Refractive errors, including cylindrical and spherical errors, play a major role in vision. Although refractive errors can result from either cylindrical or spherical errors, most individuals may have both types at the same time. Some studies have shown that astigmatism has a relationship with refractive errors, especially myopia.1,2 Similarly, some reports indicate that the type of astigmatism is related to the degree of ametropia.3,4 This relationship may be affected by several factors. First, because spherical and cylindrical refractive errors are related to age, gender, corneal status, and some other factors, their relationship can also be affected by these factors. Studies in this regard have mostly evaluated preschool and school children1,2.5 or assessed spherical errors based on spherical equivalent (SE).1,5
The relationship between sphere and cylinder has previously been demonstrated in a large sample population by Farbrother et al.4 and Mandel et al.3 One of the limitations of most studies is focusing on refractive astigmatism only, whereas corneal astigmatism and residual astigmatism can also affect spherical refractive error. Because corneal astigmatism comprises the major part of total astigmatism of the eye, its relationship with spherical refractive error is expected to be similar to that with refractive astigmatism, but the relationship of residual astigmatism with spherical equivalent and cylinder components are unknown. In this study, we used data from the first phase of the Shahroud Eye Cohort Study to assess the relationship of SE and cylinder components and the relationship between residual astigmatism and spherical refractive error.
Patients and Methods
This report is based on data from the first phase of the Shahroud Eye Cohort Study. The detailed methodology has been published elsewhere,6 and only a brief description is presented here.
The target population of this study was 40- to 64-year-old citizens of Shahroud. Using multistage sampling, 6,311 individuals were selected from 300 clusters. To apply random selection of cases from all districts of Shahroud, each of the nine health centers was regarded as a stratum and the number of clusters was calculated proportionate to the population served by the health center. After approaching the head household of the cluster, evaluation of the neighboring houses continued with the adjacent household in a clock-wise direction until all individuals in each cluster (20 individuals) were selected. In each household, the interviewers invited 40- to 64-year-old members of the family for a complete eye examination. A total of 5,190 individuals (82.2%) participated in the study.
Participants were interviewed and received ophthalmic examinations. First, refraction testing and keratometry was performed with Topcon AR 8800 autorefractometer (Topcon Corporation, Tokyo, Japan). The results of autorefraction were refined through objective retinoscopic refraction testing, which were regarded as manifest refraction. Then, subjective refraction was tested. Ophthalmologic examinations were performed before and after pupil dilation. Slit-lamp biomicroscopy and measurement of intraocular pressure were done before dilation and clinical lens opacities grading, slit-lamp evaluation of vitreous opacities, and direct and indirect ophthalmoscopy were performed after dilation. Individuals with a history of cataract surgery were excluded from this report.
In this report, we used sphere and cylinder error from manifest refraction tests. Refractive errors were converted to SE, calculated as the sphere error plus half the negative cylinder error in diopters (D).
Corneal astigmatism was calculated based on the results of anterior corneal keratometry as measured by the autokeratorefractometer. In all cases, astigmatism was recorded with a negative sign.
To calculate residual astigmatism, we used a vector analysis method that makes the following assumptions:
Corneal astigmatism is determined at the corneal plane
Refraction is determined at the spectacle plane with Vertex distance = 12 mm
[Residual astigmatism vector] = [vector of refractive astigmatism at the corneal plane] – [vector of corneal astigmatism]
We considered astigmatism as with-the-rule (WTR) if its axis was 0 ± 30 degrees and against-the-rule (ATR) if the axis was 90 ± 30 degrees. Other axial values were regarded as oblique. We further explored astigmatism in its orthogonal components (J0 and J45) using cylinder power and the cylinder axis using equations:
where C is the cylinder power and A is the axis. J0 represents WTR (positive J0) and ATR (negative J0) astigmatism, whereas J45 represents oblique astigmatism.
Myopia was defined as an SE less than −0.5 D and hyperopia was defined as an SE greater than 0.5 D. Individuals who had a history of cataract surgery or were pseudophakic for any reason were excluded from the analysis.
