ARTICLE

Q 2015 ASC

Published by

Multiple regression analysis in nomogramdevelopment for myopic wavefront laser

in situ keratomileusis: Improvingastigmatic outcomes

Bruce D. Allan, MD, FRCOphth, Hala Hassan, BSc (Hons), Alvin Ieong, BSc (Hons)

RS an

Elsev

PURPOSE: To describe and evaluate a new multiple regression–derived nomogram for myopicwavefront laser in situ keratomileusis (LASIK).

SETTING: Moorfields Eye Hospital, London, United Kingdom.

DESIGN: Prospective comparative case series.

METHODS: Multiple regression modeling was used to derive a simplified formula for adjustingattempted spherical correction in myopic LASIK. An adaptation of Thibos’ power vector methodwas then applied to derive adjustments to attempted cylindrical correction in eyes with 1.0 diopter(D) or more of preoperative cylinder. These elements were combined in a new nomogram(nomogram II).

RESULTS: The 3-month refractive results for myopic wavefront LASIK (spherical equivalent%11.0 D; cylinder %4.5 D) were compared between 299 consecutive eyes treated using theearlier nomogram (nomogram I) in 2009 and 2010 and 414 eyes treated using nomogram IIin 2011 and 2012. There was no significant difference in treatment accuracy (variance in thepostoperative manifest refraction spherical equivalent error) between nomogram I andnomogram II (P Z .73, Bartlett test). Fewer patients treated with nomogram II had more than0.5 D of residual postoperative astigmatism (P Z .0001, Fisher exact test). There was nosignificant coupling between adjustments to the attempted cylinder and the achieved sphere(P Z .18, t test).

CONCLUSIONS: Discarding marginal influences from a multiple regression–derived nomogramfor myopic wavefront LASIK had no clinically significant effect on treatment accuracy. Thibos’power vector method can be used to guide adjustments to the treatment cylinder alongsidenomograms designed to optimize postoperative spherical equivalent results in myopic LASIK.

Financial Disclosure: No author has a financial or proprietary interest in any material or methodmentioned.

J Cataract Refract Surg 2015; 41:1009–1017 Q 2015 ASCRS and ESCRS

Laser in situ keratomileusis (LASIK) results arecommonly tracked using scatterplots of attemptedchange (x-axis) versus achieved change (y-axis) inmanifest refraction spherical equivalent (MRSE) diop-tric values.1 Systematic trends toward overcorrectionor undercorrection of the MRSE can be identifiedeasily in these plots using simple linear regressionanalysis in which a regression line is fitted using

d ESCRS

ier Inc.

the least-squares method. This line is described bythe equation

AchievedMRSE changeZa� ðAttemptedMRSE changeÞ � b

Using the slope coefficient (a) from this equation,subsequent results can be improved by adjusting thepercentage treatment energy boost/deboost parameter

http://dx.doi.org/10.1016/j.jcrs.2014.08.042 10090886-3350

1010 DEVELOPMENT OF A MYOPIC WAVEFRONT LASIK NOMOGRAM

available on most excimer laser platforms, using theequation

% boost=deboostZ ð1� aÞ=a� 100

The dioptric value of the intercept constant (b) canthen be subtracted from the target sphere for each sub-sequent treatment to move the regression line closer tothe ideal (attempted MRSE change Z achieved MRSEchange) position. The task then is to reduce the resid-ual variance or scatter of data points around theregression line.2,3

Many factors other than attempted MRSE changemight influence the achieved MRSE change values inLASIK. These include optical zone size,4,5 age,4 andhigher-order aberrations (HOAs).6–8 We recentlydescribed a LASIK nomogram development methodbased on multiple regression analysis designed totake into account factors other than the attemptedMRSE change.3 Briefly, this approach derives a regres-sion equation that can be used as for simple linearregression to steer percentage adjustments to overalltreatment energy (%boost or deboost) based on theslope coefficient for the 4.0mmpupil wavefront refrac-tion spherical equivalent (WRSE); however, dioptricadjustments to the target sphere are calculated indi-vidually for each eye by subtracting the sum of theweighted additional factors plus the intercept constantfrom the multiple regression equation. In our initialiteration of nomogramdevelopment formyopic wave-front LASIK based on this approach, we found that theMRSE minus the 4.0 mm pupil WRSE, maximumpupil minus 3.0 mm pupil WRSE, and central

Submitted: May 29, 2014.Final revision submitted: June 23, 2014.Accepted: August 12, 2014.

