Statistical guidelines for clinical studies of human vision.

Statistical analysis of data can be complex and different statisticians may disagree as to the correct approach leading to conflict between authors, editors, and reviewers. The objective of this article is to provide some statistical advice for contributors to optometric and ophthalmic journals, to provide advice specifically relevant to clinical studies of human vision, and to recommend statistical analyses that could be used in a variety of circumstances. In submitting an article, in which quantitative data are reported, authors should describe clearly the statistical procedures that they have used and to justify each stage of the analysis. This is especially important if more complex or 'non-standard' analyses have been carried out. The article begins with some general comments relating to data analysis concerning sample size and 'power', hypothesis testing, parametric and non-parametric variables, 'bootstrap methods', one and two-tail testing, and the Bonferroni correction. More specific advice is then given with reference to particular statistical procedures that can be used on a variety of types of data. Where relevant, examples of correct statistical practice are given with reference to recently published articles in the optometric and ophthalmic literature.

Three-dimensional magnetic resonance imaging of the phakic crystalline lens during accommodation.

PURPOSE: To quantify changes in crystalline lens curvature, thickness, equatorial diameter, surface area, and volume during accommodation using a novel two-dimensional magnetic resonance imaging (MRI) paradigm to generate a complete three-dimensional crystalline lens surface model. METHODS: Nineteen volunteers, aged 19 to 30 years, were recruited. T(2)-weighted MRIs, optimized to show fluid-filled chambers of the eye, were acquired using an eight-channel radio frequency head coil. Twenty-four oblique-axial slices of 0.8 mm thickness, with no interslice gaps, were acquired to visualize the crystalline lens. Three Maltese cross-type accommodative stimuli (at 0.17, 4.0, and 8.0 D) were presented randomly to the subjects in the MRI to examine lenticular changes with accommodation. MRIs were analyzed to generate a three-dimensional surface model. RESULTS: During accommodation, mean crystalline lens thickness increased (F = 33.39, P < 0.001), whereas lens equatorial diameter (F = 24.00, P < 0.001) and surface radii both decreased (anterior surface, F = 21.78, P < 0.001; posterior surface, F = 13.81, P < 0.001). Over the same stimulus range, mean crystalline lens surface area decreased (F = 7.04, P < 0.005) with a corresponding increase in lens volume (F = 6.06, P = 0.005). These biometric changes represent a 1.82% decrease and 2.30% increase in crystalline lens surface area and volume, respectively. CONCLUSIONS; The results indicate that the capsular bag undergoes elastic deformation during accommodation, causing reduced surface area, and the observed volumetric changes oppose the theory that the lens is incompressible.

Vergence analysis reveals the influence of axial distances on accommodation with age and axial ametropia.

Despite numerous investigations, the aetiology and mechanism of accommodation and presbyopia remains equivocal. Using Gaussian first-order ray tracing calculations, we examine the contribution that ocular axial distances make to the accommodation response. Further, the influence of age and ametropia are also considered. The data show that all changes in axial distances during accommodation reduce the accommodation response, with the reduction in anterior chamber depth contributing most to this overall attenuation. Although the total power loss due to the changes in axial distances remained constant with increasing age, hyperopes exhibited less accommodation than myopes. The study, therefore, enhances our understanding of biometric accommodative changes and demonstrates the utility of vergence analysis in the assessment of accommodation.

Theoretical evaluation of the cataract extraction-refraction-implantation techniques for intraocular lens power calculation.

PURPOSE: To evaluate theoretically three previously published formulae that use intra-operative aphakic refractive error to calculate intraocular lens (IOL) power, not necessitating pre-operative biometry. The formulae are as follows: IOL power (D) = Aphakic refraction x 2.01 [Ianchulev et al., J. Cataract Refract. Surg.31 (2005) 1530]; IOL power (D) = Aphakic refraction x 1.75 [Mackool et al., J. Cataract Refract. Surg.32 (2006) 435]; IOL power (D) = 0.07x(2) + 1.27x + 1.22, where x = aphakic refraction [Leccisotti, Graefes Arch. Clin. Exp. Ophthalmol.246 (2008) 729]. METHODS: Gaussian first order calculations were used to determine the relationship between intra-operative aphakic refractive error and the IOL power required for emmetropia in a series of schematic eyes incorporating varying corneal powers, pre-operative crystalline lens powers, axial lengths and post-operative IOL positions. The three previously published formulae, based on empirical data, were then compared in terms of IOL power errors that arose in the same schematic eye variants. RESULTS: An inverse relationship exists between theoretical ratio and axial length. Corneal power and initial lens power have little effect on calculated ratios, whilst final IOL position has a significant impact. None of the three empirically derived formulae are universally accurate but each is able to predict IOL power precisely in certain theoretical scenarios. The formulae derived by Ianchulev et al. and Leccisotti are most accurate for posterior IOL positions, whereas the Mackool et al. formula is most reliable when the IOL is located more anteriorly. CONCLUSION: Final IOL position was found to be the chief determinant of IOL power errors. Although the A-constants of IOLs are known and may be accurate, a variety of factors can still influence the final IOL position and lead to undesirable refractive errors. Optimum results using these novel formulae would be achieved in myopic eyes.

