0008_jrs_waring_standard graphs for reporting refractive surgery

$: 0008_JRS_Waring_Standard Graphs for Reporting Refractive Surgery$
459Journal of Refractive Surgery Volume 16 July/August 2000

S P E C I A L A R T I C L E

One of the most diffi cult problems facing refrac-tive surgeons is comparison of results among refractive surgical procedures. The need for

accurate comparisons among different studies is espe-cially acute because of the increasing variety of refrac-tive surgical techniques and procedures.

For example, how can refractive surgeons know how to compare the outcomes of laser in situ keratomileusis (LASIK) surgery with the Nidek EC-5000 scanning ex-cimer laser to those with an Autonomous LadarVision fl ying spot laser or a Bausch & Lomb 217Z Zyoptics wavefront-guided laser? If the refractive results with the Nidek laser are reported as the number of eyes ±0.50 diopter (D) of desired outcome, those with the Autono-mous laser as the mean spherical equivalent refraction, and those with the Bausch & Lomb as the number of eyes ±1.00 D of desired outcome, the surgeon has no basis for comparison of these refractive outcomes, and is left guessing.

In 1992, I published a monograph suggesting stan-dard methods for reporting refractive surgical proce-dures (Waring GO. Standardized data collection and reporting for refractive surgery. Refract Corneal Surg 1992;8(suppl):1-42). These standards were never wide-ly adopted, and authors and companies reported their fi ndings in a variety of ways, sometimes confusing. For example, some reported only the number of eyes that saw 20/25 uncorrected, obviously because the re-sults looked much better than they would if the stan-dard 20/20 or better criterion were used. None of the ophthalmic societies or standards organizations have made a formal proposal for standardized reporting of refractive surgery results. No journal has required its authors to present material in a standardized manner that would allow comparison among articles (Koch D,

Kohnen T, Obstbaum S, Rosen ES. Format for report-ing refractive surgical data. J Cataract Refract Surg 1998;24:285-287).

Therefore, to simplify matters, I propose here a set of six standard graphs* that should be included in any paper reporting the results of a series of cases. The idea is simple for authors to adopt, easy for editors to insist upon, and friendly for readers to digest. Graphs from different papers can be arranged side by side, allowing a direct visual comparison of the outcomes of different procedures and techniques.

This idea was proposed initially by Thomas Neu-hann, MD. The specifi c graphs and their presenta-tion have been developed by joint efforts of the edito-rial staffs of the Journal of Refractive Surgery and the Journal of Cataract and Refractive Surgery, including Drs Wallace Chamon, Daniel Epstein, Jack Holladay, Michael Knorz, Thomas Kohnen, Doug Koch, Ron Krueger, Stephen Obstbaum, Jeffrey Robin, Emanuel Rosen, Jonathan Talamo, and myself.

Such a requirement imposes an additional burden on the authors, but assists them in their ultimate goal—clear communication of their fi ndings. The Table (pg. 465) presents sources of software that authors can use to generate these graphs. All graphs can be created eas-ily except the scattergram, which requires some special consideration.

Each fi gure is arranged with clearly labeled X and Y axes with the units of measure. Relevant numerical information is present within the graph itself so that the numbers can be read directly from the graph, rather than requiring the reader to search along the Y axis for the actual number. A box within the graph presents the number of eyes and follow-up time (112 consecutive eyes at 3 months in the examples), so the population reported is immediately identifi ed. Relevant summary numbers are presented in a second box to allow the reader to see “the answer” at a quick glance.

Standard Graphs for Reporting Refractive SurgeryGeorge O. Waring III, MD, FACS, FRCOphth

From Inview, Atlanta, Ga.

