March 2011
Volume 52, Issue 3
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Clinical and Epidemiologic Research  |   March 2011
Correlation between Refractive Error, Corneal Power, and Thickness in a Large Population with a Wide Range of Ametropia
Author Affiliations & Notes
  • Tahra AlMahmoud
    From the Department of Surgery, Faculty of Medicine and Health Sciences, United Arab Emirates University, Al Ain, United Arab Emirates; and
  • David Priest
    Department of Ophthalmology, University of Ottawa Eye Institute, Ottawa, Ontario, Canada.
  • Rejean Munger
    Department of Ophthalmology, University of Ottawa Eye Institute, Ottawa, Ontario, Canada.
  • W. Bruce Jackson
    Department of Ophthalmology, University of Ottawa Eye Institute, Ottawa, Ontario, Canada.
  • Corresponding author: David Priest, University of Ottawa Eye Institute/Ottawa Health Research Institute, Ottawa Hospital General Campus, 501 Smyth Road, Ottawa, Ontario K1H 8L6, Canada; dpriest@ohri.ca
Investigative Ophthalmology & Visual Science March 2011, Vol.52, 1235-1242. doi:10.1167/iovs.10-5449
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      Tahra AlMahmoud, David Priest, Rejean Munger, W. Bruce Jackson; Correlation between Refractive Error, Corneal Power, and Thickness in a Large Population with a Wide Range of Ametropia. Invest. Ophthalmol. Vis. Sci. 2011;52(3):1235-1242. doi: 10.1167/iovs.10-5449.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: To determine the correlations between mean keratometry (KM), central corneal thicknesses (CCT), and cycloplegic spherical equivalent (SE) in patients with a wide range of ametropia.

Methods.: Retrospective analysis of the excimer laser surgery database at the University of Ottawa Eye Institute between 1993 and 2008 was performed. This study included 3395 eyes from 1858 subjects. The refractive error ranged from +6.75 to −14.00 D. CCT was obtained either by ultrasound pachymetry or anterior segment tomography. Keratometry was determined using an autokeratorefractometer.

Results.: In the myopic group, the SE was observed to be inversely proportional to the KM (correlation coefficient, −0.18; P < 0.01). The KM and CCT were also inversely proportional (−0.11; P < 0.01). In hyperopes, a correlation between the cycloplegic SE and KM was also found (−0.25; P < 0.01), but the CCT did not correlate with either of these metrics. A direct correlation for the myopic group was found between KM and the difference in power of the principal meridians (keratometric astigmatism [KA]) (0.08; P < 0.01). This relationship was not observed for the hyperopic group. Within the myopic group the SE correlated with the refractive astigmatism (RA) (−0.04; P = 0 0.04). In all groups, a strong correlation was observed between RA and KA (0.78; P < 0.01).

Conclusions.: In the myopia group, the KM showed close correspondence with KA and an inverse relationship with SE and CCT. In hyperopes, an inverse correlation between the KM and SE was found, but no correlation with CCT was evident.