Operator-induced errors in Hartmann-Shack wavefront sensing: model eye study.

PURPOSE: To evaluate the effects of instrument realignment and angular misalignment during the clinical determination of wavefront aberrations by simulation in model eyes. SETTING: Aston Academy of Life Sciences, Aston University, Birmingham, United Kingdom. METHODS: Six model eyes were examined with wavefront-aberration-supported cornea ablation (WASCA) (Carl Zeiss Meditec) in 4 sessions of 10 measurements each: sessions 1 and 2, consecutive repeated measures without realignment; session 3, realignment of the instrument between readings; session 4, measurements without realignment but with the model eye shifted 6 degrees angularly. Intersession repeatability and the effects of realignment and misalignment were obtained by comparing the measurements in the various sessions for coma, spherical aberration, and higher-order aberrations (HOAs). RESULTS: The mean differences between the 2 sessions without realignment of the instrument were 0.020 microm +/- 0.076 (SD) for Z(3)(-1)(P = .551), 0.009 +/- 0.139 microm for Z(3)(1)(P = .877), 0.004 +/- 0.037 microm for Z(4)(0) (P = .820), and 0.005 +/- 0.01 microm for HO root mean square (RMS) (P = .301). Differences between the nonrealigned and realigned instruments were -0.017 +/- 0.026 microm for Z(3)(-1)(P = .159), 0.009 +/- 0.028 microm for Z(3)(1) (P = .475), 0.007 +/- 0.014 microm for Z(4)(0)(P = .296), and 0.002 +/- 0.007 microm for HO RMS (P = 0.529; differences between centered and misaligned instruments were -0.355 +/- 0.149 microm for Z(3)(-1) (P = .002), 0.007 +/- 0.034 microm for Z(3)(1)(P = .620), -0.005 +/- 0.081 microm for Z(4)(0)(P = .885), and 0.012 +/- 0.020 microm for HO RMS (P = .195). Realignment increased the standard deviation by a factor of 3 compared with the first session without realignment. CONCLUSIONS: Repeatability of the WASCA was excellent in all situations tested. Realignment substantially increased the variance of the measurements. Angular misalignment can result in significant errors, particularly in the determination of coma. These findings are important when assessing highly aberrated eyes during follow-up or before surgery.

Accuracy of cornea and lens biometry using anterior segment optical coherence tomography.

We assess the accuracy of the Visante anterior segment optical coherence tomographer (AS-OCT) and present improved formulas for measurement of surface curvature and axial separation. Measurements are made in physical model eyes. Accuracy is compared for measurements of corneal thickness (d(1)) and anterior chamber depth (d(2)) using-built-in AS-OCT software versus the improved scheme. The improved scheme enables measurements of lens thickness (d(3)) and surface curvature, in the form of conic sections specified by vertex radii and conic constants. These parameters are converted to surface coordinates for error analysis. The built-in AS-OCT software typically overestimates [mean+/-standard deviation(SD)]d(1) by +62+/-4 mum and d(2) by + 4 +/- 88 microm. The improved scheme reduces d(1) (-0.4 +/- 4 microm) and d(2) (0 +/- 49 microm) errors while also reducing d(3) errors from +218 +/- 90 (uncorrected) to +14 +/- 123 microm (corrected). Surface x coordinate errors gradually increase toward the periphery. Considering the central 6-mm zone of each surface, the x coordinate errors for anterior and posterior corneal surfaces reached +3 +/- 10 and 0 +/- 23 microm, respectively, with the improved scheme. Those of the anterior and posterior lens surfaces reached +2 +/- 22 and +11 +/- 71 microm, respectively. Our improved scheme reduced AS-OCT errors and could, therefore, enhance pre- and postoperative assessments of keratorefractive or cataract surgery, including measurement of accommodating intraocular lenses.

Non-invasive phakometric measurement of corneal and crystalline lens alignment in human eyes.