Correspondence: George O. Waring III, MD, FACS, FRCOphth, Inview, 301 Perimeter Center North, Ste 600, Atlanta, GA 30346. Tel: 678.222.5102; Fax: 404.250.9006; E-mail: [email protected] *Updated June 2005.

journalofrefractivesurgery.com460

Standard Graphs for Reporting Refractive Surgery/Waring

Scattergrams have the advantage of presenting the outcome of every eye, so that nothing is lost in means or averages and outliers can be easily identifi ed. Since the most important outcome of refractive surgery is the re-fraction, we selected the scattergram of the attempted refractive change vs. the achieved refractive change for each eye. For a scattergram to accurately represent the outcome visually, the scale of the X and Y axes must be the same (A). Unfortunately, many software programs do not allow this presentation, usually allowing a larger spread along the X axis than along the Y axis (B). Authors should make every attempt to keep the X and Y axes on the same scale (A), but it may be necessary to accept disparate axis scales (B).

Figure 1. Scattergrams of attempted vs. achieved refraction

Source of Data for Example GraphsThe data displayed in the various graphs are from the Emory Vision Correction Center, Atlanta, Georgia, an early series of eyes done with the Nidek EC-5000 laser and the Chiron Automated Corneal Shaper microkeratome for the correction of myopia. The series of 112 consecutive eyes at 3 months after laser in situ keratomileusis (LASIK) are part of a larger study, and the data are not presented to represent overall clinical results from the series, but rather are selected only to create the graphic examples.

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This bar graph represents the postoperative spherical equivalent refraction in small steps. It is possible to take the data in the graph and see easily how many eyes fall within whatever categories the reader wishes to quantify: plano to �0.50 D, �0.50 D, �1.00 D. The full range of refractive results is also presented. At the present time, the gold standard for refractive outcome is to be within �0.50 D of the desired result, and this number is displayed in the summary box. In the future, a more exact summary number may be used.

Figure 2. Spherical equivalent refractive outcome bar graph



Refractive outcome is commonly reported as the spherical equivalent refraction, which is computed as the spherical component added to one-half of the cylindrical component, respecting the sign of the cylinder—but this can be misleading. For example, two eyes after a refractive surgical procedure may have refractions of: Eye #1, �1.00 �2.00 � 90°, and Eye #2, �1.00 �2.00 � 180°; the spherical equivalent refraction of Eye #1 is plano— clearly a perfect result, whereas the spherical equivalent refraction of Eye #2 is �2.00 D, not a very good outcome. Of course, the plano representation of Eye #1 is misleading because of the residual astigmatism. This problem is solved by computing the defocus equivalent, which is simple to compute. To get the spheroequivalent, take the sphere [respecting sign], and add half the cylinder [respecting sign]. Then, to calculate the defocus equivalent, take the spheroequivalent and add one-half of the cylinder, ignoring the sign. Thus, in the above example, the defocus equivalent of Eye #1 is 1.00 D, and the defocus equivalent of Eye #2 is 3.00 D (note there is no sign); the defocus equivalent values more accurately represent the reality of the refractive state of the two eyes.

The defocus equivalent bar graph is presented as a cumulative graph, building in one direction and presenting the number of eyes with a given defocus equivalent value. The defocus equivalent was fi rst defi ned by Holladay et al in 1991 (Holladay JT, Lynn MJ, Waring GO, Gemmill M, Keehn CG, Fielding B. The relationship of visual acuity, refractive error, and pupil size after radial keratotomy. Arch Ophthalmol 1991;109:70-76) to eliminate the inequity between eyes that had similar spheroequivalent refractions but different amounts of astigmatism. The defocus equivalent is proportional to the area of the blur circle of the conoid of Sturm.

[Updated 5/2001]

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Figure 3. Defocus equivalent bar graph



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Figure 4. Uncorrected visual acuity bar graph

The bar graph depicting visual acuity has two components.Component #1 is the spectacle-corrected visual acuity at baseline; this is important because it is helpful to

know the overall visual potential of the population before looking at the postoperative vision. For example, con-sider a group of eyes with a baseline refraction of �1.00 to �4.00 D that are receiving intracorneal ring segments; the vast majority of these eyes will be able to see 20/20 or better with spectacle correction before surgery. Con-trast this to a group of eyes with a refraction of �15.00 to �25.00 D that are receiving a phakic intraocular lens. It is likely that less than half of these eyes can see 20/40 or better with spectacle correction before surgery. Thus, interpreting the postoperative uncorrected visual acuity results would be different in these two populations, the number of eyes seeing 20/20 or better without correction being a fair and appropriate criterion to apply to the low myopia eyes receiving intracorneal ring segments, but a less appropriate criterion applied to high myopia eyes that receive phakic intraocular lens.

