial keratotomy data using such tech­niques as multiple regression analysis provides yet another means of studying the extent to which these factors can contribute to predictability of visual outcome as a result of RK surgery.

However, a number of limitations must be noted in the application of regression analysis to determine pre­dictive equations or guidelines for surgery as opposed to merely determining which factors affect the refractive outcome of radial keratotomy.

For example, one cannot extrapolate results outside the range of the variable in the data set from which the data were derived. For instance, the surgeon only used 8, 12, or 16 incisions so the results of a four-incision RK procedure cannot be predicted accurately from these data. Likewise, since the surgeon attained incision depths of between 66% and 99%, the results of radial keratotomies with less than 66% cannot be accurately predicted.

As a corollary, in areas where the data are sparse the prediction accuracy in that range is likewise suspect. Since the surgeon operated upon few patients over the age of 50 (3%), the relationship between age and refractive out­come in this range is less clear than is this relationship in patients between 20 and 35 years of age which was the age range of the majority of patients. This same argument is true for patients with abnormally high or low preop­erative keratometry or intraocular pressure measurements. Thus, "average" cases are better predicted and prediction accuracy of cases with values at the extreme of normal is suspect. Surgeon variability has not been tested in our model since one person performed all of the surgery.

Another limitation of regression analysis is that this method cannot readily differentiate the fit oflinear versus nonlinear forms of a variable in the regression equation. ~n one model we studied, the square of the preoperative Intraocular pressure appeared to be slightly more predic­tive than the linear form. However, the model using the squared form predicted that with lOP greater than 21 the refractive effect decreased, a result clearly at odds with clinical observation. This points to the fact that the strict a~p~ication of statistics without an understanding of the clImcal aspects of the system involved is potentially dan­gerous. In areas where data are scarce, clinical judgment may be the only tool available upon which to make a surgical judgment.

OPTICAL ZONE SIZE

In our study the area of the optical clear zone selected by the surgeon was the single most important factor de­termining refractive change in RK, explaining one fourth to one half of the variability of the procedure. Within the range of 3.0 mm to 4.5 mm optical clear zone, reduction of the optical zone size by 0.5 mm resulted in slightly less than 1.0 D of additional myopia correction on the average (Fig 3, top left). This approximately 2: 1 ratio between my­opia correction in diopters and optical zone size in mm

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SANDERS, et al • RADIAL KERATOTOMY

EFFECT OF OPTICAL ZONE SIZE 6

ON CHANGE IN SPHERICAL EQUIVALENT

5.5

5

4.5

.. 3.5

3

2.5

2 3 .00 3.50 4.00

OPT/CAL ZONE SIZE C SERIES I + SERIES 2

EFFECT OF PATIENT AGE AND SEX ON CHANGE IN SPHERICAL EQUIVALENT

5.5

4.5 --2.5

2+--------------------,--------------------4 25

MALES -r 0 Series 1

L + Series 2

35

PATIENT AGE

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l 6 Series 2

45

4.50

EFFECT OF INTRAOCULAR PRESSURE 6 .-__________ O_N __ C_H_A_N_G_E_'N __ S_P_H_E_R_'C_A~L~E~Q~U_'V_A=L=EN_T __________ -,

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5

4.5

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3.5

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2.5

10 15 20 25

INTRAOCULAR PRESSURE C SERIES 1 + SERIES 2

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EFFECT OF INCISION DEPTH 6

ON CHANGE IN SPHERICAL EQUIVALENT

5.5

5

4.5

4

3 .5

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2.5

2 70 80 90 100

INCISION DEPTH c SERIES I • SERIES 2

EFFECT OF NUMBER OF INCISIONS QN CH"NGE IN SPHERICAL EQUIVALENT 6,-----------------__ ~ ____ ~~~~ ________ --.

