ACTA O P H T H A L M O LOG I CA 71 (1993) 51-56

The effect of age on human corneal thickness

Statistical implications of power analysis

Andrew Siu and Peter Herse

Department of Optometry, University of Auckland, Auckland, New Zealand

Abstract. The corneal thickness of 108 human subjects, ranging from 17 to 75 years of age, was measured using ultrasound pachometry. One central, four mid-periphe- ral and four peripheral corneal positions along the verti- cal and horizontal meridians were assessed using ultra- sound pachometry. No significant differences were found in the thicknesses of the central, midperipheral or pe- ripheral cornea with increasing age using analysis of va- riance. These results suggest that ageing has no signif- cant effect on human corneal thickness between the ages of 16 to 75 years. However the high Type I1 error prob- ability (p = 0.90) suggests that 108 subjects (18 in each age group) were insufficient to adequately answer the ques- tion. Thus power analysis may help explain the conflict- ing reports available in literature. The diversity in data interpretation may be due to the statistically small sample sizes used in most studies. Power analysis shows that at least 80 subjects are needed in each age group (480 subjects in total) before a statistically reliable test of the null hypothesis is possible. This study emphasizes the importance of power analysis in calculating an adequate sample size.

Key words: pachometry - cornea - age - statistics - type II error.

Previous optical pachometry studies have reported that corneal thickness decreases with age in both central( Alsbirk 1978; Olsen & Ehlers 1984; Swee- ney & Holden 1990) and peripheral locations (Mar- tola & Baum 1968). Yet other reports have shown no significant variation in corneal thickness with age (Kruse Hansen 1971; Olsen 1982). Does corneal thickness vary with age and what is the source of the apparent conflict in literature? It is the pur- pose of this study to more fully investigate the vari-

ation in human cornael thickness with age across a range of corneal locations using current ultra- sound pachometry techniques.

Materials and Methods

108 male subjects were invited to participate in the study. The age of the subjects ranged from 17 to 75 years. The subjects were divided into 6 age groups of 16 to 25,26 to 35,36 to 45,46 to 55,56 to 65, and 66 to 75 years (18 in each group). Those subjects with histories of recent contact lens wear, ocular disease or diabetes were excluded from the study. Subjects with mean spherical refractive errors greater than k3.00 SD were excluded. Human sub- jects ethics approval and individual informed con- sent were obtained before the measurements were commenced. Corneal thickness was measured using an ultrasound pachometer (Allergan Hum- phrey 850). The vibrational frequency of the hand- held ultrasound probe was 20 MHz and the veloc- ity of the ultrasound was 1640 m/s. The corneal thickness of the central, four midperipheral (mid- way between the central cornea and the limbus) and four peripheral (1 mm from the limbus) cor- neal positions were measured as shown in Fig. 1. The corneal locations were visually judged by re- ference to the limbus and the pupil of the eye. Three sequential measurements were made at each corneal location before proceeding to the next position. The mean of the three readings was recorded as the corneal thickness at that particular position. Measurements were completed within

51 4*

-1

Mid-peripheral

SUPERIOR

Peripheral

T E M P 0 R A L

N A S A L

9 8 4

I INFERIOR I ~~

Fig. I . Corneal locations measured by the ultrasound pa-

chome ter.

seven minutes. Only the right eye of each subject was used. Visual judgement of corneal position may have resulted in some variance with repeated measures, however, it is argued that this variance is minimal as demonstrated in laboratory animal ex- periments (Chan et al, 1983). Measurement of ob- lique corneal sections was eliminated as the ultra- sound pachometer had an automatic alignment feature that only allowed measurement of corneal thickness when the probe was perpendicular (k 10 degrees) to the corneal surface. One drop of topi- cal anaesthetic (0.5% proparacaine) was instilled

Table 1. Variation of corneal thickness with age in the central, mid-pheral and peripheral human cornea. Values given are the estimate of the mean f 1 SD. n = 18 in each group.

15 25 35 45 55 65 75

AGE (years) Fig. 2.

Variation of the peripheral and central corneal thickness with age. The unfilled circles represent the averaged data from the 4 peripheral locations. The filled circles repre- sent the data from the central cornea. The solid lines rep- resent the best fitting linear regressions through the data. The data from the mid-peripheral locations are not

plotted to improve clarity.

into the eye before commencing the measurement procedure. The subject was reclined on a bed and was asked to fixate a red dot on the ceiling to mi- nimize eye movements. The measurements were saved by depressing a foot switch following an alignment tone emmitted by the pachometer. All measurements were taken between 11 am and 5 pm. Statistical analysis was performed using the SAS statistics program running in an IBM PC envi- ronment.

Results

As no statistical difference was found between the measurements taken at the 4 peripheral locations (ANOVA followed by Scheffe Test, a = 0.05), these data were averaged to produce a single estimate of peripheral corneal thickness. This procedure was similarly performed on the data obtained from the mid-peripheral locations. The mean thicknesses measured at the central, mid-peripheral and pe- ripheral corneal locations in each age group are summarized in Table 1.

As expected, the central cornea was found to be significantly thinner than the other corneal loca- tions across al l age groups (ANOVA followed by Tukey Test, a = 0.05). Fig. 2 illustrates the variation of central corneal thickness with increasing age.

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No significant difference was found between the central corneal thicknesses of the 6 age groups (ANOVA, p = 0.64). Linear regression analysis showed no significant correlation between age and central corneal thickness (r=0.04; p=O.67). The mean central corneal thickness over all age groups was 530 Fm. This value lies within literature ranges of 514 to 540 pm (Ehlers & Hansen 1976; Alsbirk 1978; H~vding 1983; Villasenor et al. 1986).