From Moorfields Eye Hospital, London, United Kingdom.

Supported in part by the National Institute for Health Research(NIHR) Biomedical Research Centre based at Moorfields Eye Hos-pital NHS Foundation Trust and University College London Instituteof Ophthalmology. The views expressed are those of the authorsand not necessarily those of the NHS, the NIHR, or the Departmentof Health.

Steve Morton, Abbott Medical Optics, Inc., provided technicaladvice on wavefront laser in situ keratomileusis treatment usingthe Customvue platform and vector analysis of astigmatism results.

Presented at the XXXI Congress of the European Society ofCataract and Refractive Surgeons, Amsterdam, the Netherlands,October 2013.

Corresponding author: Bruce D. Allan, MD, FRCOphth, Cornea &External Disease Service, Moorfields Eye Hospital, 162 City Road,London EC1V 2PD, United Kingdom. E-mail: bruce.allan@ucl.ac.uk.

J CATARACT REFRACT SURG

pachymetrywere statistically significant additional in-fluences on the achievedMRSE change.We then calcu-lated and applied dioptric adjustments to the targetpostoperative MRSE for each eye treated using theequation

Dioptric adjustmentZ � 1� ½0:444� ðMRSE� 4:0mmpupil WRSEÞ þ 0:206

� ðMax pupil� 3:0mmpupil WRSEÞ þ 0:0018

� ðcentral corneal pachymetry in micronsÞ � 0:87�� target postoperative sphere

We found that customizing the dioptric adjustmentto the target postoperative MRSE for each eye usingthis multiple regression–derived nomogram duringtreatment planning significantly reduced residualvariance in postoperative MRSE results in comparisonwith an earlier consecutive case series treated usingthe same myopic wavefront LASIK Customvue plat-form (version 3.67) treatment planning software, aWavescan aberrometer, and the Customvue S4 IR ex-cimer laser (all Abbott Medical Optics, Inc.). A similarapproach can be applied using most commerciallyavailable excimer laser platforms, and the principleof using multiple regression analysis to take intoaccount factors other than the attempted MRSEwhen planning treatments is equally applicable tononwavefront-guided LASIK.

In addition to dioptric adjustments to the targetpostoperative sphere, dioptric adjustments to thetarget cylinder are available on most refractive exci-mer lasers. After optimization of the achieved MRSE,the next logical target for nomogram development isto reduce the postoperative refraction cylinder.

Standard refractive reporting charts describe astig-matic results in terms of dioptric cylinder powerwithout reference to the cylinder axis (absolute cylin-der).9 Absolute cylinder results do not distinguishbetween undercorrection and overcorrection. Forexample, reducing the absolute cylinder from 2.0 diop-ters (D) preoperatively to 1.0 D postoperatively couldrepresent a 50% undercorrection if the axis of the pre-operative cylinder and postoperative cylinder is thesame, or a 50% overcorrection if the axes are 90 degreesapart. Vector analysis, in which polar coordinates aretransformed to coordinates described by orthogonalvectors in Cartesian space using double-angle plots,10

overcomes this difficulty. Using this method, the dis-tance between the preoperative and postoperative cyl-inder coordinates, calculated using the rules of vectorsubtraction, defines the achieved cylinder change. Scat-terplots of the attempted cylinder change (the preoper-ative absolute cylinder) versus the achieved cylinder

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change can then be used to guide dioptric adjustmentsto the cylinder in LASIK treatment planning.