Component #2 is a cumulative bar graph of uncorrected visual acuities after surgery. The visual acuities begin at 20/10 and proceed in log units. This is important because as refractive surgery improves, the goal is to identify accurately the number of eyes that see 20/10, 20/12.5, 20/16, and 20/20; these fi ner distinctions will be used more and more to differentiate among refractive surgery procedures. The X axis represents the full spectrum of visual acuities as demonstrated on the National Eye Institute Vision charts, and as more offi ces and clinics adopt these charts as the standard for measuring visual acuity, it will be easier to make sense of the measurement. As long as different studies use different visual acuity charts under different testing circumstances, comparison of visual acuities among studies will be somewhat fl awed.

Of course, if one wishes to eliminate the effects of magnifi cation and optical distortion and vertex power imposed by spectacle lenses, especially in high ametropes, a preoperative contact lens-corrected visual acuity would be the most appropriate standard for comparison to postoperative uncorrected visual acuity.



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Figure 5. Change in spectacle-corrected visual acuity bar graph

The bar graph depicts the change in spectacle-corrected visual acuity from baseline to the postoperative ex-amination in terms of the number of Snellen lines changed. This is the most commonly used measure of safety because it answers the question, “If the refractive outcome is not totally acceptable, can the patient put glasses on again and see as well as they did before surgery?” A change of 1 Snellen line is within the range of normal biological variability for repeated measures, and therefore is not a meaningful change. A change of 2 or more Snellen lines has been generally adopted as the standard for safety, and is reported in the summary box. Some groups recommend reporting a loss of “more than 2 lines” as the standard, which of course makes it easier to have a “safe” procedure. Ideally, this change would be measured by counting the total number of letters seen on the chart and computing a Snellen line equivalent.



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Figure 6. Stability of refraction graph

The timeline depicts the mean spherical equivalent refraction and one standard deviation depicted by the er-ror bars at various intervals after surgery. This allows determination of stability of the refraction, but the intervals chosen and the time depicted will depend on examination frequency in any given series. Percent of eyes that changed by �0.50 D is given for the total follow-up time in the summary box. The error bars are important be-cause a wide spread of the standard deviation would show that there is considerable instability in the refraction, even though the means may show minimal change over time.

TABLEStandard Graph Software Sources*

Outcomes Analysis Software, Inc.PO Box 1097Rancho Santa Fe, CA 92067, USATel/Fax: 858.856.4462; E-mail: [email protected]

Datagraph med(Medical Data Analysis Software)Ingenieurbüro PiegerTreidelsweg 8, D-90530 Wendelstein, GermanyTel: 49.9129.27382; Fax: 49.9129.27163; E-mail: [email protected]

SigmaPlot, SPSS Science

Excel, Microsoft Corporation

The Journal of Refractive Surgery provides no specific endorsement of the above listed software packages.



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Scattergram of attempted vs. achieved refraction

Spherical equivalent refractive outcome bar graph

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Defocus equivalent bar graph Visual acuity bar graph (SCVA = spectacle corrected visual acuity, UCVA = uncorrected visual acuity)

Change in spectacle-corrected visual acuity bar graphStability of refraction graph. Error bars indicate one standard deviation.

All six graphs can be presented on one page of a standard sized journal. This would allow the reader to scan easily the six fi gures to get the overall graphic picture of the major outcome variables. In addition, single pages from different articles could be displayed side by side for rapid visual comparison on the results.

Figure 7. Composite plate

0008_jrs_waring_standard graphs for reporting refractive surgery

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