We describe a non-invasive phakometric method for determining corneal axis rotation relative to the visual axis (beta) together with crystalline lens axis tilt (alpha) and decentration (d) relative to the corneal axis. This does not require corneal contact A-scan ultrasonography for the measurement of intraocular surface separations. Theoretical inherent errors of the method, evaluated by ray tracing through schematic eyes incorporating the full range of human ocular component variations, were found to be larger than the measurement errors (beta < 0.67 degrees , alpha < 0.72 degrees and d < 0.08 mm) observed in nine human eyes with known ocular component dimensions. Intersubject variations (mean +/- S.D.: beta = 6.2 +/- 3.4 degrees temporal, alpha = 0.2 +/- 1.8 degrees temporal and d = 0.1 +/- 0.1 mm temporal) and repeatability (1.96 x S.D. of difference between repeat readings: beta +/- 2.0 degrees , alpha +/- 1.8 degrees and d +/- 0.2 mm) were studied by measuring the left eyes of 45 subjects (aged 18-42 years, 29 females and 16 males, 15 Caucasians, 29 Indian Asians, one African, refractive error range -7.25 to +1.25 D mean spherical equivalent) on two occasions.

Posterior retinal contour in adult human anisomyopia.

PURPOSE: It is well documented that myopia is associated with an increase in axial length or, more specifically, in vitreous chamber depth. Whether the transverse dimensions of the eye also increase in myopia is relevant to further understanding of its development. METHODS: The posterior retinal surface was localized in two-dimensional space in both eyes of young adult white and Taiwanese-Chinese iso- and anisomyopes (N = 56), from measured keratometry, A-scan ultrasonography, and central and peripheral refraction (+/-35 degrees) data, with the aid of a computer modeling program designed for this purpose. Anisomyopes had 2 D or more interocular difference in their refractive errors, with mean values in their more myopic eyes of -5.57 D and in their less myopic eyes of -3.25 D, similar to the means of the two isomyopic groups. The derived retinal contours for the more and less myopic eyes were compared by way of investigating ocular shape changes that accompany myopia, in the posterior region of the vitreous chamber. The presence and size of optic disc crescents were also investigated as an index of retinal stretching in myopia. RESULTS: Relative to the less myopic eyes of anisometropic subjects, the more myopic eyes were more elongated and also distorted into a more prolate shape in both the white and Chinese groups. However, the Chinese eyes showed a greater and more uniform relative expansion of the posterior retinal surface in their more myopic eyes, and this was associated with larger optic disc crescents. The changes in the eyes of whites displayed a nasal-temporal axial asymmetry, reflecting greater enlargement of the nasal retinal sector. CONCLUSIONS: Myopia is associated with increased axial length and a prolate shape. This prolate shape is consistent with the proposed idea that axial and transverse dimensions of the eye are regulated differently. The observations that ocular shape changes are larger but more symmetrical in Chinese eyes than in eyes of whites warrant further investigation.

Cling film as a barrier against CJD in Goldmann-type applanation tonometry.

PURPOSE: To determine the feasibility of taking intra-ocular pressure (IOP) readings with Goldmann-type applanation tonometer probe covered with cling film to avoid transmission of Creutzfeldt-Jakob disease (CJD). METHODS: Data were collected on two occasions from the right eyes of 30 healthy subjects using a Perkins applanation tonometer. On each occasion, a single tonometry measurement was made with and without cling film covering. RESULTS: Cling film covering brought about a statistically significant IOP bias (-0.8 mmHg on first occasion and -1.17 mmHg on second occasion). The 95% limits of agreement, between readings made with and without cling film covering, were +/-3.4 mmHg on first occasion; +/-2.5 mmHg on second occasion. A statistically significant reduction of inter-sessional repeatability was observed for readings taken with cling film (+/-5.2 mmHg) compared to those made without (+/-3.9 mmHg). CONCLUSIONS: Even if the above findings are found to be acceptable, given the known intra-subject variations of this type of tonometry (+/-4 mmHg), ethical and legal considerations relating to the barrier properties of cling film are likely to prevent its routine use by optometrists.

Cling film as a barrier against CJD in corneal contact A-scan ultrasonography.

PURPOSE: To determine the validity of covering a corneal contact transducer probe with cling film as protection against the transmission of Creutzfeldt-Jakob disease (CJD). METHODS: The anterior chamber depth, lens thickness and vitreous chamber depth of the right eyes of 10 subjects was recorded, under cycloplegia, with and without cling film covering over the transducer probe of a Storz Omega Compu-scan Biometric Ruler. Measurements were repeated on two occasions. RESULTS: Cling film covering did not influence bias or repeatability. Although the 95% limits of agreement between measurements made with and without cling film covering tended to exceed the intrasessional repeatability, they did not exceed the intersessional repeatability of measurements taken without cling film. CONCLUSIONS: The results support the use of cling film as a disposable covering for corneal contact A-scan ultrasonography to avoid the risk of spreading CJD from one subject to another.