Central corneal thickness (CCT) is an important parameter in patient screening before any refractive surgeries. Keratometry measurement has also been identified as a contributing factor that influences visual outcome in hyperopic patients after refractive procedures. 1 Two of the main risk factors associated with the development of postrefractive corneal ectasia are CCT below 500 μm and mean keratometry greater than 47.00 D. 2 It is important to better understand the relationship between risk factors and other ocular parameters (i.e., refractive error) to optimize refractive treatments. 
Several studies have shown that axial length (AL) is strongly correlated to the degree of refractive error. 3 5 Corneal radius of curvature (CR) has also been studied extensively. Although some studies reported no correlation between refractive error and CR in different refractive groups, 6 others have found that myopic subjects have a smaller CR than emmetropes. 7,8  
Keratometric values are obviously related to CR. Consequently, hypotheses can be made about the relationship between keratometry and the refractive status of an eye, but it is not clear how keratometry correlates to ocular parameters within a population with a wide range of refractive errors. 
CCT has become very important for the interpretation of intraocular pressure 9 and prerefractive procedure assessment; however, little is known about its distribution within a population with a wide range of refractive errors. 
The first aim of this study was to determine the range, distribution, and correlation of various ocular parameters in a large number of patients with a broad range of refractive errors. Our secondary goal was to develop linear models for the keratometry and central corneal thickness that describe how these factors are distributed in potential refractive surgery patients. 
Methods
This study is a retrospective analysis of the preoperative data of all patients who underwent primary refractive surgery procedures between March 1993 and October 2008 at the University of Ottawa Eye Institute. Exclusion criteria were previous laser refractive or other ocular surgery, history of corneal injury, and incomplete data that preclude analysis. Complete data were available from a total of 3395 eyes (1858 subjects), with 51% right eyes and 61.7% females. This study adheres to the Declaration of Helsinki and was approved by the Ottawa Hospital Research Ethics Board. 
One week before treatment all patients had a complete baseline ocular examination including manifest followed by cycloplegic refraction, corneal pachymetry, and keratometry; age and sex were also recorded. Cycloplegic refraction was obtained 30 minutes after instillation of tropicamide (1% Mydriacyl; Alcon Inc., Hunenberg, Switzerland). Manifest refraction was undertaken by determination of best vision sphere and Jackson's cross-cylinder technique. All refractions were performed using a phorapter (Ultramatic RX Master PHOROPTOR; Reichert, Depew, NY) with a vertex distance of 12.5 mm. For the analysis, cycloplegic refraction was used as the measure of spherical refractive error, and the cylinder power and axis were kept the same as the manifest refraction. The spherical equivalent (SE) was calculated as the sum of the sphere and half the refractive astigmatism (RA) in diopters (D). Outcome measures of relevance for this study were refraction, keratometry, CCT, age, and sex. 
Ultrasound (US) pachymetry (DGH 500; DGH Technology, Exton, PA) was used to measure central corneal thickness (CCT) before 2003. Thereafter, these data were obtained using anterior segment tomography (Pentacam; Oculus, Wetzlar, Germany), which uses the Scheimpflug system to provide topography maps of the anterior and posterior corneal surfaces and pachymetry maps in a noninvasive fashion. The minimal corneal thickness was chosen as the parameter for analysis. Corneal keratometry in the flat (K1) and steep (K2) axes were determined by using one of two keratometers (Zeiss Humphrey automatic refractor/keratometer 599; Humphrey Instruments, San Leandro, CA; or Topcon KR-3000 autorefractor keratometer; Topcon, Paramus, NJ). The mean keratometry measure (KM) was used for data analysis, and it was calculated as the sum of K1 and K2 divided by two. The keratometric astigmatism (KA) was calculated as the difference in power between the principal meridians (i.e., K2 minus K1). 
The dataset was analyzed using two approaches. Initially, analysis was performed with all the data included in this study as a single group. For the second analysis, the data were subdivided into two refractive groups, the myopes (SE < 0) and the hyperopes (SE > 0). The eyes with a spherical equivalent equal to zero were excluded in this analysis. 
The first step in the analysis was calculating Pearson product-moment correlation coefficients to identify any statistically significant correlations between any of the outcome measures SE, RA, KM, KA, CCT, and age. To identify any data bias, ANOVA was then applied to determine whether statistically significant differences exist in the mean values of the metrics due to sex or right and left eyes. 
Based on the results of the initial tests, multivariant linear regression models were created. These models were developed to quantify the dependence of keratometry and CCT on the other outcome measures of the study. Graphs are presented that display the most dominate relationship for each of the multivariant regressions. Best-fit lines were calculated from bivariant linear regression and are displayed in the figures to help visualize the relationship between the two variables. Although principal-axis analysis would provide the best method to quantify the relationship between two variables in this dataset, its application is beyond the scope of this project. 
In our study many patients contributed data from both eyes, but these observations cannot be considered independent from one another even though they originate from different eyes. To account for this, the linear regression incorporated a Huber/White robust estimate of variance. 10,11 This test pools the data from a single subject into a cluster and then treats the clusters as if they are independent of each other. This method is preferable to the various means of selecting a single eye to analyze because it utilizes all available data and avoids potential bias from patients who have contributed only one eye to the study. 12 All analyses were carried out using a general-purpose statistical package (Intercooled Stata 7.0; Stata Corporation, College Station, TX), and the level of statistical significance was set at P < 0.05. 
Results
Demographic data relating to 3395 eyes from 1858 subjects who presented for refractive surgery (Table 1) revealed the range and distribution of the metrics describing the three datasets. The prevalence of myopia was 90%, and 51% of the analyzed data were from the right eye. No statistically significant difference (ANOVA) in the mean value of metrics was found between right and left eyes. However, there were differences in the mean values of SE, KM, KA, and CCT between male and female subjects (Table 2). 
Table 1.
 
Demographics
Table 1.
 
