Standardised approach to the reporting and presentation of refractive data: electronic patient record

Refractive error and refractive power are core measures in ophthalmology, optometry and vision science. Refractive error measures what is missing, that is, a departure from emmetropia whereas refractive power for example, keratometry measures what is present. Refractive error is used to determine outcomes for many conditions, such as myopia or hypermetropia, amblyopia, anisometropia, outcomes of corneal transplants, progression of keratoconus and cataract and refractive surgery.

Sphere/cylinder x axis (  ) is one of the core measures used for paraxial optics (light rays close to the optical axis and so relatively independent of the angle of incidence) and thin Gaussian lenses and forms the basis of most clinical work.

  is used to evaluate and report refractive data as the lenses in the trial lens case or phoropter are made as combinations of spheres and cylinders.    is a compound number, the components of which S, C and axis, are dependent on each other. Despite this, it is common for the components to be viewed and treated incorrectly as independent variables. For example, S is used to measure the spherical component of a person’s refractive error and the cylinder (C) either on its own or in combination with the axis (A) to reflect and measure the person’s astigmatism. For groups of patients and for comparison of outcomes, it is also common in the literature for the components of   , that is S, C or    to be separately (independently) added together without transformation, and for statistical measures to be calculated to evaluate and report outcomes. For example, it is not uncommon to see reports in the literature where C has been used to measure the change in astigmatism before and after an intervention.

A spherical equivalent (SEq) is an often-used measure, because of its simplicity as a scalar variable and it is easily calculated as   . Despite its usefulness there is an obvious weakness of the SEq, as there are an infinite number of refractive errors having the same SEq value. It is important to note that although the term SEq is widely used, the preferable term is the nearest equivalent sphere1 (NES) as there may be other formulae than    used to provide a measure. SEq is also an insensitive measure. It has been shown following cataract surgery for example, that if    is used as a compound number to measure refractive outcome, many more patients are identified as refractive outliers than using the NES or the Cylinder, or an aggregation of NES and Cylinder.2 Such patients are more likely to depend on spectacles or contact lenses for distance correction due to uncorrected astigmatic errors.3

For cataract surgery, refractive aims continue to evolve, from leaving the eye aphakic, inserting a standard intraocular lens (IOL), devising the first regression IOL power formulae to the current development of multi-variable formulae. Relying on NES to achieve better outcomes, however, results in a law of diminishing returns as we have achieved only a modest improvement in NES using multivariable formulae and highly sophisticated biometry machines, compared with immersion ultrasound and a third generation IOL formulae from 20 years ago. It is clear, therefore, that more sensitive measures such as the actual refractive error that is,    are needed.4 In essence    provides a more tailored approach when planning cataract surgery whether using monofocal or toric IOLs.

As noted above, there have been many attempts to treat the components of the refractive error    as independent terms despite an abundance of evidence to show that these approaches are flawed and lose information.5–10

For example, consider the following two refractive (paraxial) powers:    and   . If they were to be added together without transformation, what would be the result? There are three possibilities depending on whether each component is treated independently or dependently.3

(1) If they are treated independently as scalar values, this leads to the following situation,

  , which is incorrect.

(2) If the sphere and cylinder powers are added independently, this leads to

or   , which again is incorrect.3

(3) If, however, they are treated dependently, then

or   , which is the correct result.3

To avoid these errors, refractive data needs to be treated as a compound number, that is,   .7 Importantly, it has been shown that as a compound measure, the Sphere/Cylinder x Axis allows a measure of refractive blur as a global outcome and surrogate marker of vision.11 12

There are well established robust methods to measure differences and changes in refractive error and to present this information as   .7–11 13 14 These methods transform refractive error into components which are independent; equivalent to plotting a point using X, Y and Z axes (which are orthogonal to each other and therefore independent). Once transformed, compound number calculations such as differences, total, mean, SD, significance tests etc, can legitimately be undertaken6 8 prior to the data being transformed back into the standard familiar format of   . These methods provide accurate information needed clinically to decide whether there has been a meaningful change or progression in a condition.

The proposal, therefore, is not to disregard the NES, but to record and analyse refractive errors as Sphere/Cylinder x Axis (  ) in addition to current practice which uses (  ). Provision of both within an electronic medical or patient record has the potential to identify options to improve outcomes whether it be optimisation of IOL formula or a reduction in astigmatism.

Examples of clinical scenarios can be informative.

• A cataract surgeon may want to compare the expected to actual refractive outcome following surgery. If the expected or intended outcome following cataract surgery is    but the actual post-operative outcome is    (  ), how should the difference be calculated that is, how far is the actual from the intended? Both the intended and actual have a SEq of   , so no apparent difference. Using the difference in cylinders is gives −0.50 (calculated as a scalar) or    if calculated treating the cylinder independently as a vector (both are incorrect). The actual difference in the refractive outcome, however, when treating the intended and actual outcome as compound numbers is    (for intended minus actual). Note the order is important that is, one needs to stipulate whether intended minus actual or actual minus intended as the axis of the difference will change by 90 degrees.

• A Paediatric Ophthalmologist will want to know the correct magnitude of a child’s anisometropia and/or whether a child’s refractive error has changed due to treatment of their amblyopia. As an example, if the refractive error of a child’s right eye is    and left eye is   , the anisometropia (right eye minus left eye) is   . Note if using the NES this difference would be just 0.25 D.