In this study, analysis of variance was used to compare refractive astigmatism at different levels of ametropia based on spherical refractive error. Linear regression was used to evaluate the relationship between SE and refractive astigmatism, and the correlation between different types of astigmatism was assessed. The correlation between astigmatism axis and SE was determined using logistic regression and odds ratio. All results are based on analysis of right eye data.
After receiving information on the course of the study, all participants signed an informed consent. The Ethics Committee of Shahroud University of Medical Sciences approved the study, which was conducted in accordance with the tenets of the Declaration of Helsinki.
Of the 5,190 participants, data of 131 individuals were excluded from the analysis due to a history of cataract surgery or pseudophakia, and 86 participants had incomplete refraction data; therefore, final analyses were conducted with data from 4,973 participants. Mean (± standard deviation [SD]) age of the participants was 50.7 ± 6.2 years and 57.5% were female. Mean (± SD) SE and mean absolute SE were −0.29 ± 1.82 D (range: −22.75 to 11.25 D) and 0.95 ± 1.57 D (range: 0 to 22.75 D), respectively. Mean (± SD) refractive, corneal, and residual astigmatism were −0.68 ± 0.82 D (range: −8.00 to 0 D), −0.79 ± 0.72 D (range: −8.75 to 0 D), and −0.69 ± 0.47 D (range: −6.69 to 0 D), respectively.
Mean (± SD) J0 and J45 components of refractive astigmatism were −0.07 ± 0.46 D (range: −3.20 to 3.76 D) and 0.02 ± 0.26 D (range: −2.46 to 3.03 D), respectively. Mean J0 and J45 were 0.03 ± 0.46 D (range: −4.11 to 3.22 D) and −0.18 ± 0.21 D (range: −3.48 to 1.19 D) for corneal astigmatism and −0.07 ± 0.38 D (range: −2.83 to 3.29 D) and 0.10 ± 0.14 D (range: 0 to 2.62 D) for residual astigmatism, respectively.
SE and Refractive Astigmatism
Mean refractive astigmatism was −1.10 ±1.08 D (range: −7.75 to 0 D) in myopes, −0.69 ± 0.86 D (range: −8.00 to 0 D) in hyperopes, and −0.47 ± 0.52 D (range: −6.25 to 0 D) in emmetropes. Mean refractive astigmatism was significantly higher in myopes and hyperopes than emmetropic cases (P < .001). The U-shaped correlation between refractive astigmatism and SE is demonstrated in Figure 1. Results indicated a 0.671 D increase in SE with every 1.0 D increase in refractive astigmatism. This correlation was stronger among myopes (0.664) compared to hyperopic (0.230) and emmetropic (0.033) cases.
Figure 1. Relationship between spherical equivalent and refractive astigmatism. The circles represent the outliers and the stars represent the extreme outliers.
Correlation of refractive astigmatism with corneal and residual astigmatism was r = 0.695 and r = 0.324, respectively (P < .001). There was no correlation between corneal astigmatism and residual astigmatism (r = −0.013, P = .356).
As Figure 2 shows, changes in refractive astigmatism were more related to changes in corneal astigmatism. Mean residual astigmatism was −0.76 ± 0.51 D (range: −5.81 to 0 D) in myopes, −0.73 ± 0.56 D (range: −6.69 to 0 D) in hyperopes, and −0.64 ± 0.41 D (range: −5.75 to 0 D) in emmetropes (P < .001). As demonstrated in Figure 2, changes in residual astigmatism was negligible at different levels of SE but residual astigmatism increased at higher levels of SE in myopes; every 1.0 D increase in residual astigmatism was associated with 0.376 and 0.077 D myopic (P = .004) or hyperopic (P = .224) shift, respectively.
Figure 2. Types of astigmatism in different degrees of spherical equivalent.
Mean SE in individuals with WTR, ATR, and oblique astigmatism (cylinder refractive error ⩽ −1.0 D) was −1.48, −0.67, and −1.14 D, respectively (P < .001). At higher levels of SE, the prevalence of WTR astigmatism increased and the prevalence of ATR astigmatism decreased in our population (Table A, available as supplemental material in the PDF version of this article).