Demographics
Variable Complete Dataset (n = 3395) Myopes (n = 3091) Hyperopes (n = 284)
Mean ± SD Range Mean ± SD Range Mean ± SD Range
SE, D −3.90 ± 3.07 −14.00 to 6.75 −4.58 ± 2.21 −14.00 to −0.13 3.21 ± 1.53 0.13 to 6.75
RA, D 0.80 ± 0.86 0.00 to 6.00 0.80 ± 0.85 0.00 to 6.00 0.81 ± 0.90 0.00 to 5.25
KM, D 43.95 ± 1.47 38.38 to 48.75 44.02 ± 1.43 38.88 to 48.75 43.17 ± 1.67 38.38 to 48.25
KA, D 1.05 ± 0.74 0.00 to 5.75 1.05 ± 0.72 0.00 to 5.75 1.09 ± 0.85 0.00 to 4.50
CCT, μm 544 ± 34 414 to 659 543 ± 34 441 to 659 552 ± 37 414 to 645
Age, y 40 ± 10 19 to 84 39 ± 10 19 to 84 51 ± 9 21 to 71
Table 2.
 
Demographics of the Male and Female Groups
Table 2.
 
Demographics of the Male and Female Groups
Variable Females (n = 2048) Males (n = 1347)
Mean ± SD Range Mean ± SD Range
SE, D −4.07 ± 3.06 −11.63 to 6.75 −3.65 ± 3.06 −14.00 to 6.25
RA, D 0.78 ± 0.83 0.00 to 6.00 0.83 ± 0.89 0.00 to 5.25
KM, D 44.21 ± 1.40 38.38 to 48.75 43.54 ± 1.47 38.75 to 48.25
KA, D 1.08 ± 0.74 0.00 to 5.75 1.01 ± 0.73 0.00 to 4.75
CCT, μm 543 ± 34 438 to 659 545 ± 33 414 to 645
Age, y 40 ± 10 19 to 71 40 ± 10 19 to 84
Keratometry
Weak but statistically significant correlations to KM were observed (Table 3) for SE, KA, CCT, and age in the complete dataset. For the myopic group, KM correlated with the SE, KA, and CCT, whereas KM correlated only with the SE in the hyperopic group. 
Table 3.
 
Correlation Analysis
Table 3.
 
Correlation Analysis
  Correlation Analysis
The multivariate linear model for KM was developed as a function of SE, CCT, age, and sex (Table 4). SE and sex were the only significant variables in all datasets. CCT was only a significant variable in the myopic and complete groups. Age was not a significant factor once the other significant variables were taken into account. 
Table 4.
 
Mulitvariate Linear Regression of KM
Table 4.
 
Mulitvariate Linear Regression of KM
  Mulitvariate Linear Regression of KM
Across the entire range of refractive errors in this study, the KM was found to increase by 0.11 D for every diopter of decrease in refractive error (Fig. 1). The SE versus KM slope became statistically significant when range was −3.5 D ≤ SE ≤ 2.5 D (this subgroup included 1292 observations). When KM was stratified by sex (Fig. 2) male eyes were observed to have significantly flatter corneas than female eyes (average KM: male, 43.54; female, 44.21) across the entire range of refractive errors. A comparison of the relationship between KM and SE of the male and female groups (Table 5) revealed there was no statistically significant difference in the rate of change of KM as a function of SE (slope of curves in Fig. 2), but the difference in their intercepts was statistically significant. KM for male eyes was approximately half a diopter lower than female eyes with the same SE. 
Figure 1.
 
The correlation between KM and SE is shown in both a scatter plot (A) and a box plot (B). The line in both graphs is the linear regression (r 2 = 0.06, P < 0.0001). A box plot displays statistical values for ranges of data. The line within the box marks the median. The boundary of the box indicates the 25th and 75th percentile. Error bars represent the 10th and 90th percentiles. Symbols mark the 5th and 95th percentiles. The number of data points in the range for each box is also displayed. The gap in the plots is because our population is made up of potential refractive surgery patients (i.e., there were no emmetropes and relatively few with “near emmetropia” refractive error).
Figure 1.
 
The correlation between KM and SE is shown in both a scatter plot (A) and a box plot (B). The line in both graphs is the linear regression (r 2 = 0.06, P < 0.0001). A box plot displays statistical values for ranges of data. The line within the box marks the median. The boundary of the box indicates the 25th and 75th percentile. Error bars represent the 10th and 90th percentiles. Symbols mark the 5th and 95th percentiles. The number of data points in the range for each box is also displayed. The gap in the plots is because our population is made up of potential refractive surgery patients (i.e., there were no emmetropes and relatively few with “near emmetropia” refractive error).
Figure 2.
 
Correlation plots between KM and SE stratified by sex. The linear regression lines (male: r 2 = 0.06, P < 0.0001, female: r 2 = 0.05, P < 0.0001) show that on average males eyes exhibit less KM than female eyes with the same SE.
Figure 2.
 