Astigmatism is an important measure. Despite this, for the majority of patients undergoing cataract surgery, astigmatism does not form part of the outcomes used to measure the quality of clinical services.15 Nevertheless, studies have shown that residual astigmatism has a far greater effect on unaided distance vision compared with residual spherical error.3 In fact, with the current standards of refractive outcomes using monofocal non-toric IOLs in a non-selected population, patients are seven times more likely to need distance glasses due to uncorrected astigmatism, compared with uncorrected spherical refractive error.16

The cylinder component of    is often equated with astigmatism.1 The cylinder (C) does contain or spans astigmatism but also contains a spherical equivalent of    (if one accepts the concept of a spherical equivalent). For example, if the NES of a cylinder is subtracted from the cylinder, a Jackson cross-cylinder (JCC) results, that is,   .1 In contrast a JCC always has a spherical equivalent of zero and is therefore, a pure paraxial measure of astigmatism. JCCs can be added but always result in a JCC.1 Similarly, adding spherical equivalent, always results in a spherical equivalent. In contrast a cylinder (C) power when added to another cylinder C may result in a sphere e.g.,    or a spherocylinder, for example,   , rather than always another cylinder.

The    representation of refractive data, therefore, can be transformed and decomposed into an NES and a JCC, that is,   . For example,    has an NES of +0.50 and a JCC   . This provides a measure of the amount of sphere present (NES) and the amount of astigmatism.

For example, if a patient’s astigmatism changes from    to    this represents a change in astigmatism of    . A JCC lends itself to toric IOL calculations which predict a post op cross-cylindrical value at the corneal or spectacle plane.

The methods of analysing spherocylindrical outcomes using Long’s formalism13 have been available for decades but as they require more calculation, they have not been adopted in routine clinical practice. To analyse refractive and keratometric data, requires transformation into Long’s formalism, following which any number of robust analyses can be undertaken.2 4 Note, refractive powers such as    may be decomposed into a    and a    and then added following transformation into Long’s formalism as shown below.

In recent years, electronic patient records (EPRs) have replaced paper records, and this has greatly expanded the capabilities for performing audit and analysing outcomes. EPRs can carry out calculations automatically in the background that is, transform the data, analyse and then transform the data back into    thereby providing clinicians with the information needed to improve clinical practice.16 17 In addition, there are many other derivatives that can be calculated once the data has been transformed into Long’s formalism e.g.,   , including blur strength which can be used as surrogate outcomes for unaided vision.12 14 18 19 It should be noted that Fick introduced the ideas of applying matrices and linear algebra to dioptric power20–22 while Long (1976)13 and Keating (1980/1),23 24 working independently, provided conversion equations from clinical notation to power matrices and back to clinical notation.

Rubin et al,25 have reviewed issues which affect the analysis of refractive state such as data normality, transformations, outliers and anisometropia. They provide a review of the methods needed for analysing and representing dioptric power and concentrate on the optimal approach to understanding refractive state in addressing pertinent clinical and research questions. They demonstrate the need to use power matrices rather than power vectors for the analysis of refractive state. For example, identification of outliers in refractive data and the need to be able to transform samples of dioptric power towards normality.

In a second article, Evans and Rubin26 review the basic principles of linear optics and discuss the use of linear optics in quantitative analysis with application to clinically important issues such as chromatic aberrations, positioning and design of IOL and magnification. They demonstrate how the application of linear optics is needed for the understanding of paraxial optical systems for example, astigmatic, tilted and decentred IOLs which clinicians commonly encounter.

The important issue is that all of these analyses can be undertaken within an EPR providing the clinician with robust systems for the analysis of refractive data

Encouraging EPR providers to analyse refractive and keratometric data in the correct format would facilitate many audit and research studies which would in turn bring benefits to patients.2 4 Specifically, the routine compound number analysis of    refractive data can provide added value to patients through provision of clear clinically accessible information to eye health professionals when planning an intervention. By complimenting existing NES-based approaches there is potential to enhance the care of individual patients and the provision of accurate summary outcomes for tracking groups of patients. Moving forwards, it is highly desirable therefore that EPRs are upgraded to transform refractive data into Long’s formalism for analysis, and then to transform and present the data back into    for eye health professionals. As the widespread use of EPRs has greatly expanded our ability to audit our outcomes, we should take advantage of automation of robust refractive calculations which could be included within EPRs.

Linked articles

Vision Science | 1 April 2022

Comparison of the Near Eye Tool for Refractive Assessment (NETRA) and non-cycloplegic subjective refraction

Nabeela Hasrod, Alan Rubin

Review | 1 April 2022

Dioptric power and refractive behaviour: a review of methods and applications

Alan Rubin, Tanya Evans, Nabeela Hasrod

Review | 1 April 2022

Linear optics of the eye and optical systems: a review of methods and applications

Tanya Evans, Alan Rubin

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Footnotes

• Contributors: All authors developed and wrote the editorial.

• Funding: The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

• Competing interests: Mr. Khawaja has acted as a consultant to Abbvie, Aerie, Google Health, Novarits, Reichert, Santen and Thea

• Provenance and peer review: Commissioned; internally peer reviewed.

Ethics statements

Patient consent for publication:

Not applicable.

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