The results of logistic regression in Table A show the relationship between the level of SE and the type of refractive astigmatism based on axis. Also, Table 1 summarizes the prevalence of myopia and hyperopia by type of refractive astigmatism based on axis; in the myopic group, the odds of WTR astigmatism were 1.64 times higher than in myopes and the odds of ATR astigmatism were lower.
Table 1: Association of Myopia and Hyperopia With Type of Refractive Astigmatism Based on Simple Logistic Regression
Figure 3A shows the percentage of different types of refractive astigmatism based on the level of SE; most cases of WTR astigmatism were detected in individuals with myopia, whereas ATR astigmatism was more prevalent in those who were nearly emmetropic and those with low hyperopia.
Figure 3. The percentage of different types of (A) refractive astigmatism and (B) residual astigmatism in different degrees of spherical equivalent.
Figure 3B illustrates the association of SE and the axes of residual astigmatism in cases with 1.0 D or more residual astigmatism; those with residual WTR astigmatism had the lowest SE compared to those with residual ATR and oblique astigmatism (P < .001). Although WTR astigmatism was the most common type of residual astigmatism in all levels of SE, the prevalence of residual ATR and oblique astigmatism significantly increased among myopes and hyperopes at higher levels of SE (P < .001).
In 1982, Fulton et al.7 described the relationship between myopia and astigmatism in 298 myopic children, which became the focus of further studies.1,2,5 In 2004, Guggenheim et al.8 published a statistical note in which they clearly showed the relationship between sphere and cylinder refractive error. In the current report, we aim to demonstrate the relationship between SE and cylinder to clinicians in a simple way. We observed high astigmatism in individuals with high hyperopia and myopia. The relationship between astigmatism and myopia has been already reported by Heidary et al.,1 Gwiazda et al.,2 and Fulton et al.7 These reports defined myopia based on SE, and thus this relationship was overestimated. We observed a mean refractive astigmatism of approximately 1.7 D in cases with more than 4.0 D myopia, which was higher compared to individuals with emmetropia or even low hyperopia. Also, based on spherical error, we observed a relationship between the level of myopia and refractive astigmatism. Increased myopia is often accompanied by changes in axial length or corneal curvature,9 which can lead to curvature and axial asymmetry and an increased chance of astigmatism. In a report by Gwiazda et al.,2 two mechanisms were proposed for the relationship between myopia and astigmatism in children. First, the defocus caused by astigmatism results in myopia and, second, ocular growth can cause myopia and astigmatism. According to our findings, astigmatism also increased at higher levels of hyperopia; this observation was previously reported by Mandel et al.3 and Farbrother et al.4
Astigmatism was more prevalent among individuals with high hyperopia compared to those with high myopia. This finding makes Gwiazda et al.’s second hypothesis4 less likely. It is possible that, unlike in myopic individuals, this relationship does not exist in hyperopic individuals due to the smaller ocular biometrics. However, considering the higher astigmatism in individuals with high hyperopia, we propose another hypothesis regarding the relationship between them. Because newborns have high hyperopia and astigmatism, we believe that the relationship we observed in the participants of this study has continued to exist since birth due to failed emmetropization. Overall, considering the high astigmatism seen in participants with high ametropia, it could be that a lack of synchrony among different components during ocular growth and emmetropization causes high levels of myopia, hyperopia, and astigmatism. Another hypothesis would be that the mismatch between the axial length and refractive power of the eye, which is mostly congenital, may activate compensatory mechanisms in the eye that could modify one’s refractive error. For instance, we know that the cornea tends to be steep among myopes; nonetheless, the cornea could be flat in young cases of axial myopia where the cornea is undergoing a compensation process, during which asymmetrical changes in the corneal curvature can be responsible for astigmatism.
Similar to Mandel et al.3 and Farbrother et al.,4 we showed that astigmatism axes correlated with the level of ametropia such that individuals with WTR astigmatism mostly had high levels of ametropia, whereas those with ATR astigmatism were mostly emmetropic. However, there is one difference between our findings and the above-mentioned studies; Mandel et al.3 and Farbrother et al.4 reported that individuals with ATR astigmatism mostly had low myopia, but we found those with ATR astigmatism mostly had low hyperopia. Overall, it is possible to see WTR astigmatism in high ametropia due to squinting, especially in those with uncorrected refractive errors. It is possible that the vertical pressure of squinting on the cornea is responsible for WTR astigmatism.