Using the power vector notation of Thibos et al.,11,12

the cylinder component of a spherocylindrical lens isdescribed independent of the sphere by 2 Jacksoncross-cylinder vectors (J0 and J45) at 45 degrees (90 de-grees in a double-angle plot). Here, we describe theapplication of this method to pretreatment cylinderadjustment alongside a second iteration of ourmultiple regression analysis–derived nomogram forrefining the treatment sphere in myopic wavefrontLASIK. Results for the new nomogram incorporatingcylinder adjustments (nomogram II) are comparedwith results in consecutive cases treated with theearlier nomogram (nomogram I).3

PATIENTS AND METHODS

The project design was reviewed by theMoorfields ResearchGovernance Committee and approved as a prospective auditproject. In accordance with the Declaration of Helsinki,informed consent information given to all patients includeda lay explanation of the limitations of treatment accuracy, thepossible need for repeat treatment, and the use of nomogramadjustments in treatment targeting.

Treatment Details

Table 1. Multiple regression analysis.*

Independent Variable

PartialCorrelationCoefficient

AdjustedR2

PValue

4.0 mm WRSE 1 98.2 .000MRSE � WRSE 0.421 98.6 .000Max � 3.0 mm WRSE d d O.15Pachymetry d d O.15

4.0 mmWRSEZ 4.0 mm pupil wavefront refraction spherical equivalent;Max – 3.0 mmWRSE Z Maximum pupil minus 3.0 mm pupil wavefrontrefraction spherical equivalent; MRSE � WRSE Z manifest refractionspherical equivalent minus 4.0 mm pupil wavefront refraction sphericalequivalent; pachymetryZ central corneal thickness; WRSEZwavefrontrefraction spherical equivalent*Stepwise multiple regression analysis oF 222 consecutive eyes treatedwith wavefront-guided myopic LASIK using nomogram I. In this anal-ysis, only 4.0 mm WRSE and MRSE – WRSE remained as significant in-fluences (threshold P!.15).

Eligibility for LASIK was determined using standardcriteria.13 Aberrometry was performed using a Wavescanaberrometer (software version 3.67). A minimum of 3 scansper eye were taken, alternating between right eyes and lefteyes, after up to 5 minutes of dark adaptation or adjustmentof ambient lighting with the aim of attaining scans with a7.0 mm pupil. Pharmacologic pupil dilation was not used.Aberrometric refraction findings were refined by manifestrefraction in office-lighting conditions. Cycloplegic refrac-tion was used to crosscheck for accommodation in caseswith a large disparity between the manifest refraction andthe aberrometric refraction or in which accommodationwas suspected based on pupil movement during aberrome-try. Single scans were selected as a basis for treatment afterreviewing Hartmann-Shack and infrared camera images.Criteria taken into account in scan selection included imagequality, image centration, wavefront diameter (largest diam-eter, closest to measured pupil diameter), and regularity ofthe array of centroid markers within the perimeter of quali-fying spots. Treatment programming, performed using Cus-tomvue treatment planning software (version 5.22), includeda 5% (nomogram I) or 9% (nomogram II) treatment energyboost in all cases based on regression analysis of earlier re-sults. The treatment energy boost is a percentage adjustmentto overall treatment energy applied equally to the correctionof all elements of defocus including sphere, cylinder, andHOAs. Additional dioptric adjustments to the attemptedtreatment sphere were determined according to the multipleregression analysis–derived nomogram used (nomogram Ior nomogram II). Additional dioptric adjustments to the at-tempted cylinder correctionwere applied as described belowto patients treated using nomogram II. No pretreatmentdioptric adjustments to the attempted cylinder were per-formed for patients treated using nomogram I. Further

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adjustments (up to 1.20 D) were used to target mini-monovision in presbyopic patients.

All LASIK flaps were created with an Intralase iFS150 Hz femtosecond laser (Abbott Medical Optics, Inc.)(diameter 8.5 to 9.0 mm; cut depth 100 to 110 mm). A Cus-tomvue S4 IR excimer laser was used throughout. No alter-ations to the default optical zone (6.0 mm) or blend zone(8.0 mm) diameters were made. Variation in the time be-tween flap elevation and the commencement of treatment(and therefore tissue hydration) was minimized by lockingthe pupil and iris-tracking mechanism before flap elevationwhen possible; interface gas bubbles were used as a guideto depth (z-axis) focus. Microscope light and ambient roomlight levels were minimized during eye-tracking engage-ment and laser treatment to help patients maintain goodfixation.

The postoperative treatment regimen comprised unpre-served topical levofloxacin 0.3% and dexamethasone 0.1%every 2 hours for 1 week with topical fluorometholone 4times a day for the succeeding 2 weeks and unpreservedtopical lubricants as required.

