N, ational Eye Institute statistics for 1968

Quantitative guidelines for exotropia surgery Alan B. Scott, A. Jane Mash, and Arthur Jampolsky The effect of numerous preoperative variables on the amount of surgical correction attained was assessed in a population of intermittent exotropic patients; 54 had bilateral recession surgery, 48 had recess resect surgery. By appropriate multivariate statistical analyses, about 95 per cent of the variance in results of surgery (expressed as change in deviation from preoperative to the postoperative time in prism diopters per millimeter of surgical correction) could be accounted for. A workable scheme for utilizing this data base to guide future surgery is presented in the form of quantitative formulae. In addition to this empirical derivation, insights are provided into the mechanics of ocular muscle operations and the maturation of the eye as it affects strabisvius surgery. Expansion of this approach to a wider ranger of cases and to additional types of cases should result in a greater descriptive and surgical accuracy from strabismus surgery. N, ational Eye Institute statistics for 1968 indicate that 80,000 eye operations were done on patients under 15 years of age most of these for strabismus. Up to 60 per cent of operative results are unsatisfactory, even in the hands of acknowledged experts. 1 - - The treatment for strabismus has changed little over several decades and can be reasonably expected to continue as an important treatment modality for the future. In response to the need for more definitive guidelines to plan surgical procedures, we have derived quantitative formulations incorporating the simultaneous influence of various factors. It is amazing that such systematic consideration of multiple factors From the Smith-Kettlewell Institute of Visual Sciences, Institute of Medical Sciences, 2232 Webster St., San Francisco, Calif. 94115. This research was supported by National Institutes of Health Grants EY 00037, EY 01186, and EY 00299, and The Smith-Kettlewell Eye Research Foundation. Submitted for publication Oct. 3, 1974. 428 is almost wholly missing from the literature. Elementary guidelines such as 1 ml. of surgery for each two prism diopters of deviation have been recognized as inadequate as the effects of other influences have not been considered.*' 4 For example, the change in deviation for each millimeter of surgery increases as the preoperative deviation increases. 5 - <! Individual differences in age, amblyopia, duration of strabismus, incommitance, etc., require adjustments. Unfortunately, the basis for determining the amount of adjustment is generally not specified, and such guidelines only specify that the amount of surgery should be increased or decreased. The surgeon must guess how much this correction factor ought to be. The formulae presented here provide methods for determining the amount of surgery to be performed based on the specific conditions of the patient. Subjects and methods Subjects. Individuals whose pre- and postoperative data served as the basis for the analysis were patients seen at Pacific Medical Center, San Francisco, by the authors. The dates of their

Volume 14 Number 6 Exotropia surgery 429 first visits range from 1949 to 1966. Records of patients to be included in this study were selected with the following restrictions: (1) primary deviation of intermittent exotropia; (2) no previous surgery; (3) surgical correction by either recess-resect procedures (RR) or symmetrical bilateral recession procedures (BLR) with no additional surgical procedures; and (4) less than 20 years of age at time of surgery. Patients satisfying these criteria included 48 (54 per cent male) in the RR group and 54 (33 per cent male) in the bilateral group. Among these individuals, patients who had been examined at 7 ± 2 months postoperatively formed the subgroups which were used for analysis of surgical result at the second time period. This additional criterion reduced the main groups to 28 RR patients and 30 bilateral recession patients. Clinical and surgical methods. Patients were examined preoperatively and postoperatively and surgery was performed by the authors. Surgical procedures included either lateral rectus recession with medial rectus resection or symmetrical bilateral rectus muscle recession. Measurements were made at the end of the surgical procedure. No additional procedures were performed. The decision on the type of surgical procedures and amount of surgery to be performed were estimated by the surgeon on the basis of general guidelines and clinical experience and cannot be explicated. Analytical rationale. Variability in surgical results is a function of the combined effect of differences in many preoperative conditions. Also, various preoperative measures are not independent, but rather are mutually associated to different degrees. Therefore, it is misleading to separately calculate effects of such variables on the effect of surgery. It is necessary to utilize multivariate procedures in order to provide a valid analytic description of the variability in surgical results. Among the several pragmatic uses of multiple