A nonparametric test was used for statistical testing because the distributions were not normally distributed. Kruskal-Wallis analysis of variance showed a statistically significant change in the shape of the distributions with age. The Wilcoxon rank sum test with Bonferroni correction for all possible pairwise comparisons revealed that although the distributions for each adjacent age group were not statistically different (i.e., less than 65 vs. 65 to 69; 65 to 69 vs. 70 to 74;. . .80 to 84 vs. 85 or more), all other comparisons were highly statistically significantly different. Inspection of Fig. 4 shows little change in the distribution of the oblique component with age, and statistical testing revealed no significant differences. In addition, most people have small amounts of the oblique component.
Even though Fig. 3 shows the dramatic changes in the distributions of primary astigmatism with age, it does not clearly reveal the number of people with significant negative primary astigmatism. Fig. 5 shows the percentage of people in each age group with ≥1.00 or ≥2.00 D of negative primary astigmatism. The youngest age group (less than 65 years) had little astigmatism, whereas in the oldest group, nearly 50% had ≥1.00 D of primary negative astigmatism (67% had ≥0.75 D of primary astigmatism). A large number also had ≥2.00 D of astigmatism. In subjects 85 years and over, nearly 20% showed 2.00 D of primary negative astigmatism (against-the-rule). The proportion of people with 1.00 D or more of positive primary astigmatism (with-the-rule) was very small, ranging from ∼7% in the youngest group (less than 65) to ∼3% in the oldest group (85 or more) (data not shown).
The percentage of people in each age group with significant anisometropia (of 1 D or more) is shown in Fig. 6 for both the spherical component, primary cylinder component, and the equivalent sphere. Anisometropia was common. Using spherical equivalents, the percentage of anisometropia rose from nearly 10 to 25% over the studied age range. Differences in the primary astigmatism between the eyes of 1.00 D or more were found in 1.5% of the youngest group; this number increased to 26% in the oldest group (85 and older), whereas spherical error anisometropia increased from 20 to 43% over the same age range.
Table 2 shows the mean refractive error components for males and females for right and left eyes as well as the dioptric differences between the genders and the statistical significance levels using t-tests. For the sample as a whole, males were less hyperopic using both spherical error and equivalent sphere (right and left eyes analyzed separately). Males also had larger amounts of primary astigmatism, whereas there were no differences in the oblique astigmatic component. Primary positive astigmatism of 1.00 D or more was found in 2.8% of males and 5.4% of females, whereas primary negative astigmatism of 1.00 D or more was found in 32.8% of males and 24.2% of females. No gender differences were found for anisometropia for either sphere, equivalent sphere, primary, or oblique astigmatism.
Refractive Error and Education
Other studies have reported a relationship between refractive error and education, finding higher prevalence of myopia in more educated samples. 12–14 Within our sample, we found no significant differences in mean spherical equivalent refractive error or primary cylinder between subjects who had ≤12 years of schooling, 13 to 15 years, or >15 years of schooling. However, as a whole, our sample was significantly less hyperopic (in spherical equivalents) than other samples. Fig. 7 compares our sample to the Beaver Dam, 12 Baltimore, 12 Blue Mountains, 14 and Reykjavik 16 aging studies by plotting the percentage in each age group with spherical equivalent refractive errors of more than +0.50 D and less than −0.50 D in the right eye. These cutoffs were previously chosen and published. Only the results for white participants are included in the Baltimore Eye Survey results. For all age groups, the SKI participants showed less hyperopia and more myopia than the other studies. In the SKI sample as a whole (aged 75, for right eyes), 48.7% showed hyperopia more than +0.5 D and 26.3% showed myopia more than −0.5 D, whereas 40.2% had hyperopia +1.00 D or greater and 22.2% had myopia −1.00 D or more. The nonmonotonic changes with age in spherical equivalent in the SKI sample was due to the increasing astigmatism and general flattening of the spherical component vs. age curve between the ages of 67 and 82 years.