Correlation plots between KM and SE stratified by sex. The linear regression lines (male: r 2 = 0.06, P < 0.0001, female: r 2 = 0.05, P < 0.0001) show that on average males eyes exhibit less KM than female eyes with the same SE.
Table 5.
 
Comparison of Linear Regression on KM and SE by Sex
Table 5.
 
Comparison of Linear Regression on KM and SE by Sex
Coeff. ± Std. Err. ANOVA
Male Female P Power
Slope −0.116 ± 0.017 −0.107 ± 0.014 0.68
Intercept 43.12 ± 0.08 43.78 ± 0.07 <0.001 1.00
The KA was strongly correlated to RA in all datasets (r = 0.78, P < 0.001). KA was also correlated to KM in the myopic and complete datasets but not for the hyperopic group. Weak but statistically significant correlations were also observed between KA and age for both the myopic (r = 0.05, P < 0.04) and hyperopic groups (r = −0.32, P < 0.001). This correlation was not significant when the complete dataset was analyzed. 
A multivariate linear regression model of KA was developed as a function of RA, KM, age, and sex (Table 6). RA and sex were the only significant variables in all datasets. KM was a significant variable only in the myopic group. Age was not a significant variable in the models developed for all three groups. 
Table 6.
 
Multivariate Linear Regression of KA
Table 6.
 
Multivariate Linear Regression of KA
  Multivariate Linear Regression of KA
The strong correlation between KA and RA (Fig. 3) reveals that, on average, an astigmatic refractive error will be accompanied by a corresponding difference in the principal meridian of the cornea that is 70% of the cylinder power of the refraction. Stratifying the KA and RA data by sex revealed that male eyes had significantly less difference in their principal meridians than female eyes. Linear regression of KA and RA for the male and female groups (Table 7) showed there was no statistically significant difference in their slopes, but the difference in their intercepts was statistically significant. The KA of male eyes is approximately 0.1 D less than in female eyes with the same RA. 
Figure 3.
 
Scatter plots and regression lines of the correlation between KA and RA for the complete dataset (A) and stratified by sex (B). The regression line for the complete group (r 2 = 0.61, P < 0.0001) shows the ratio between KA and RA is not 1:1. After stratifying by sex, the regression lines (male: r 2 = 0.65, P < 0.0001, female: r 2 = 0.59, P < 0.0001) reveal that on average male eyee exhibit less KA than female eyes with the same RA.
Figure 3.
 
Scatter plots and regression lines of the correlation between KA and RA for the complete dataset (A) and stratified by sex (B). The regression line for the complete group (r 2 = 0.61, P < 0.0001) shows the ratio between KA and RA is not 1:1. After stratifying by sex, the regression lines (male: r 2 = 0.65, P < 0.0001, female: r 2 = 0.59, P < 0.0001) reveal that on average male eyee exhibit less KA than female eyes with the same RA.
Table 7.
 
Comparison of Linear Regression on KA and RA by Sex
Table 7.
 
Comparison of Linear Regression on KA and RA by Sex
Coeff. ± Std. Err. ANOVA
Male Female P Power
Slope 0.653 ± 0.018 0.686 ± 0.017 0.21
Intercept 0.462 ± 0.017 0.548 ± 0.016 <0.001 0.94
Central Corneal Thickness
Several weak but statistically significant correlations were observed for the CCT, and the nature of the correlations varied between datasets. In the complete dataset CCT correlated to SE, KM, and age (Table 3). Only KM and age correlated with CCT in the myopic group, whereas CCT correlated with RA, KA, and age in the hyperopic group. 
A multivariate linear regression model of CCT was developed as a function of SE, KM, age, and sex (Table 8). CCT was inversely correlated to KM in only the complete dataset and myopic groups (r = −0.11, P < 0.01) (Fig. 4). In the myopic group, CCT decreased at a rate of 2.6 μm/D of increase in KM. 
Table 8.
 
Multivariate Linear Regression of CCT
Table 8.
 
Multivariate Linear Regression of CCT
  Multivariate Linear Regression of CCT
Figure 4.
 
Scatter (A) and box (B) plots of the correlations between CCT and KM for the myopic subjects. The line in both graphs is the linear regression (r 2 = 0.01, P < 0.0001).
Figure 4.
 
Scatter (A) and box (B) plots of the correlations between CCT and KM for the myopic subjects. The line in both graphs is the linear regression (r 2 = 0.01, P < 0.0001).
Opposite results were observed in the correlations between CCT and age in the myopic and hyperopic groups (Fig. 5). In the myopic group the CCT increased at a rate of 0.36 μm/year, whereas it decreased 0.6 μm/year in the hyperopic group (Table 8). 
Figure 5.
 