regression, the one of principal interest here involves the construction of formulae that will provide adequate and reliable prediction of surgical effect in order to estimate the amount of surgery indicated as a function of a patient's preoperative condition. Therefore, the change in deviation (effect) per millimeter of surgery was designated the dependent variable, allowing linear regression techniques. Direct prediction of millimeter of surgery was found to have a curvilinear relationship with at least some of the predictor variables. The analyses involved the necessary assumption that the amount of correction achieved was the amount intended. In some cases this was inaccurate. As this discrepancy is minimized, additional accuracy will be possible. These formulae, which are applicable to the treatment of exotropic patients by either RR procedures or symmetrical bilateral recession procedures, incorporate multiple adjustments for individual differences in several preoperative and surgical conditions. We found the following conditions of significant predictive value: (1) Magnitude of the preoperative deviations in prism diopters (pd). Among the RR group, the near deviation exceeds the distance deviation in six cases. Consequently, it became apparent in the analyses that it was more appropriate to analyze the surgical effect on the larger deviation whether assessed for near or for distance. Among the bilateral recession group, the magnitude of the near deviation never exceeded the distance deviation so the larger deviation was always the one assessed for distance. (2) Magnitude of the difference between the distance and near deviations. (3) Age at time of surgery (in years). (4) The average of the spherical equivalences calculated for right and left eyes (in diopters). (5) The absolute value of the difference between the spherical equivalences for the two eyes. This is regarded here as an index of anisometropia and is referred to as such in the tables. (6) Magnitude of the difference in distance deviation between the primary position and up gaze. (7) Magnitude of the difference in distance deviation between the primary position and down gaze and (8) For the RR group only: the ratio of the number of millimeters of resection to the number of millimeters of recession. Originally, a large set of predictor conditions was considered. Conditions without significant predictive value were eliminated in step-wise fashion. Among those excluded were: sex, vertical deviations,. preoperative progression rate, over and under actions, and visual acuity. Thus, the effective predictor conditions differ slightly in the RR and BLR groups. This does not necessarily suggest that these excluded conditions are not important. It is possible that the conditions included (above) reflect the presence of such excluded conditions (i.e., are correlated with them), thereby providing indirect indices. Although indirect indices would probably not account for all the variance imposed by these conditions, they would serve to reduce their effect below the level of significance. Indices of surgical result were considered for three intervals of time following surgery. The initial measures are based on the first data recorded postoperatively for each patient; the average time was approximately one month for both groups. For the second interval, data from an at 7 ± 2 months following surgery was selected. The indices for the third interval are based on data from the last recorded for each patient. This time interval is quite variable: it averages about 42-6 months for the

430 Scott, Mash, and Jampolsky Investigative Ophthalmology June 1975 Table I. Means and standard errors with ranges for preoperative measures for the RR group (N = 48) Age at time of surgery Magnitude of larger deviation Magnitude of smaller deviation Difference between larger and smaller deviations up gaze down gaze Vertical deviation Average spherical equivalent Anisometropia Mean ± S.E. 6.3 ± 0.5 25.3 ± 1.0 19.2 ± 1.2 6.1 ± 0.9-0.1 ± 0.3-0.3 ± 0.4 ± 0.05 ± 0.56 ± 0.3 0.2 0.13 0.12 Range 1.5 to 17.4 20 to 45 5 to 35 Oto 16-8 to 10-10 to 8 Oto 6-2.00 to +2.00 Oto 3.25 Table II. Means and standard errors with ranges for preoperative measures for the bilateral group (N = 54) [Mean ± S.. Range Age at time of surgery 5.9 ± 0.5 1.5 to 19.1 Magnitude of larger deviation 25.5 ±1.0 20 to 45 Magnitude of smaller deviation 10.1 ± 1.2 0 to 45 Difference between larger and smaller deviations 15.4 ±1.2 0 to 40 up gaze 0.9 ± 0.5-4 to 20 down gaze 0.6 ±0.6-17 to 20 Vertical deviation 0.6 ± 0.2 0 to 5 Average spherical equivalent 0.18 ±0.14-2.28 to+1.68 Anisometropia 0.57 ±0.11 Oto 2.13 RR group and 34 ± 5 months for the bilateral group. The variability in this time interval can be related to several factors. Since there are individual differences in postoperative drift rates, the length of time involved for a patient's condition to appear reasonably stable or to be definitely deteriorating will vary. Once the attending doctor considered that a patient's condition had stabilized with an acceptable correction, the patient would probably not be required to return for subsequent s. If a patient's