Our results show that the well-known change in astigmatism with age after maturity (e.g., Hirsch 1) continues into old age. The primary astigmatic component changed monotonically from near zero in our youngest age group (less than 65 years) to negative primary astigmatism of increasing amount with age. Young observers have mostly positive primary refractive astigmatism 24 (with-the-rule).
Because we did not measure any components of the eye such as corneal astigmatism, we cannot draw conclusions on the cause of this substantial change in refractive astigmatism with age. The Reykjavik study 16 measured corneal astigmatism and refractive astigmatism and suggested that the corneal changes toward more against-the-rule astigmatism were responsible for the refractive astigmatic changes because both changed similarly and linearly with age. They did not present any data showing what proportion of refractive astigmatism could be accounted for by corneal astigmatism. Others have reported a steepening of corneal curvature with age. A cross-sectional study 25 of corneal curvature in Asian eyes using corneal topography reported a linear increase in corneal curvature in the horizontal meridian with age. The vertical meridian also steepened with age but with a much shallower slope. Between the ages of 60 and 70, the average cornea was reported to be fairly spherical with little or no astigmatism and after age 70, against-the-rule astigmatism became predominant. These authors did not separate their results by gender.
Goto et al. 26 reported more against-the-rule corneal astigmatism in men in their group of 93 people over 50 years of age (mean, 67.6 years). Using a location 1.5 mm eccentric from corneal topography data, 75.5% of the men showed against-the-rule astigmatism (amount not specified—we guess of any amount), whereas 72.5% of the women showed with-the-rule astigmatism (of any amount). Even though corneal astigmatism differs from refractive astigmatism, there is a linear relationship between them. 27, 28 With this correlation in mind, the data set of Goto et al. 26 is quite different from ours. In our group, 69% of men and 65% of women showed primary negative (against-the-rule) refractive astigmatism of 0.1 D or more. The males did, however, have a significantly larger amount of primary negative astigmatism than the females (−0.60 D vs. −0.38 D average of the two eyes). The population in the Goto et al. 26 study were all Asian (Japanese), whereas our population was all white. Racial differences may need to be taken into account when analyzing astigmatic errors and their change with age. Kame et al. 29 compared changes in corneal astigmatism with age in 494 Asian eyes to previous studies involving white eyes and found a greater rate of change of corneal astigmatism in the Asian eyes. Nevertheless, it is clear that the corneal changes with age contribute substantially to the increasing prevalence of negative primary astigmatism in subjects over age 70 years.
Refractive Error and Education
We examined the relation between refractive errors and education level in our group and found no significant difference. However, our results show a much higher prevalence of myopia (and less prevalence of hyperopia) than other population studies. The SKI sample is an unusually highly educated sample with high socioeconomic status. In this sample, 93% finished high school, and 50% finished college. The average number of years of education was 16 years for the three youngest groups, 15 for the next two groups, and 14 years of education for those 85 and over. (37% of those 85 and over had completed college!). This group with 56% women attended college during the 1920s. This is a remarkably high level of education compared with, for example, the Beaver Dam study, 12 where only around 13% of the sample had more than 15 years of education or the Blue Mountains Study, 14 where only about 6% had more than 15 years of schooling compared with 50% in our study. The educational level in the Baltimore Study 13 was quite low, with only 34.6% of white participants having completed high school. The Reykjavik study 16 did not report the average educational level of their participants, but it is likely that most subjects had at least finished high school.
Why does anisometropia prevalence increase from <10% to >25% (for equivalent sphere)? The prevalence of anisometropia of 1.00 D or more in children and young adults is on the order of 3%. 30, 31 The 10% prevalence found in our youngest age group (subjects between 58 and 64 years) is already significantly higher than that found in young children and young adults but similar to other aging studies (e.g., Wang et al. 13). The significant increase in anisometropia in maturity, which further worsens among the oldest old, suggests that the emmetropization mechanisms that maintain virtually identical refractive error in the two eyes during growth in children and young adults fail in old age.