5.5

3 .5

3

2 .5

2 +-----------------------------------------------~ 8 16

NU"'SER OF INCISIONS o SERIES 1 + SERIES 2

EFFECT OF KERATOMETRY READINGS ON CHANGE IN SPHERICAL EQUIVALENT 6,-------------------------------------------,

5.S

5

4.5

4

3 .5

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2+--------------r-------------,-------------4 42 46 48

KERATO"'ETRY READINGS C SERIES 1 • SERIES 2

Fig 3. The effect of preoperative and surgical variables on change in spherical equivalent as predicted by the series 1 and series 2 regression equations. Mean or median values for the other factors known to affect spherical equivalent in the regression equations were used when each variable was examined individually. All graphs have the same Y scale so that the steepness of the curves reflect the relative effect of each variable on refractive outcome within the physiologic range. The following variables were found to affect outcome: top left, optical zone size-nonlinear representation is due to the use of the area rather than diameter of the central zone in the equation; top right, mean incision depth; middle left, patient age and sex; middle right. number of incisions; bOl/om left, preoperative intraocular pressure; and bOl/om right, preoperative average keratometry.

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OPHTHALMOLOGY • SEPTEMBER 1985 • VOLUME 92 • NUMBER 9

has also been found by Thornton. 12 In the smaller optical zone size range (3.25 mm or less), decreases in optical zone size may possibly result in much larger changes in refractive outcome. Evidence for this is the reported case of marked overcorrection due to inadvertent surgical in­cursion into the central clear zone.6 It is likely that with larger clear zones (above 4.5 mm), as the clear zone is increased even further, refractive effect may drop off rap­idly.

INCISION DEPTH

The exact mathematical relationship between incision depth and refractive outcome is unknown primarily due to the difficulties in accurately measuring incision depth. Nevertheless, there is little doubt that deeper corneal in­cisions result in more refractive effect. In a series of studies on cadaver eyes, Jester et a1.9 demonstrated that the most important factor in producing significant corneal flatten­ing was depth of the incision. We found that incision depth was second only in importance to optical clear zone (Fig 3, top right) and could explain an additional 7 to 16% of the variability in refractive outcome, depending on the series studied.

Determining just how to attain the desired incision depth may also be a problem since ultrasonic pachymetry instruments differ in design and calibration as do diamond knives and the gauge blocks used to assess blade extension. Because of these variations, the surgeon must "titrate" or individualize his method of setting his diamond knife based on ultrasonic pachymetry and postoperative slit­lamp observation of previously achieved results in order to obtain his desired corneal incision depth.

PATIENT AGE AND SEX

It is a well known clinical phenomenon that older pa­tients show more effect for the same amount of surgery than younger ones. This age related increase may be due to an increase in scleral rigidity. In addition, our study revealed that young females do not receive as much re­fractive effect for the same amount of surgery as young males; this difference tends to diminish with age (Fig 3, middle left). It is interesting to speculate that possibly these differences could be related to hormonal influences on collagen and that with the aging process the hormonal differences between men and women decrease.

NUMBER OF INCISIONS

The refractive effect of varying the number of incisions in animal and cadaver eyes has been summarized in detail by Salz.1O We have found that a 16-incision RK increases the effect of an 8 incision case by approximately 0.5 D to 1.5 D. (Fig 3, middle right) In our study, 16-incision radial keratotomies were performed in cases with 3 mm optical zones that required somewhat more correction than could be expected with 8 incisions. Others have suggested the effect of an additional 8 incisions at the time of surgery can be as much as 1.75 D to 2.0 D. Rowsey et al has shown less effect with 16 incisions than with 8 incisions.8

1242

As Salz lO has pointed out, the amount of additional effect in a 16-incision case may depend on the depth of the original 8 incisions.

INTRAOCULAR PRESSURE

It is generally believed that a higher postoperative in­traocular pressure results in more refractive effect with RK surgery. 11 Some surgeons even advocate the use of steroids in undercorrected individuals to induce an in­crease in intraocular pressure and thus a greater effect. We have found that preoperative intraocular pressure may have some slight predictive value. With all other factors being equal, a patient with a preoperative intraocular pressure of 20 mmHg could expect to obtain as much as 0.25 to 0.5 D more effect from the same amount of surgery as a patient with a preoperative tension of 10 mmHg (Fig 3, bottom left). Thornton believes that the effect of surgery is lessened with preoperative pressures below 11 mmHg and enhanced with pressures above 19 mmHg.12

PREOPERATIVE AVERAGE KERATOMETRY

One can expect a slightly greater effect from the same amount of surgery in a patient with a steep cornea than in a patient with a flat cornea. The difference in refractive effect was only about I D within the physiologic range of preoperative keratometry measurements from 42 D to 46 D (Fig 3, bottom right).