deviation were unstable and drifting back to its original magnitude, a second surgery might be performed, resulting in the end of his data that could be included in this study. Other individuals who were regular patients of the eye clinic might continue to have periodic s even though their conditions might have been regarded as stabilized at an earlier date. For these reasons, it was not possible to apply some standard criterion with regard to time in selecting a third that would provide as representative an index of each patient's resultant and/ or stabilized condition. In spite of this lack of standardization, final measures can provide some meaningful indications of long-term results of these two types of surgical treatments. Analytical methods. Partial regressions were calculated by standard multivariate techniques. 7 Tests of significance presented include Student's t-test (t) and Chi square (x 2 ), which are listed with the associated degrees of freedom (df). The symbol "R" in the tables refers to the multiple correlation between the set of predictor variables and the "change in deviation per millimeter" variable. The symbol "R 2 " is the coefficient of multiple determination which indicates the proportion of the variance in the dependent variable that can be explained by variance in the set of predictor variables. Results and discussion Means and standard errors as well as ranges of various indices of the preoperative condition for the two groups are presented in Tables I and II. Recession of the lateral rectus muscles was the preferred procedure when the exodeviation for distance was twice or more the exodeviation for near. The two groups did not differ for any other preoperative measure. The average amount of surgery performed is similar for the two groups: 11.0 ± 0.2 (ranging from 8.5 to 13 mm.) for the RR group and 10.7 ± 0.3 (ranging from 7 to 16 mm.) for the BLR group. Several indices of the result of surgery are presented in Table III. The change in deviation is the difference between the preoperative measure and the measure taken at the time interval indicated. This value, divided by the total millimeters of surgery yields the effect per millimeter of surgery. Comparison of the first and last intervals indicates the amount of postoperative change of deviation (drift) that occurred. For the RR group the amount of drift was 5.5 ± 1.1 pd for the larger deviation and 4.7 ± 0.9 pd for the small deviation. This represents a significant increase in the magnitude of the residual deviation (t = 5.0 and 5.2 df = 4, for the larger and

Volume 14 Number 6 Exotropia surgery 431 Table III. Means and standard errors of indices of surgical result for first and final postoperative s Change in larger deviation Effect per millimeter Change in smaller deviation Effect per millimeter Difference between larger and smaller deviations Drift in surgical correction for larger deviation Drift in surgical correction for smaller deviation Drift in reduction of difference between larger and smaller deviations RR First 23.0 ± 1.2 2.0731 ±0.0979 18.4 ± 1.3 1.6458 ±0.1042 1.6 ±0.6 group Final 17.5 ± 1.4 1 5608 ±0.1194 13.7 ± 1.6 1 2006 ±0.1355-5.5 ± 1.1-4.7 ±0.9-0.7 ±.6 2.3 ± 0.8 Bilateral recession group First 20.7 ± 1.3 1.9320 ± 0.1154 8.9 ± 1.3 0.7805 ±0.1038 3.6 ± 0.9-0.4 ± 0.8-1.2 ±0.7 +0.6 ±0.9 Final 20.3 ± 1.6 1.8902 ±0.1420 7.7 ± 1.5 0.6593 ±0.1229 2.9 ± 1.0 Table IV. Per cent of patients within each group for categories of surgical result by magnitude of residual deviation Postoperative deviation (amount in pd) Eso>2 0±2 3-10 Exo Exo>10 First RR 12.5 54.2 22.9 10.4 Postoperative time Final RR 6.2 22.9 37.5 33.3 Bilateral 9.3 24.1 48.1 18.5 Bilateral 1A 31.5 33.3 27.8 smaller deviations, respectively). About 40 per cent of this occurred by the 7 ± 2 month time interval. For the BLR group the amount of drift for the larger deviation was 0.4 ± 0.8 and 1.2 ± 2.0 pd for the smaller deviation. These measures do not differ much between the first and last intervals suggesting that bilateral recession results in a more stable postoperative condition. Possible reasons for this are discussed below. A breakdown of surgical results for the larger deviation by the percentage which showed various amounts of residual deviation is presented in Table IV. "Eso > 2" represents overcorrections; "0 ± 2" is considered within the range of normal or physiologic hetereophoria 8,9; "3-10 exo" represents undercorrections of 10 pd or less, traditionally considered an acceptable result; "exo > 10" represents residual deviations greater than 10 pd which might require consideration of further surgery. At the initial postoperative time the RR groups showed better results than the BLR group (- = 11.5, df = 3). However, at the final postoperative time, the groups were not different. From this classification it is apparent that individuals within both groups did experience a change in magnitude and, occasionally, in type of deviation. Among the RR group 31 per cent showed no (0 ± 2 pd) change between the two postoperative times compared with 43 per cent for the BLR group. For the 32 RR patients who displayed a change in deviation, the mean amount of change (either increase or decrease) was 9.9 ± 1.0 pd. The 31 BLR patients who experienced a change in deviation averaged 7.1 ± 0.6 pd, an amount significantly less than the other group (t = 2.5, df = 61), but which nevertheless indicates that there are individual differences for drift obscured by the stable mean level. The variability in surgical result as well as the variability in drift patterns is, in part, a function of differences in preoperative conditions previously discussed. A partial regression coefficient, resulting