Limitations of the Study
We were not able to get refractive records for all of the original random sample due to either refusal of the participant or lack of response from their eye doctors. For those with medical records, some participants were excluded due to lack of refractive information in the records or a finding that the participant had cataract surgery on either eye. However, there is no evidence of age, gender, education, or socioeconomic status bias in the included sample (Table 1). (Race is not an issue—virtually all the observers in the original sample of 900 were white [96%]). The visual acuity of the included refractive sample did not differ from those not included, allaying fears that the sample was biased toward those seeking eye care due to vision problems. This is a retrospective study using medical records. The refractions were obviously determined by different observers, which is likely to increase the variability of the findings.
The spherical refractive error changes in the direction of more hyperopia with increasing age. This is particularly true for the oldest old. In addition, the prevalence of clinically significant astigmatism and the average amount of astigmatism increase substantially with age. Many of the oldest old have surprisingly large amounts of astigmatism. The primary astigmatic component becomes negative (against-the-rule). The positive primary astigmatic component (with-the-rule) is definitely not the rule. Oblique astigmatism is fairly uncommon but also increases with age. Anisometropia (≥1 D) also increases significantly with age, suggesting failure of emmetropization mechanisms with age. Both the spherical and astigmatic components show dramatic increases in prevalence of anisometropia. The considerable changes in all refractive components, the large amounts of astigmatism, and the high prevalence of anisometropia underscore the importance of regular refractive care for the aging population because it is well known that hyperopia, astigmatism, and anisometropia of clinically significant amounts, if uncorrected, results in reduced visual function.
This study was supported by National Eye Institute, National Institutes of Health grant EY09588 to JAB and the Smith-Kettlewell Eye Research Institute. We thank the volunteers at the Buck Center for Research in Aging.
aThe formulas used in this paper are most similar to those used by Humphrey 22 and differ from those of Thibos et al. 20 by a factor of two for the cylindrical components.
1. Hirsch MJ. Refractive changes with age.In: Hirsch MJ, Wick R, eds. Vision of the Aging Patient. Philadelphia: Chilton, 1960: 63–82.
2. Hirsch MJ. Summary of current research on refractive anomalies. Am J Optom Arch Am Acad Optom 1966; 43: 755–62.
3. Hyams SW, Pokotilo E, Shkurko G. Prevalence of refractive errors in adults over 40: a survey of 8102 eyes. Br J Ophthalmol 1977; 61: 428–32.
4. Baldwin WR, Mills D. A longitudinal study of corneal astigmatism and total astigmatism. Am J Optom Physiol Opt 1981; 58: 206–11.
5. Fledelius HC. Prevalences of astigmatism and anisometropia in adult Danes: with reference to presbyopes’ possible use of supermarket standard glasses. Acta Ophthalmol (Copenh) 1984; 62: 391–400.
6. Aine E. Refractive errors in a Finnish rural population. Acta Ophthalmol (Copenh) 1984; 62: 944–54.
7. Fledelius HC, Stubgaard M. Changes in refraction and corneal curvature during growth and adult life: a cross-sectional study. Acta Ophthalmol (Copenh) 1986; 64: 487–91.
8. Saunders H. A longitudinal study of the age-dependence of human ocular refraction: I. Age-dependent changes in the equivalent sphere. Ophthalmic Physiol Opt 1986; 6: 39–46.
9. Saunders H. A longitudinal study of the age dependence of human ocular refraction: III. The mediation of changes from direct to inverse astigmatism examined by means of matrices of transition probabilities. Ophthalmic Physiol Opt 1987; 7: 175–86.
10. Lavery JR, Gibson JM, Shaw DE, Rosenthal AR. Refraction and refractive errors in an elderly population. Ophthalmic Physiol Opt 1988; 8: 394–6.