As demonstrated, residual astigmatism had no significant correlation with corneal astigmatism. Because residual astigmatism is related to lenticular astigmatism, lack of a strong correlation was expected. However, it was interesting to find a correlation between residual astigmatism and spherical refractive error; we observed more changes in spherical refractive error at higher amounts of this type of astigmatism, especially myopia; every 1.0 D increase in residual astigmatism was associated with 0.376 D myopic shift in myopes and 0.077 D hyperopic shift among hyperopic cases. The axial length in this group of patients appears to grow asymmetrically and increases in lenticular astigmatism can lead to increases in residual astigmatism; this is while residual astigmatism did not correlate with corneal astigmatism among hyperopes. Because the growth of the globe in hyperopes is not pathologic as in myopes, residual astigmatism is less affected by changes in spherical refractive error in this group.
In cases of laser refractive surgery, it should be kept in mind that although astigmatism in individuals with high myopia is mostly corneal, the percentage of residual astigmatism in these individuals is higher than in those with other types of ammetropia. However, because residual astigmatism is correlated with spherical refractive error, the relationship between them can be a statistical artifact8 rather than a pure biological association. Thus, in addition to taking these facts into consideration, more studies are needed with more precise methods to confirm the relationship between residual astigmatism and spherical refractive error.
Increases in spherical refractive error in myopes and hyperopes are associated with increases in refractive and residual astigmatism. Although cases of refractive WTR astigmatism mostly have high refractive error, residual WTR astigmatism was more prevalent in our cases of near emmetropia than other levels of refractive error. Because the cornea undergoes ablation during keratorefractive surgery, ignoring the role of residual astigmatism could compromise the predictability of results.
- Heidary G, Ying GS, Maguire MG, Young TL. The association of astigmatism and spherical refractive error in a high myopia cohort. Optom Vis Sci. 2005;82:244–247. doi:10.1097/01.OPX.0000159361.17876.96 [CrossRef]
- Gwiazda J, Grice K, Held R, McLellan J, Thorn F. Astigmatism and the development of myopia in children. Vision Res. 2000;40:1019–1026. doi:10.1016/S0042-6989(99)00237-0 [CrossRef]
- Mandel Y, Stone RA, Zadok D. Parameters associated with the different astigmatism axis orientations. Invest Ophthalmol Vis Sci. 2010;51:723–730. doi:10.1167/iovs.09-4356 [CrossRef]
- Farbrother JE, Welsby JW, Guggenheim JA. Astigmatic axis is related to the level of spherical ametropia. Optom Vis Sci. 2004;81:18–26. doi:10.1097/00006324-200401000-00006 [CrossRef]
- Fan DS, Rao SK, Cheung EY, Islam M, Chew S, Lam DS. Astigmatism in Chinese preschool children: prevalence, change, and effect on refractive development. Br J Ophthalmol. 2004;88:938–941. doi:10.1136/bjo.2003.030338 [CrossRef]
- Fotouhi A, Hashemi H, Shariati M, et al. Cohort Profile: Shahroud Eye Cohort Study [published online ahead of print April 23, 2013]. Int J Epidemiol.
- Fulton AB, Hansen RM, Petersen RA. The relation of myopia and astigmatism in developing eyes. Ophthalmology. 1982;89:298–302.
- Guggenheim JA, Zayats T, Prashar A, To CH. Axes of astigmatism in fellow eyes show mirror rather than direct symmetry. Ophthalmic Physiol Opt. 2008;28:327–333. doi:10.1111/j.1475-1313.2008.00576.x [CrossRef]
- Gonzalez Blanco F, Sanz Fernandez JC, Munoz Sanz MA. Axial length, corneal radius, and age of myopia onset. Optom Vis Sci. 2008;85:89–96. doi:10.1097/OPX.0b013e3181622602 [CrossRef]
Association of Myopia and Hyperopia With Type of Refractive Astigmatism Based on Simple Logistic Regression
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