Nomogram II: Sphere Adjustment

A sample of 222 consecutive eyes treated with nomogramI from the series we reported earlier3 was reanalyzed usingMinitab 15 statistical processing software (Minitab, Inc.)after tabulation of the following indices in an Excel spread-sheet (Microsoft Corp.): 3-month postoperative and preoper-ative sphere, cylinder, axis, patient age, sex, 4.0 mm pupilWRSE, maximum pupil minus 3.0 mm WRSE, and centralcorneal pachymetry. Best subsets and stepwise multipleregression modeling were applied as previously described3

to derive the following regression equation used for calcula-tion of pretreatment adjustments to the target postoperativesphere for each eye treated with nomogram II (Table 1):

Dioptric adjustment to attempted treatment sphereZ � 1

� ½0:422� ðMRSE� 4:0mmpupilWRSEÞ þ 0:024�� target postoperative sphere

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The underlying boost to overall treatment energy calcu-lated at 9% was applied fully for patients treated usingnomogram II, whereas a more conservative 5% boost wasapplied to patients treated using nomogram I. Changes tothe overall treatment energy (%boost/deboost) were appliedto all cases in each nomogram iteration with a user defaultsetting in the numeric entry field marked “nomogramadjustment” in the Customvue 5.22 treatment planningsoftware.

Nomogram II: Cylinder Adjustment

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Figure 1. Attempted versus achieved cylinder in eyes treated withnomogram I (no pretreatment adjustment to the cylinder) (top) andnomogram II (a 10% boost to attempted cylinder correction,Table 2) (bottom) showing a reduced trend toward undercorrectionof cylinder for patients treated with nomogram II (LASIK Z laserin situ keratomileusis; SIRCZ surgically induced refractive change).

The 3-month postoperative manifest refraction cylinderresults in 132 consecutive eyes with a preoperative mani-fest refraction cylinder equal of 1.0 D or more treatedusing nomogram I were tabulated against the preoperativemanifest refraction cylinder values in the same eyes in anExcel spreadsheet. All degree values for axis were con-verted to radians to enable trigonometric functions inExcel. The Jackson cross-cylinder value for achieved cylin-der change was then calculated as described by Thiboset al.11:

J0preZ��Cpre

�2�cos 2apre

J45preZ��Cpre

�2�sin 2apre

J0postZ��Cpost

�2�cos 2apost

J45postZ��Cpost

�2�sin 2apost

JCCachievedZSQRTh�J0post � J0pre

�2 þ �J45post � J45pre

�2i

where C is the dioptric value of the cylinder, a is the cylinderaxis in radians, SQRT is the square root, JCC is the Jacksoncross cylinder, and JCCachieved is the dioptric value for thesurgically induced refractive change (Jackson crosscylinder).

A scatterplot of the attempted cylinder versus achievedcylinder (absolute cylinder) was then created (Figure 1, top)using

Attempted cylinderZCpre

Achieved cylinderZ2� JCCachieved

A variety of regression line options were then fitted tothe scatterplot. Inspection of R2 values for each regressionequation showed that simple linear regression providedthe best fit (highest R2 value). A clear trend toward under-correction was evident. Based on this, a 0.1 D correctionwas added to the attempted cylinder for each 1.0 D increasein preoperative cylinder (Table 2) for eyes treated withnomogram II.

Statistical Comparison of Nomogram I andNomogram II

Graphic and descriptive data presentation was pre-pared in Excel. Except where indicated, Minitab 15 wasused for all analyses. Data from consecutive eyes treatedwith each nomogram were summarized descriptively us-ing standard reporting charts for refractive surgery9 andplots of attempted correction versus achieved astigmaticcorrection. The Bartlett testA was used to determine

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whether variance in the postoperative MRSE errordiffered between groups. Using a threshold of 0.5 D todefine clinically significant residual postoperative astig-matism, a 2-tailed Fisher exact test was used to determinewhether there were significantly more patients with morethan 0.5 D postoperative astigmatism in either group.Simple linear regression analysis, using a t test comparingthe slope to zero to generate a P value in a scatterplot ofpreoperative cylinder adjustment versus postoperative

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Table 2. Astigmatism adjustment applied in nomogram II.