Finally, in the strictest sense, our work does not produce a predictive equation based on known preoperative or surgical variables alone since our incision depth mea­surements were determined postoperatively and could not have been known preoperatively. In spite of the limitations noted in this report, we believe it is worthwhile to use this type of analysis to serve as the basis for a clinical tool that helps beginning RK surgeons have a good starting point and helps experienced ones to "fine tune" their surgery.

REFERENCES

1. Villasenor RA. The history of radial keratotomy. In: Sanders DR, Hof­mann RF, eds. Refractive Surgery: A Text of Radial Keratotomy. Tho­rofare NJ: Slack, 1985; 1-8.

2. Fyodorov S, Durnev VV. Operation of dosage dissection of corneal circular ligament in cases of myopia of mild degree. Ann Ophthalmol 1979; 11 :1855-90.

3. Bores LD, Myers W, Cowden J. Radial keratotomy: an analysis of the American experience. Ann Ophthalmol1981; 13:941-8.

4. Hoffer KJ, Darin JJ, Pettit TH, et al. Three years experience with radial keratotomy; the UCLA study. Ophthalmology 1983; 90:627-36.

5. Nirankari VS, Katzen LE, Karesh JW, et aI. Ongoing prospective clinical study of radial keratotomy. Ophthalmology 1983; 90:637-41.

6. Arrowsmith PN, Sanders DR, Marks RG. Visual, refractive, and ker­atometric results of radial keratotomy. Arch Ophthalmol 1983; 101: 873-81.

7. Deitz MR, Sanders DR, Marks RG. Radial keratotomy: an overview of the Kansas City study. Ophthalmology 1984; 91 :467-77.

8. Rowsey JJ, Balyeat HD, Rabinovitch B, et al. Predicting the results of radial keratotomy. Ophthalmology 1983; 90:642-54.

SANDERS, et al • RADIAL KERATOTOMY

9. Jester JV, Venet T, Lee J, et aI. A statistical analysis of radial keratotomy in human cadaver eyes. Am J Ophthalmol1981; 92:172-7.

10. Salz JJ. Pathophysiology of radial keratotomy incisions. In: Sanders DR, Hofmann RF, eds. Refractive Surgery: A Text of Radial Keratotomy. Thorofare NJ: Slack, 1985; 73-85.

11. Sanders DR, Deitz MR. Factors affecting predictability of radial ker­atotomy. In: Sanders DR, Hofmann RF, eds. Refractive Surgery: A Text of Radial Keratotomy. Thorofare NJ: Slack, 1985; 61-72.

12. Thornton SP. Thornton Guide for Radial Keratotomy Incisions and Optical Size. Nashville TN: Spencer Thornton, 1981.

Discussion by

Roger F. Meyer, MD, David C. Musch, PhD

Radial keratotomy for the correction of myopia has been the subject of much interest and controversy among ophthalmolo­gists over recent years. 1,2 A difficult problem has been the inability to accurately predict the effect of the procedure prior to surgery.3,4 This is an excellent study combining clinical and biostatistical methods in an effort to simultaneously quantify the effects of a number of independent variables on the refractive outcome of the radial keratotomy procedure.

