## Introduction

Cataract surgery is the most common operation performed in the National Health Service (NHS), with around 330 000 procedures carried out each year in England.1 Phacoemulsification and removal of cataract with implantation of a synthetic intraocular lens (IOL) provides significant patient benefit.2 Benchmark standards for refractive outcomes after cataract surgery have been put forward by The Royal College of Ophthalmologists. It is recommended that the postoperative spherical equivalent should be within 1 dioptre of that aimed for in 85% of operations, and within 0.5 dioptres in 55% of operations.1 3 Refractive outcomes have generally improved with time as a result of refinements in operative techniques, acquisition of increasingly accurate biometric data and the refinement of biometric formulae used to calculate the IOL power.4–6 Although these have led to a progressive reduction in spherical equivalent prediction errors, it is not a good predictor of spectacle independence.7 The analogy is that spectacle prescriptions are not prescribed or dispensed as a spherical equivalent but as a sphero-cylinder.

Laser vision correction (LVC) has become increasingly popular for the correction of refractive errors, commonly laser in-situ keratomileusis (LASIK), laser epithelial keratomileusis (LASEK) or photorefractive keratectomy (PRK). Many patients who have previously undergone LVC are now developing cataract and presenting for surgery.8 The formulae which are commonly used for IOL power calculation, such as the SRK-T and Hoffer Q formulae, are prone to error in patients who have had LVC for a number of reasons.9–14 Standard formulae assume a fixed relation between the anterior and posterior corneal surface curvatures. This assumption does not hold for eyes which have undergone myopic LVC as the anterior corneal curvature is reduced, so that the ratio between the anterior and the posterior curvature is altered, along with the total corneal power and index of refraction.15 16 In addition, keratometers measure the central corneal zone and assume a sphero-cylindrical shape to the cornea, which is no longer true after LVC.17 All third and fourth generation IOL calculation formulae also use the central corneal power to help predict the effective lens position (ELP). In patients with myopic ablation patterns, however, the central cornea has been flattened, and these formulae predict a falsely shallow ELP, thereby recommending insufficient IOL power, causing postoperative hyperopic surprise.16 18 19 Higher order aberrations induced by LVC are also not taken into account in standard practice.

All of these factors can lead to inaccuracies in biometric calculations using standard formulae and a large deviation from the expected refractive outcome for the IOL power selected. These 'refractive surprises' can lead to very unhappy patients with the need for further risk-prone procedures such as IOL exchange or further LVC. A number of methods have been introduced to measure or estimate the true corneal power after LVC. The Clinical History Method (CHM), introduced by Holladay in 1989, calculates the corneal power by subtracting the change in manifest refraction at the corneal plane induced by the refractive surgical procedure from the corneal power obtained before refractive surgery.20 There are however, a number of limitations to the CHM. The relevant historical information may be unavailable and of questionable reliability. There may also have been changes in the corneal curvature since the initial LVC procedure. A number of alternative methods have since been proposed for calculating the IOL power required.12 21–23 Recent work has suggested that the Masket Method, the Haigis-L, the Shammas post-Lasik (Shammas-PL) and the Barrett True-K formulae give some of the most reliable predictions for choosing IOL power.24–28

An important issue when considering IOL power calculations and refractive outcomes which has often been overlooked is the effect of uncorrected residual sphero-cylindrical refractive error, even though these appear to have a marked adverse effect on unaided vision.7 This means that the advantages and disadvantages of different approaches to improve refractive outcomes in patients undergoing cataract surgery who have had refractive laser surgery may not be readily apparent.

Other approaches have been applied to treat the components of the refractive error as independent terms, that is, separation of the sphere and cylinder. They are not, however, independent variables and a change in one is invariably associated with a change in the other.29–31 Attempts to treat the components of a refractive power independently, regardless of whether the cylinder is treated as a vector or a scalar number, will introduce errors and potentially lead to statistically erroneous conclusions.32–35

There are now informative and established methods to treat the analysis of refractive errors appropriately and which are easily applicable to assess refractive outcomes following cataract surgery.36–39 The purpose of this study was to compare the differences between the intended and actual postoperative refractive outcomes using the CHM, Masket, Shammas-L, Haigis-L and the Barrett True-K formula methods following cataract surgery in patients who had undergone previous LVC. Outcomes in LVC patients were also compared with a group of control patients who had not undergone LVC. We used an innovative analytical technique using the sphero-cylindrical error with refractive outcome data being transformed into components of Long’s formalism before transformation back into sphero-cylindrical notation. Analysis using the spherical equivalent error was also presented for reference.