Preop Manifest RefractionCylinder (D)

Addition to TreatmentCylinder (D)

0 to 0.99 0.01 to 1.99 0.12 to 2.99 0.23 to 3.99 0.34 to 4.99 0.4

Table 3. Cases excluded from analysis.

Exclusion Criterion

Number

Nomogram I Nomogram II

Lost to follow-up 18 61CTK 0 4Ectasia 1 0LINE syndrome 2 2Cataract 2 0Amblyopia 1 5

CTK Z central toxic keratopathy; LINE Z LASIK Z inducedneuroepitheliopathy

1013DEVELOPMENT OF A MYOPIC WAVEFRONT LASIK NOMOGRAM

MRSE, was used to examine whether there was anycoupling between cylinder adjustment and the achievedrefraction sphere.

RESULTS

After exclusions (Table 3), data from 414 eyes treatedwith myopic wavefront LASIK in 2011 and 2012with nomogram II were available for analysis. Thesedata were compared with 299 eyes treated in 2009and 2010 in a dataset previously described for nomo-gram I. The age and sex profile and ranges of attemp-ted myopic and cylindrical correction were similar inboth groups (Table 4).

Refractive and visual results for nomogram I andnomogram II are presented in the standard format inFigure 2 and summarized in Table 4. Visual resultswere similar; however, more eyes treated with nomo-gram I had an uncorrected distance visual acuity(UDVA) at the 20/16 or better level (Figure 2, A andB) both preoperatively and postoperatively. Therewas no significant difference in treatment accuracy(variance in the postoperative MRSE error) between

Table 4. Myopic LASIK results: nomogram I versus nomogramII.

Parameter Nomogram I Nomogram II

Eyes (n) 299 414Patients (n) 165 215Year of treatment 2009 to 2010 2011 to 2012Mean age (y) 39.9 G 9.0 37.6 G 9.7Mean attempted sphere (D) 4.1 G 2.2 4.0 G 2.1Mean attempted cylinder (D) 0.83 G 0.65 0.85 G 0.74Mean MRSE error (D) �0.19 G 0.32 �0.04 G 0.34Variance 0.102 0.106R2 0.983 0.978% G1.0 D of target SE (%) 98 99% G0.5 D of target SE (%) 88.3 90.8UDVA* R20/20 (%) 84.2 83.8UDVA* R20/40 (%) 99.5 99.4

Means G SDMRSEZmean refraction spherical equivalent; SEZ spherical equivalent;UDVA Z uncorrected distance visual acuity (monocular)*Excludes monovision eyes, which were deliberately undertreated.

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nomogram I and nomogram II (P Z .73, Bartlett test;Figure 2, E and F). The ratio of overcorrection to under-correction was well balanced for nomogram II, inwhich a 9% boost was applied, whereas a trend to-ward undercorrection was evident for patients treatedwith nomogram I (Figure 2, G and H).

Fewer patients treated with nomogram II had morethan 0.5 D residual postoperative astigmatism (P Z.0001, Fisher exact test; Figure 2, I and J), and therewas a reduced trend toward undercorrection ofastigmatism in patients treated with nomogram II(Figure 1).

Pretreatment cylinder adjustment had no significanteffect on posttreatment MRSE results (Figure 3).

DISCUSSION

This study evaluated a second iteration (nomogram II)of a multiple regression analysis–based nomogram formyopic wavefront LASIK incorporating a simplemethod of refining astigmatic results and a simplifiedcalculation of preoperative adjustment to the treat-ment sphere. Refractive results were better in patientstreated with nomogram II. Postoperative astigmatismwas reduced with the application of a 10% dioptricaddition to the treatment cylinder, and the balance ofundercorrections and overcorrections was improvedby the application of an additional 4% overall treat-ment energy boost. We could not find correspondingimprovements in postoperative UDVA.