11. Lee KE, Klein BE, Klein R. Changes in refractive error over a 5-year interval in the Beaver Dam Eye Study. Invest Ophthalmol Vis Sci 1999; 40: 1645–9.
12. Katz J, Tielsch JM, Sommer A. Prevalence and risk factors for refractive errors in an adult inner city population. Invest Ophthalmol Vis Sci 1997; 38: 334–40.
13. Wang Q, Klein BE, Klein R, Moss SE. Refractive status in the Beaver Dam Eye Study. Invest Ophthalmol Vis Sci 1994; 35: 4344–7.
14. Attebo K, Ivers RQ, Mitchell P. Refractive errors in an older population: the Blue Mountains Eye Study. Ophthalmology 1999; 106: 1066–72.
15. Bengtsson B, Grodum K. Refractive changes in the elderly. Acta Ophthalmol Scand 1999; 77: 37–9.
16. Gudmundsdottir E, Jonasson F, Jonsson V, Stefánsson, Sasaki H, Sasaki K and the Iceland-Japan Co-Working Study Groups. “With the rule” astigmatism is not the rule in the elderly. Reykjavik Eye Study: a population based study of refraction and visual acuity in citizens of Reykjavik 50 years and older. Acta Ophthalmol Scand 2000; 78: 642–6.
17. Haegerstrom-Portnoy G, Schneck ME, Brabyn JA. Seeing into old age: vision function beyond acuity. Optom Vis Sci 1999; 76: 141–58.
18. Brabyn J, Schneck M, Haegerstrom-Portnoy G, Lott L. The Smith-Kettlewell Institute (SKI) longitudinal study of vision function and its impact among the elderly: an overview. Optom Vis Sci 2001; 78: 264–9.
19. Reed D, Satariano WA, Gildengorin G, McMahon K, Fleshman R, Schneider E. Health and functioning among the elderly of Marin County, California: a glimpse of the future. J Gerontol A Biol Sci Med Sci 1995; 50: M61–9.
20. Thibos LN, Wheeler W, Horner D. Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error. Optom Vis Sci 1997; 74: 367–75.
21. Raasch T. Clinical refraction in three-dimensional dioptric space revisited. Optom Vis Sci 1997; 74: 376–80.
22. Humphrey WE. Automatic retinoscopy: the Humphrey vision analyser. Optician 1977; 173: 7–16.
23. McKendrick AM, Brennan NA. The axis of astigmatism in right and left eye pairs. Optom Vis Sci 1997; 74: 668–75.
24. Hirsch MJ. Changes in astigmatism after the age of forty. Am J Optom Arch Am Acad Optom 1959; 36: 395–405.
25. Hayashi K, Hayashi H, Hayashi F. Topographic analysis of the changes in corneal shape due to aging. Cornea 1995; 14: 527–32.
26. Goto T, Klyce SD, Zheng X, Maeda N, Kuroda T, Ide C. Gender- and age-related differences in corneal topography. Cornea 2001; 20: 270–6.
27. Grosvenor T, Quintero S, Perrigin DM. Predicting refractive astigmatism: a suggested simplification of Javal’s rule. Am J Optom Physiol Opt 1988; 65: 292–7.
28. Grosvenor T, Ratnakaram R. Is the relation between keratometric astigmatism and refractive astigmatism linear? Optom Vis Sci 1990; 67: 606–9.
29. Kame RT, Jue TS, Shigekuni DM. A longitudinal study of corneal astigmatism changes in Asian eyes. J Am Optom Assoc 1993; 64: 215–9.
30. Hirsch MJ. Anisometropia: a preliminary report of the Ojai Longitudinal Study. Am J Optom Arch Am Acad Optom 1967; 44: 581–5.
31. Almeder LM, Peck LB, Howland HC. Prevalence of anisometropia in volunteer laboratory and school screening populations. Invest Ophthalmol Vis Sci 1990; 31: 2448–55.
Keywords:© 2002 American Academy of Optometry
SKI study; aging; astigmatism; anisometropia; hyperopia; gender differences