Scatter plot of the correlation between CCT and age stratified by refractive error. The regression lines (myopic: r 2 = 0.01, P < 0.0001, hyperopic: r 2 = 0.03, P = 0.02) reveal that the average CCT increased with age for myopes and decreased with age for hyperopes.
Figure 5.
 
Scatter plot of the correlation between CCT and age stratified by refractive error. The regression lines (myopic: r 2 = 0.01, P < 0.0001, hyperopic: r 2 = 0.03, P = 0.02) reveal that the average CCT increased with age for myopes and decreased with age for hyperopes.
Figure 5 also shows that there was a small group of hyperopes aged <30 years that appear to make the regression line statistically significant. When the hyperopic group is analyzed for eyes with ages greater than 30 years, the correlation between age and CCT (P = 0.15) was not statistically significant. 
Discussion
The primary outcome of interest for the present study was the assessment of the distribution of ocular parameters in patients undergoing preoperative refractive surgery assessment. Significant scatter was observed between the metrics; despite this many statistically significant correlations were found. 
Although axial length has been demonstrated to be related with spherical equivalent refractive error and with progression of myopia, 13,14 the relationship between cornea power and refractive error has been subject of debate. Some researchers have demonstrated no relationship between the refractive error and corneal radius, 6 whereas other authors have found that the most myopic subjects have smaller corneal radii. 7,8,15 Others found the AL to be more related to the refractive error than the CR. 3 In our study the KM showed close correspondence with the cycloplegic refraction. We found that as mean refractive error decreases, the mean KM values increased (cornea steepens) across the entire range of refractive errors. Only a few studies have investigated whether a correlation exist between keratometry and refractive error where corneas are found to be steeper in myopes than emmetrope eyes. 16 We found a rate of 1.00 D change in SE corresponding to a 0.11 D change in the KM over the full range of data. However, low refractive powers “para emmetropic” range did not show the same correlation. The linear relationship between KM and SE becomes significant from the higher power that tilted the data at the ends. This may support the suggestion from Grosvenor and Scott 17 that the cornea is an emmetropizing factor for preserving emmetropia or low myopia, but it is not able to exert an emmetropizing effect of excessive eye growth. In addition, Tayah et al. 18 showed that the eyes with lower ametropia had correlations between ocular components and refractive error more frequently than those observed for emmetropia and eyes with higher ametropia. 
A prevalence rate of myopia more frequently associated with female children as well as adults has been reported. 13,19,20 We also found that more myopic refractive error was associated with female sex, and for a constant level of refractive error female corneas were steeper. Axial length also might contribute to this finding, as González Blanco et al. 3 found that AL in men is approximately 0.5 mm greater than in women. 3 This could partially be related to constitutional differences such as height and weight between male and female populations. 3,13,14,21  
We also noticed that as the mean refractive error decreased, the cornea became thinner in the myopic group; this thinning was not related to the degree of myopia but to the mean keratometry. Although from a theoretical point of view the corneal curvature could influence thickness values up to 25%, the clinical studies results are controversial. 22 Although some researchers reported that the CCT correlated negatively with the mean keratometric measurement, 23 26 other studies concluded that there is no correlation between corneal thickness and corneal curvature. 27,28  
Emmetropization is a complex phenomenon; we discovered a strong correlation between the KA in the principal meridians and cylinder refractive error. The KA increases in myopic eyes as a function of mean corneal power at a ratio of 0.67. The possibility of this being an indicator of degree of emmetopization and its effect on the refractive state of the eye needs to be investigated. 
Sex and ethnicity have been reported to contribute to differences in keratometry. Our study showed the mean keratometry in women to be steeper, and there is a larger difference in keratometric power of the principal meridians for constant cylinder compared with men. Fanny et al. 29,30 found that mean keratometry in black African women was significantly higher than in men. Goh et al. 13 and Lin et al. 30 reported flatter cornea in young male adults. 
The CCT have a large spectrum of distribution that might vary among populations of different ethnic background. 31 Fam et al. 32 reported a mean CCT of 535 μm in Chinese adults; similar findings were also reported by Lekskul et al. 33 in a Thai community. It appears, however, that the accepted mean CCT for a normal cornea in clinical practice is between 537 and 554 μm. 34 36 Generally a pachymetry value thinner than 500 μm has been accepted as a cutoff value for safe refractive surgery. 37 The average CCT in our study was 544 μm (range, 414–659 μm); this is very close to the Singapore Malay Eye Study, which obtained a CCT from 3239 individuals with a mean of 541 μm. 38  
Studies that attempted to evaluate the correlation between the degree of myopia and CCT have shown conflicting results. Some reported no correlation between corneal thickness and refractive error. 25,27,32,33,39 Others have reported the association of lower corneal thickness, steeper cornea, and myopia. 6,28 Our data revealed that the cycloplegic SE correlates directly to the CCT when the analysis is performed for a large range of refractive errors. This finding was not statistically significant when we looked at myopic and hyperopic groups separately. However, we found that age correlated with CCT in subjects with myopia. Rüfer et al. 40 showed a significant difference in the mean CCT between young (aged 10–39 years) and older (40–80 years) subjects: 591 ± 41 μm and 600 ± 39 μm, respectively. 