432 Scott, Mash, and Jampolsky Investigative Ophthalmology June 1975 3.5 3.0 = 2.5 2 2.0 j 1.5 1.0 RECESS-RESECT SURGERY Table V. Partial regression coefficients and Y-intercepts for two time intervals for prediction of effect per millimeter of RR surgery Variable Preoperative deviation Age at time of surgery Average spherical equivalent Anisometropia Ratio of millimeters of resection to millimeters of recession Distance (larger) deviation Initial Final 0.0721-0.0435 0.0347-0.0349-0.4575 0.0754-0.0403-0.0032-0.0531-0.2673 15 20 25 30 PREOPERATIVE DEVIATION 35 40 Fig. 1. Association between preoperative deviation and the initial effect in prism diopters per millimeter of surgery for recession-resection surgery (lower line), compared with the association between multiple preoperative variables and the effect in prism diopters per millimeter of surgical correction. Note the difference in slope of the line and the greatly smaller standard deviations. from a multiple regression analysis, describes the change in the dependent variable per unit change in an associated predictor variable while all other predictor variables are held constant. The Y-intercept value is the mean effect per millimeter of surgery adjusted for the covariates, i.e., adjusted to zero values or levels for all predictor variables. For both groups, the multiple correlations (between the observed and predicted values for the effect per millimeter of surgery) are quite high in all cases. The proportion of the total variance in the effect per millimeter of surgery that was explained by differences in the predictor variables is given by "R 2 " in Tables V and VI. It is interesting that the predictor variables were found (empirically) to be different for the RR and BLR groups. In Fig. 1, two regression lines are presented which compare the relationship when only one preoperative condition, magnitude of deviation, is considered and the regression line when additional preoperative variables are considered. In the first case the observed effect per millimeter Y-intercept Multiple R R 2 1.0271 0.97 0.94 0.7621 0.98 0.96 Table VI. Partial regression coefficients and Y-intercepts for two time intervals for prediction of effect per millimeter of symmetrical bilateral recession surgery Variable Pre-operative deviation Difference between distance and near deviations Age at time of surgery Average spherical equivalent up gaze down gaze Y-intercept Multiple R R 2 Distance (larger) deviation Initial 0.0547 0.0162-0.0486 0.0609 0.0274 0.0190 0.9084 0.97 0.94 Final 0.0541 0.0164-0.0692 0.0473 0.0071 0.0199 1.0499 0.97 0.94 is regressed on the preoperative deviation yielding a regression coefficient of 0.058 ± 0.011. This univariate regression accounts for 36 per cent of the variance and results in fairly wide confidence limits. The other regression utilized the effect per millimeter adjusted for differences in the other covariates (see Table V), yielding a regression coefficient of 0.072 ± 0.007. This multivariate regression accounts for 94 per cent of the variance and thus results in greatly enhanced accuracy of prediction. It is reasonable to regard age as an index of size of the globe, or eye muscle length, although it could well be indexing ad-

Volume 14 Number 6 Exotropia surgery 433 Table VII. An example of calculation of amount of surgery for RR surgery (see text for explanation) Variable Patient's measure Regression coefficient Larger preoperative deviation Age at surgery* Average spherical equation Anisometropia Ratio of millimeters resection to millimeters recession 25 6.0 + 1.50 0.50 0.67 0.0754 = -0.0403 = -0.0032 = -0.0531 = -0.2673 = Y-intercept = Sum = Effect/mm. = 1.8850-0.2418-0.0048-0.0266-0.1791 0.7621 2.1948 25 Preop dev. 2.2135 Effect/mm. 11.4 mm. of surgery Recession: 6.8 mm. Resection: 4.6 mm. If age is greater than age 8, use age 8.0. ditional components. The observed asymptotic relationship of age effect corresponds to the anatomic maturation of the eye. 11 Application of the descriptive formulae is limited to the ranges of the predictor variables represented in the particular sample (see Tables I and II) on which the regression analysis was based. The adequacy of the description of interrelationships of variables is unknown beyond the limits of these ranges. It is quite probable and reasonable that these relationships do become nonlinear at some more extreme values. For example, in the case of age, there is no assurance that its apparent uniform effect between the ages of 8 and 19 will remain constant at 40 or more since individual differences in factors, other than growth, associated with age may be