Calculation of the dioptric adjustment to the treat-ment sphere in nomogram II was simplified withoutclinically significant loss of treatment accuracy. Ageandmaximum pupil minus 3.0 mm pupil WRSE drop-ped out as statistically significant influences (Table 1),leaving the difference between manifest and aberro-metric refraction (MRSE minus the 4.0 mm pupilWRSE) as the only remaining modifier for the treat-ment sphere in addition to the percentage boost basedon the WRSE. Although age and maximum pupilminus 3.0 mm pupil WRSE were found to be

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Figure 2. Visual and refractive 3-month postoperative outcomes for patients treated with nomogram I and nomogram II presented in thestandard format (CDVA Z corrected distancevisual acuity; UDVA Z uncorrected distancevisual acuity).

1014 DEVELOPMENT OF A MYOPIC WAVEFRONT LASIK NOMOGRAM

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--

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Figure 3.Relationship between dioptric addition to the pretreatmentcylinder (Table 2) and postoperative SE error for patients treatedwith nomogram II, showing a weak trend towards more hyperopicoutcomes for patients with a larger pretreatment cylinder adjust-ment. This trend was not statistically significant (PZ.18, t test; R2

Z 0.015) (MRSE Z manifest refraction spherical equivalent).

1015DEVELOPMENT OF A MYOPIC WAVEFRONT LASIK NOMOGRAM

statistically significant modifiers of the achievedMRSE in multiple regression modeling to developnomogram I, gains in the modified R2 with the addi-tion of these factors to the model were small.3 In retro-spect, and in accordance with the parsimony principlefor model building in multiple regression analysis,B

we might reasonably have left these factors out ofour original model; the finding that they were nolonger influential in a reanalysis of results from treat-ments applied using nomogram I is not surprising.

Cylindrical values are heavily skewed toward the0.0 to 1.0 D range in most myopic LASIK datasets.Repeatability of manifest refraction cylinder, and inparticular cylinder axis values, is relatively low inthis range.14 We therefore discarded eyes with a pre-operative cylinder less than 1.0 D from our starting da-taset for analysis of astigmatism. We used more than0.5 D as a threshold for clinically significant postopera-tive astigmatism because retreatment would not nor-mally be indicated for lower levels of postoperativeastigmatism. Applying different thresholds using thesame statistical test, fewer patients treated using nomo-gram II had more than 0.75 D (PZ .05) and more than1.00 D (P Z .045) of astigmatism postoperatively.

We initially applied a 10% dioptric addition to thetreatment cylinder based on vector decomposition ofastigmatism without conversion to a Jackson cross-cylinder format.10 We then reanalyzed a larger datasetusing the method presented here before continuingwith a 10% addition to the treatment cylinder innomogram II. The attractive theoretical feature of

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conversion to a Jackson cross-cylinder format, asdescribed by Thibos et al.,11,12 is that the considerationof cylinder is separated mathematically from theconsideration of the SE. Adjustments for cylinderbased on this approach can therefore be used as a sim-ple add-on to any nomogram to refine MRSE out-comes in myopic LASIK.

Although Jackson cross-cylinder values have theadvantage of spherical neutrality, they are a less intu-itive measure of astigmatism for most surgeons whenreading plots of attempted change versus achievedrefractive change. Accordingly, having derived thesurgically induced refractive change to cylinder in aJackson cross-cylinder format, we doubled it toconvert back to an absolute cylinder value represent-ing the achieved astigmatic change. Note that the slopeof the regression line, which forms the basis for treat-ment adjustment, is not altered by this transformationas long as the attempted cylinder change is also plottedin an absolute cylinder format. This is simple to dobecause the aim in myopic LASIK is almost alwaysto eliminate astigmatism. The attempted astigmaticchange is therefore equal to the preoperative manifestrefraction cylinder.

We found a more than 20% undercorrection of thecylinder (Figure 1, top); however, we applied only a10% dioptric addition to the treatment cylinder innomogram II. We have observed R2 values in therange of 0.7 to 0.8 in linear regression analysis ofastigmatic data using the method we describe here.This is lower, and confidence intervals are wider,than for similar analyses of attempted sphere versusachieved sphere in myopic LASIK in which R2 valuesare typically 0.9 or more.2 We would thereforerecommend a cautious iterative approach to pretreat-ment cylinder adjustment, applying small changesinitially and reanalyzing results, rather than applyingthe full correction based on the slope constant andintercept for the scatterplot, as for optimization ofthe SE.3 Additional arguments for a cautiousapproach to cylinder adjustment include the risk forastigmatic overcorrection if adjustments to overalltreatment energy are applied simultaneously, as inthe 4% increase between nomogram I and nomogramII reported here, and the risk for spherical overcorrec-tion if changes to the tissue removal pattern associ-ated with changes in astigmatism for the laserplatform used are not spherically neutral.