In subjects with hyperopia, age was inversely correlated with CCT and SE, but these correlations disappeared if the hyperopic subjects younger than 30 years were excluded from the analysis. However, hyperopes did not present the same correlations; nonetheless some of the changes that take place at a different structural level may have contributed to this finding. Ortiz et al. 41 showed that the corneal hysteresis value was lower in older eyes and also described significant biomechanical differences between young (9–14 years) and older (60–80 years) subjects in normal control groups. Excluding subjects <14 years, he found no significant change in biomechanical properties during aging. Daxer et al. 42 described a small but significant age-related increase in collagen fibril diameter and expansion of the intermolecular spacing within the collagen fibrils in normal human corneas. In the last study, the minimum age of the corneal donors was 38 years. Considering these findings one would postulate that the clinical finding of age-related differences between the myopic and hyperopic group may favor the proposal that it may be offset by age-related changes at the ultrastructural level. Nevertheless, the interesting question regarding the relationship of ultrastructural findings, refractive state, and the age-specific timing of changes onset in the eye remains to be resolved. 
The difference between our study and other reports that showed a correlation between CCT and refractive error might be that we used cycloplegic refraction for the analysis whereas the others did not, and this might have caused some bias to the actual refractive error state of the eye. To our knowledge, this is also the first study to report associations between cycloplegic SE, KM, and CCT in a large heterogeneous group of eyes with an appropriate sampling size and a wide range of ametropia, compared with studies using small sample sizes, 39 which preclude definitive conclusion. The other explanation could be that in some reports the study populations varied (most being Chinese or Taiwanese adults and Thai populations) 32,33 from our own (predominantly Caucasian). 
In this study the data were collected over several years, and different instruments were used for the pachymetric evaluation of the central cornea area. Initially an ultrasound US pachymeter was used, and more recently a rotating Scheimpflug analysis system (Pentacam; Oculus) became available. To determine the agreement of measurement between these instruments we ran an ANOVA test that revealed that there is no significant difference in the mean values of the SE, KM, and CCT (P = 0.91, 0.99, 0.75, respectively) between the two groups. Studies showed that the average values of CCT taken by noncontact specular microscopy (Pentacam) and US pachymetry were not significantly different, 43,44 and the 95% limits of agreement were 6.47 ± 43.21 μm between the last two devices. 43  
Lackner et al. 45 showed that the rotating Scheimpflug analysis system (Pentacam)–measured CCT values were closer to US pachymetry with less variability compared with corneal tomography (Orbscan; Bausch & Lomb, Rochester, NY), and 95% limits of agreement were 9.8 ±31 μm between the rotating Scheimpflug and US. However, O'Donnell and Maldonado-Codina 46 reported slightly thinner CCT readings with the Scheimpflug device (Pentacam) than with US pachymetry with a correlation coefficient of 0.96, the coefficient of agreement of being 19.8 μm and the 95% limits of agreement found to be 6.8±19.8 μm. This finding of a thinner CCT compared with US pachymeter measurements has also been observed with partial coherence interferometry, 47 an endothelial specular (Pro-Cem 4; Alcon-Surgical, Inc., Irvine, CA), an optical pachymeter, and a US pachymeter (DGH 1000). 48 A similar trend has been reported as well for a specular microscope optical pachymeter (SP-2000P; Topcon), compared with the other pachymeter (DGH 500). 49 The reason for this difference is not clear; however, it has been pointed out by Barkana et al. 50 and Fujioka et al., 43 that according to the manufacturer, the tear film has no effect on measurements in the case of the Scheimpflug system, whereas in the case of US, several studies have documented that the US probe can displace the 7–40 μm–thick tear film, and that the epithelium can be thinned with the examination probe. 47,51,52 Another consideration could be that the US pachymetry measurement is observer dependent, and the probe should be placed exactly at the center of the cornea and perpendicular to the corneal surface, so the possibility of inconsistencies in the site of measurement of the cornea exists with each reading. Despite that, the measurement of CCT using the US pachymeter has been shown to be highly repeatable and reproducible. 53  
Instruments used for measurement of the keratometry in this study were the Zeiss Humphrey automatic refractor/keratometer 599 and the Topcon KR-3000 autorefractor keratometer. There are no articles with direct comparison of agreement or accuracy for these two instruments; however, overall similar or very close performance of these two autokeratometers is likely, given that autorefractors have similar fundamental principles of optical measurement. 
Measurement of corneal thickness and curvature and agreement of measurement methods with each other are more relevant in some clinical applications than others. In corneal refractive surgery, in cases where glaucoma diagnosis is relevant and for calculation of the power of the phakic anterior chamber lens, careful attention is required to determine the actual value. However, slight differences of readings between the devices are acceptable for the purpose of correlation studies, such as our own. 
The main strengths of this study are the uniformity of refractive error assessment and the wide range of the refractive error that is included. Cycloplegic refraction is a reliable and objective clinical method in measuring refractive error by neutralizing the accommodative efforts that might have not been relaxed during manifest refraction and that may increase the variability of the spherical component. It also have been shown that subjective cylindrical power findings are a reproducible measure with 100% limits of ±0.50 D. 54 Another strength was the limitation of age group to adults undergoing refractive surgery, thus excluding the possibility of lenticular changes that may affect the refractive status of the eye. In a Burmese population it was found that the nuclear opalescence is the strongest predictor of refractive error across all age groups. 55  
Conclusion
Analyzing the data within a wide range of ametropia, we have found that as the mean spherical equivalent decreases, the cornea generally steepens and becomes thinner. As the mean corneal power of myopes increases, the power difference between their principal meridians increases. The confirmation of these relationships could help in the development of eye models and design of new corrective strategies targeted at specific ocular components. It may also improve preoperative patients' assessment for refractive surgery. It could as well provide population-based estimates, and possible associations could be obtained. 
Footnotes
 Disclosure: T. AlMahmoud, None; D. Priest, None; R. Munger, None; W.B. Jackson, None
Footnotes
 Presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Fort Lauderdale, Florida, 2009.
The authors thank Stephen Trokel for reviewing this article and giving us valuable comments. 
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Figure 1.
 