operative. Also, the analyses suggest that increasing the amount of surgery on a muscle, relative to its length, decreases the effect per millimeter. For example, a medial rectus recessed 13 mm. will be so weakened by relaxation and loss of arc of contact that further recession will not weaken it in proportion. Thus, it is ill advised to use these formulae for patients who have extreme measures for any of the predictor variables. As our data base is extended and extreme values better represented, we will be able to investigate the nature of the interrelationships and thus determine the descriptive adequacy of the partial regression coefficients across a greater range. Examination of the signs associated with each regression coefficient indicates the direction of the influence that differences in the associated variables (relative to the group mean) had on the effect per millimeter of surgery. For example, an increasing effect per millimeter resulted with an increasing magnitude of preoperative deviation, while a decreasing effect per millimeter was associated with an increasing age (up to eight years of age). The partial regression coefficients are relatively stable in their magnitude and importance at the various postoperative times, but some exceptions may suggest reasons for the direction and magnitude of postoperative drift. For the RR group, the variable anisometropia was not important in influencing initial surgical results, but was important at the later time interval. Perhaps this was an impediment to fusion which might otherwise have stabilized the initial correction. The ratio of millimeters of resection to millimeters of recession had an important influence on the initial effect per millimeter; when less than 60 per cent (the average value in this series) of the total millimeters was allotted to recession (a ratio of 0.67), the effect per millimeter

434 Scott, Mash, and Jampolsky Investigative Ophthalmology June 1975 Table VIII. An example of calculation of amount of surgery for bilateral recession surgery (see text for explanation) Variable Patient's measure. Regression coefficient Preoperative deviation for distance Difference between distance and near deviations Age at surgery* Average spherical equation up gaze down gaze 30 10 7.5 +0.75 0 0 0.0544 = 0.0164 = -0.0692 = 0.0473 = 0.0071 = 0.0199 = 1.6320 0.1640-0.5190 0.0355 0 0 Y-intercept = Effect/mm. = 1.0490 2.3615 Sum = ; 30 2.3615 Preopdev. ' Effect/mm. 12.7 mm. of surgery 6.5 mm. per lateral rectus If age is greater than age 8, use age 8.0. was reduced. This suggests that insufficient weakening of the lateral rectus relative to the amount of tightening of the medial rectus interferes with the initial amount of correction achieved. However, with lapse of time, the muscle forces adjust for this initial "imbalance" and the proportioning of the total amount of surgery ceases to be a contributing factor in the variability of surgical result at the final time. For bilateral cases, the variance in effect per millimeter associated with differences in the change of deviation with up gaze (primarily among patients with either V pattern or no pattern, in this sample) was reduced to an unimportant level by the later postoperative time. The amount of variance associated with differences in age increased from initial to final time for the larger deviation, but decreased for the small deviation. The manner in which to calculate the number of millimeters of surgery to be performed involves the Y-intercept, the partial regression coefficients, and a given patient's measures for the factors indicated. All factors must be included; omitting one or more of them will distort the result unless it is appropriate or reasonable to assume the measure is zero. An example of the evaluation of the formula for RR operations is presented in Table VII; this example uses the regression coefficients for the final time interval. The measures obtained for a patient are multiplied by the appropriate regression coefficient. The sum of these products and the Y-intercept is the estimated or expected effect per millimeter of surgery. To obtain the number of millimeters of surgery, the preoperative deviation is divided by this sum. The total amount multiplied by the proportion that is to be allotted to recession which we suggest should be approximately 0.60 (a ratio value of 0.67). In this example, approximately 7.0 mm. of recession and 4.5 mm. of resection are the estimated amounts of surgery to be performed. An example of the evaluation of the formula for bilateral curgery is presented in Table VIII, also using the regression coefficients for the final time interval. The useful predictor variables are slightly different from those found useful in predicting the effect of RR operations (Table VII). As before, each measure for a patient is multiplied by its appropriate regression coefficient; the sum of these products plus the Y-intercept values yields the estimated effect per millimeter of surgery. Next, the preoperative deviation is divided by this sum, giving the total number of millimeters of surgery, half of which is the amount to be performed on each lateral rectus.