Two series of patients were studied before and after radial keratotomy. By using data gathered from the first series, a regression equation was constructed in an attempt to predict refractive outcome for the second series. Upon application of this equation, the predicted outcome was within 1.5 D of the actual outcome in 93% of the cases and within 1 D in 78% of cases. A second regression equation, based on information from the second series, was then constructed and applied retrospec­tively to the first series of patients. However, with these guide­lines, only 76% of the predicted outcome values were within 1.5 D of the actual value and 63% were within 1 D. It appears that the refractive outcome of the second series of patients was more predictable than the first series, regardless of which guidelines were applied. Perhaps this could be explained by several factors which were different between the two series, including use of a steel blade in the first series and diamond blade in the second,5

and a lesser degree of myopia in the second series.6 It may be that when an experienced surgeon operates on a uniform group of patients with moderate degrees of myopia, the refractive out­come of radial keratotomy one year after surgery will be quite predictable.

Several observations regarding the study methodology and data analysis deserve comment. Postoperative evaluations were performed by the operating surgeon rather than an independent observer, which may be a source ofbias.7 A number of patients were lost to follow-up, and the effect of this is a concern common to the evaluation of such studies.8 In the data analysis, the authors are to be commended for evaluating the predictive accuracy of the first series' regression equation on results from the second series. A more rigorous evaluation, however, would involve in­dependent data from another surgeon's practice. One wonders if the predictive accuracy remains high in other surgeons' out­comes. A problem in the data analysis is the use of number of eyes as the basis for analysis.9

,10 Since use of data on two eyes from one individual violates assumptions of independence nec-

From the W. K. Kellogg Eye Center, University of Michigan Medical School, Ann Arbor.

essary to regression analysis, it would have been preferable for the authors to limit their analysis to one eye per individual, chosen randomly.

Of special interest, and potential importance, is the finding of increased hyperopia four years after radial keratotomy, even though refractive change appeared to stabilize by three months after surgery. No variables tested in the present study were as­sociated with the latent hyperopic refractive change. Even though vision may not yet be affected by the latent hyperopia, over­correcting the eyes of young individuals with myopia may be­come a significant problem in a few years because presbyopia may be hastened. I I Although current studies indicate that radial keratotomy is a safe and efficacious surgical procedure,12 caution must be exercised. Long-term effectiveness is not yet predictable and late complications are poorly defined.8 The ultimate role of radial keratotomy in the treatment of myopia remains uncertain but may become more clearly defined by continued close sur­veillance and long-term follow-up studies.

References

1. Bores LD. Radial keratotomy. I. A safe, efficacious way to correct a handicap. Surv Ophthalmol1983; 28:101-5.

2. Stark WJ, Martin NF, Maumenee AE. Radial keratotomy. II. A risky procedure of unproven longterm success. Surv Ophthalmol1983; 28: 101,106-11.

3. Rowsey JJ, Balyeat HD, Rabinovitch B, et al. Predicting the results of radial keratotomy. Ophthalmology 1983; 90:642-54.

4. Nirankari VS, Katzen LE, Karesh JW, et al. Ongoing prospective clinical study of radial keratotomy. Ophthalmology 1983; 90:637-41.

5. Unterman SR, Rowsey JJ. Diamond knife comeal incisions. Ophthalmic Surg 1984; 15:199-202.

6. Cowden JW. Radial keratotomy; a retrospective study of cases ob­served at the Kresge Eye Institute for six months. Arch Ophthalmol 1982; 100:578-80.

7. Waring GO III, Arentsen JJ, Bourque LB, et al. Design features of the prospective evaluation of radial keratotomy (PERK) study. Int Ophthal­mol Clin 1983; 23(3):145-65.

8. Hoffer KJ, Darin JJ, Pettit TH, et al. Three years experience with radial keratotomy; the UCLA study. Ophthalmology 1983; 90:627-36.

9. Ederer F. Shall we count numbers of eyes or numbers of subjects? Arch Ophthalmol1973; 89:1-2.

10. Ederer F. Methodological problems in eye disease epidemiology. Ep­idemiol Rev 1983; 5:51-66.

11. Rowsey JJ, Balyeat HD. Preliminary results and complications of radial keratotomy. Am J Ophthalmol1982; 93:437-55.

12. Kremer FB, Marks RG. Radial keratotomy: prospective evaluation of safety and efficacy. Ophthalmic Surg 1983; 14:925-30.

1243