The correlation between KM and SE is shown in both a scatter plot (A) and a box plot (B). The line in both graphs is the linear regression (r 2 = 0.06, P < 0.0001). A box plot displays statistical values for ranges of data. The line within the box marks the median. The boundary of the box indicates the 25th and 75th percentile. Error bars represent the 10th and 90th percentiles. Symbols mark the 5th and 95th percentiles. The number of data points in the range for each box is also displayed. The gap in the plots is because our population is made up of potential refractive surgery patients (i.e., there were no emmetropes and relatively few with “near emmetropia” refractive error).
Figure 1.
 
The correlation between KM and SE is shown in both a scatter plot (A) and a box plot (B). The line in both graphs is the linear regression (r 2 = 0.06, P < 0.0001). A box plot displays statistical values for ranges of data. The line within the box marks the median. The boundary of the box indicates the 25th and 75th percentile. Error bars represent the 10th and 90th percentiles. Symbols mark the 5th and 95th percentiles. The number of data points in the range for each box is also displayed. The gap in the plots is because our population is made up of potential refractive surgery patients (i.e., there were no emmetropes and relatively few with “near emmetropia” refractive error).
Figure 2.
 
Correlation plots between KM and SE stratified by sex. The linear regression lines (male: r 2 = 0.06, P < 0.0001, female: r 2 = 0.05, P < 0.0001) show that on average males eyes exhibit less KM than female eyes with the same SE.
Figure 2.
 
Correlation plots between KM and SE stratified by sex. The linear regression lines (male: r 2 = 0.06, P < 0.0001, female: r 2 = 0.05, P < 0.0001) show that on average males eyes exhibit less KM than female eyes with the same SE.
Figure 3.
 
Scatter plots and regression lines of the correlation between KA and RA for the complete dataset (A) and stratified by sex (B). The regression line for the complete group (r 2 = 0.61, P < 0.0001) shows the ratio between KA and RA is not 1:1. After stratifying by sex, the regression lines (male: r 2 = 0.65, P < 0.0001, female: r 2 = 0.59, P < 0.0001) reveal that on average male eyee exhibit less KA than female eyes with the same RA.
Figure 3.
 