Volume 14 Number 6 Exotropia surgery 435 4.On 3.5- * Bilateral recession w g 3.0-2.5-2.0- Recess-resect 25 30 35 40 45 PRE-OPERATIVE DEVIATION Fig. 2. Comparison of regressions based on results of exotropia operations by different surgeons in different geographic locations. The notion that results are valid for only one institution and cannot be transferred elsewhere or applied by other surgeons is widespread. The results from the few quantitative reports in the literature and from our study are displayed in Fig. 2 showing a remarkable and encouraging concordance between investigators separated geographically and known to use different surgical techniques. Consistent differences between data (for instance, the Y-intercept value of the Adler data being higher than that of the Scott data) will be readily identified and simple to correct for in the transfer of data and results between one institution and another. We are now testing the value of these guidelines in several clinics. The editor in the introduction to Copernicus's de Revolutionibus stated "... These hypotheses need not be true or even probable. If they provide a calculus consistent with the observations, that alone is sufficient." We believe that both greater accuracy and significant analytic insights will derive from accurate quantitative analyses in the microcosm of strabismus, no less than on the cosmologic scale of Copernicus. REFERENCES 1. Raab, E. L., and Parks, M. M.: Recession of the lateral recti: early and late postoperative alignments, Arch. Ophthalmol. 82: 203, 1969. 2. Sheppard, R. W., Panton, C. M., and Smith, D. R.: The single horizontal muscle recession operation, Canad. J. Ophthalmol. 8:68, 1973. 3. Scobee, R. G.: Degrees of correction per millimeter of surgery, Am. J. Ophthalmol. 32: 1376, 1949. 4. Burian, H. M.: Strabismus: a review of the literature, Arch. Ophthalmol. 44: 146, 1950. 5. Helveston, E. M.: Atlas of Strabismus Surgery. St. Louis, 1973, The C. V. Mosby Company. 6. Hugonnier, R., and Clayette-Hugonnier, S.: Strabismus, Heterophoria, Ocular Motor Paralysis, Veronneau-Troutman, S., editor. St. Louis, 1969, The C. V. Mosby Company, pp. 631-649. 7. Bock, R. D., and Haggard, E. A.: The use of multivariate analysis of variance in behavioral research, in: Handbook of Measurement and Assessment in Behavioral Sciences,

436 Scott, Mash, and Jampolsky Investigative Ophthalmology June 1975 Whitla, D. K., editor. Boston, 1968, Addison- Wesley Publishing Co., pp. 100-142. 8. Adler, F. H.: Physiology of the Eye. St. Louis, 1973, The C. V. Mosby Company. 9. Wheeler, M. C: Introduction to Ocular Motility. New York, 1970, Cooper Square Publishers. 10. Keeney, A. H.: Chronology of Ophthalmic Development. Springfield, 111., 1951, Charles C Thomas, Publisher. 11. Fink, W. H.: Anatomy of the extrinsic muscles of the eye, in: Strabismus Ophthalmic Symposium II, Allen, J. H., editor. St. Louis, 1958, The C. V. Mosby Company, pp. 17-105. 12. Adler, F. H.: Intermittent exotropia, Trans. Pacific Coast Oto-Ophthalmol. Soc. 42: 185, 1961. 13. Ballen, P. H.: Surgical treatment of intermittent exotropia, J. Pediat. Ophthalmol. 7: 55, 1970.