Improved refractive results were not accompaniedby improved visual results for nomogram II in thisstudy. We had expected the reduced astigmatismand reduced undercorrections to lead to improve-ments in postoperative UDVA in patients treatedwith nomogram II; however, more patients treatedwith nomogram I attained a UDVA of 20/16 or better.

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Analyzing this surprising trend, we observed that pre-operative corrected distance visual acuity (CDVA)was also better in the earlier group of patients treatedwith nomogram I and that the preoperative CDVA ap-peared to drop during the 18-month period in 2011and 2012, during which the results for nomogram IIwere assessed. Refraction testing was performed bythe same experienced optometrist using the same pro-tocol throughout the study period for both nomogramI and nomogram II. Demographic indices for thecomparator groups and the range of refractive errorstreated were similar, although the rate of losses tofollow-up was higher for patients treated with nomo-gram II. Visual acuity testing was performed using theEarly Treatment Diabetic Retinopathy Study (ETDRS)logMAR acuity charts projected on a standard-resolution liquid crystal display using Test Chart2000 software (Thomson Software Solutions).Although this system was correctly calibrated wheninstalled, subsequent checks have showed changes incalibration that reduce letter size by approximately10%. Although refractive results should not havebeen affected, this reduction in projected letter sizewould have led to underestimation of visual acuitiesfor patients treated with nomogram II. Retrospec-tively, we were unable to determine the timing ofthis calibration error with any accuracy or whether itwas a step change or a drift. We were therefore unableto apply a systematic correction to our acuity resultsbased on the observed calibration error. Screen-basedvisual acuity testing charts have advantages overstandard backlit charts including ease of switchingbetween charts to prevent letter learning and adjust-ment of letter size to fit the available viewing distance.However, good correlation with measurements fromstandard backlit charts requires measures to minimizeveiling reflective glare from the screen surface and ac-curate calibration of test type size, luminance, andcontrast.15,16

Although we used ETDRS logMAR charts (5 lettersper line) to measure visual acuity, a further limitationof our study is that we collected Snellen equivalentdata, rounding up if 3 or more letters were readcorrectly on a line and down if 2 or fewer letterswere read. More accurate discrimination betweengroups could have been achieved with scoring basedon the number of letters read,17 rounding up ordown only for descriptive data presentation in thestandard format.9

Despite flaws in the visual acuity data, we believeimprovements in astigmatic refractive results pre-sented here represent proof of principle for a simplemethod of adjustment to enhance astigmatic resultsin myopic LASIK. This method can be applied in tan-dem with any nomogram development method for

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refining the treatment sphere. These data also showthat removing marginal influences from a multipleregression–derived nomogram for myopic wavefrontLASIK did not result in a clinically significant loss oftreatment accuracy.

It is important to emphasize that although themethods for nomogram development described hereare applicable to any laser system, the nomogram wederived is not. Surgeons wishing to adopt thisapproach, including those using a laser system iden-tical to the one we used, should build from the groundup using their own refractive outcome data.

-

WHAT WAS KNOWN

� Multiple regression analysis can be used to account forfactors additional to the attempted SE refraction changein the development of nomograms to enhance the accu-racy of SE refraction outcomes for myopic wavefrontLASIK.

WHAT THIS PAPER ADDS

� A simplified multiple regression–derived nomogram fromwhich marginal influences were excluded did not diminishthe accuracy of SE refraction results.

� Thibos’ power vector method, which considers astigma-tism independent of the refraction SE, can be adaptedto guide pretreatment adjustments, enhancing astigmaticresults, and used in combination with nomograms de-signed to optimize the sphere.

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OL 41, MAY 2015

First author:Bruce D. Allan, MD, FRCOphth

Moorfields Eye Hospital, London,United Kingdom