Scatter plots and regression lines of the correlation between KA and RA for the complete dataset (A) and stratified by sex (B). The regression line for the complete group (r 2 = 0.61, P < 0.0001) shows the ratio between KA and RA is not 1:1. After stratifying by sex, the regression lines (male: r 2 = 0.65, P < 0.0001, female: r 2 = 0.59, P < 0.0001) reveal that on average male eyee exhibit less KA than female eyes with the same RA.
Figure 4.
 
Scatter (A) and box (B) plots of the correlations between CCT and KM for the myopic subjects. The line in both graphs is the linear regression (r 2 = 0.01, P < 0.0001).
Figure 4.
 
Scatter (A) and box (B) plots of the correlations between CCT and KM for the myopic subjects. The line in both graphs is the linear regression (r 2 = 0.01, P < 0.0001).
Figure 5.
 
Scatter plot of the correlation between CCT and age stratified by refractive error. The regression lines (myopic: r 2 = 0.01, P < 0.0001, hyperopic: r 2 = 0.03, P = 0.02) reveal that the average CCT increased with age for myopes and decreased with age for hyperopes.
Figure 5.
 
Scatter plot of the correlation between CCT and age stratified by refractive error. The regression lines (myopic: r 2 = 0.01, P < 0.0001, hyperopic: r 2 = 0.03, P = 0.02) reveal that the average CCT increased with age for myopes and decreased with age for hyperopes.
Table 1.
 
Demographics
Table 1.
 
Demographics
Variable Complete Dataset (n = 3395) Myopes (n = 3091) Hyperopes (n = 284)
Mean ± SD Range Mean ± SD Range Mean ± SD Range
SE, D −3.90 ± 3.07 −14.00 to 6.75 −4.58 ± 2.21 −14.00 to −0.13 3.21 ± 1.53 0.13 to 6.75
RA, D 0.80 ± 0.86 0.00 to 6.00 0.80 ± 0.85 0.00 to 6.00 0.81 ± 0.90 0.00 to 5.25
KM, D 43.95 ± 1.47 38.38 to 48.75 44.02 ± 1.43 38.88 to 48.75 43.17 ± 1.67 38.38 to 48.25
KA, D 1.05 ± 0.74 0.00 to 5.75 1.05 ± 0.72 0.00 to 5.75 1.09 ± 0.85 0.00 to 4.50
CCT, μm 544 ± 34 414 to 659 543 ± 34 441 to 659 552 ± 37 414 to 645
Age, y 40 ± 10 19 to 84 39 ± 10 19 to 84 51 ± 9 21 to 71
Table 2.
 
Demographics of the Male and Female Groups
Table 2.
 
Demographics of the Male and Female Groups
Variable Females (n = 2048) Males (n = 1347)
Mean ± SD Range Mean ± SD Range
SE, D −4.07 ± 3.06 −11.63 to 6.75 −3.65 ± 3.06 −14.00 to 6.25
RA, D 0.78 ± 0.83 0.00 to 6.00 0.83 ± 0.89 0.00 to 5.25
KM, D 44.21 ± 1.40 38.38 to 48.75 43.54 ± 1.47 38.75 to 48.25
KA, D 1.08 ± 0.74 0.00 to 5.75 1.01 ± 0.73 0.00 to 4.75
CCT, μm 543 ± 34 438 to 659 545 ± 33 414 to 645
Age, y 40 ± 10 19 to 71 40 ± 10 19 to 84
Table 3.
 
Correlation Analysis
Table 3.
 
Correlation Analysis
  Correlation Analysis
Table 4.
 
Mulitvariate Linear Regression of KM
Table 4.
 
Mulitvariate Linear Regression of KM
  Mulitvariate Linear Regression of KM
Table 5.
 
Comparison of Linear Regression on KM and SE by Sex
Table 5.
 
Comparison of Linear Regression on KM and SE by Sex
Coeff. ± Std. Err. ANOVA
Male Female P Power
Slope −0.116 ± 0.017 −0.107 ± 0.014 0.68
Intercept 43.12 ± 0.08 43.78 ± 0.07 <0.001 1.00
Table 6.
 
Multivariate Linear Regression of KA
Table 6.
 
Multivariate Linear Regression of KA
  Multivariate Linear Regression of KA
Table 7.
 
Comparison of Linear Regression on KA and RA by Sex
Table 7.
 
Comparison of Linear Regression on KA and RA by Sex
Coeff. ± Std. Err. ANOVA
Male Female P Power
Slope 0.653 ± 0.018 0.686 ± 0.017 0.21
Intercept 0.462 ± 0.017 0.548 ± 0.016 <0.001 0.94
Table 8.
 
Multivariate Linear Regression of CCT
Table 8.
 
Multivariate Linear Regression of CCT
  Multivariate Linear Regression of CCT
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