No significant difference was found between age groups in the averaged data from the mid-periphe- ral cornea (ANOVA, p=O.16). Linear regression analysis showed no significant correlation between age and the averaged mid-peripheral corneal thickness (r=0.05; p=O.59). The mean mid-pe- ripheral corneal thickness over all age groups was 583 pm.

No significant difference was found between age groups in the averaged data from the peripheral cornea (ANOVA, p=O.16). Linear regression ana- lysis showed no significant correlation between age and the averaged peripheral corneal thickness (r = -0.15; p = 0.13). The mean peripheral corneal thickness over all age groups was 705 pm. This value for peripheral corneal thickness agrees with previous data in literature (Martola & Baum 1967; Waltman 1981).

Age (years)

Discussion P/C ratio The ratio of peripheral to central corneal thick- ness (P/C) has been previously used to normalize intersubject variability in central corneal thickness (Insler et al. 1987; Martola & Baum 1968). Calcu- lated PIC ratios, as well as mid-peripheral to cen- tral ratios (MP/C), for each age group are shown in Table 2. Statistical analysis of the differences be- tween the mean P/C ratios over the 6 age groups (ANOVA followed by Scheffe Test, a = 0.05) found no statistically significant difference between the age groups. Analysis of the MP/C data revealed a similar result. Thus the data of this study suggest that both the P/C and MP/C ratios do not vary sig- nificantly between the ages of 20 to 70 years. The P/C data from this study are plotted against the lit- erature values of Martola & Baum (1968) in Fig. 3. It is obvious from Fig. 3 that the results of the study do not support the data of Martola & Baum (1968). How can this discrepancy be explained? A number of experimental parameters may decrease the va-

MPIC ratio PIC ratio

1.4 1 T

5

2 1.2

a 0

0

1.1 4 10 30 50 70

AGE (years) Fig. 3.

Variation of the PIC ratio with age. The unfilled circles represent the data from this study. The error bars are f 1 SEM. The filled circles represent the data of Martola &

Baum (1968).

lidity the data of Martola & Baum (1968). The opti- cal pachometer used did not incorporate the elec- tronic readouts and accurate fixational controls used in modern optical pachometers (Mandell et al. 1988). Both eyes of each subject were analysed as independent data. Unequal sample sizes were used in each age group. It is well known that the use of correlated data and unequal sample size may com- promise the validity of statistical tests of signific- ance (Ederer 1973; Ray et al. 1985; Katz & Sommer 1988). Only one point (temporal limbus) was used as an index for the entire peripheral cornea, in comparison with this study which averaged 4 points. Thus while the experimental parameters used by Martola & Baum (1968) may have in- fluenced the data, it should be noted that the data of the present study support the PIC ratios re- ported by Martola & Baum (1968) through the age

Table 2. Variation of the PIC and MPIC ratios with age in the human cornea. Values given are the estimate of the

mean f 1 SD. n = 18 in each group.

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ranges of 20 to 40 years. The data of this study, however, do not support the relative peripheral corneal thinning reported by Martola & Baum (1968) after the age of 50 years.

Possible experimental errors It is possible that the current result may be due to experimental assumptions. Therefore it is useful to examine other possible sources of experimental error.

1) Gender differences Previous literature has reported a thinning of the central corneal thickness with age. Sweeney & Holden (1990) found a small but statistically signi- ficant negative correlation (r = -0.20) between central corneal thickness and increasing age. How- ever, it should be noted that 35% of the subject population used by Sweeney & Holden (1990) were female. This may have resulted in an artifactual in- crease in corneal thickness due to hormonal ac- tions in the younger premenopausal female popu- lation (Leach et al. 1971). A similar gender problem may have occurred in the study of Olsen & Ehlers (1984) where a slight decrease in central corneal thickness was found with increasing age (r = -0.23). Interestingly, Olsen & Ehlers (1984) re- ported that the rate of corneal thinning in males (-0.26 pm/year) was 54% less than that found in fe- males (-0.56 pmlyear), though the difference be- tween the sexes was found to be statistically insig- nificant due to the large scatter of the data. It should be noted that the conclusion of Olsen & Ehlers (1984) refutes a previous report by Olsen (1982) of no significant variation in central corneal thickness with age. In another study, Alsbirk (1978) reported a negative correlation in male Eskimo central corneal thicknes with age (r = -0.66). How- ever, 13% of the subjects used by Alsbirk (1978) were known to have some form of corneal abnor- mality. The inclusion of these subjects could have influenced the validity of this study. As there ap- pears to be some uncertainty as to the validity of the previous reports suggesting a decrease in cen- tral corneal thickness with age, are there any studies reporting that corneal thickness does not vary with age? The data of the present study are supported by Kruse Hansen (1971) and Olsen (1982) who reported no significant variation in central corneal thickness in subjects aged between 10 and 80 years.

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2) Pachometer variability Perhaps the conclusion of the present study is an artifact produced by the poor accuracy and preci- sion of the Humphrey ultrasound pachometer? A control experiment was performed to verify the ac- curacy and precision of the instrument. Firstly, a Haag-Streit optical pachometer was calibrated using a series of known thickness PMMA hard con- tact lenses (Mandell et al. 1988). The central cor- neal thicknesses,of the right eyes of 12 normal sub- jects were measured by a trained and practised ob- server. The subjects then had the central corneal thicknesses of their right eyes measured using an ultrasound pachometer (Allergan Humphrey 850). No significant difference (paired t-test, p = 0.10) was found between the mean corneal thicknesses measured by either method. However, it was noted that the average standard deviation of the readings was significantly greater (t-test, p = 0.004) using op- tical pachometry (8 pm) than when using ultra- sound pachometry (5 pm). For a more complete discussion of the accuracy and precision of the Humphrey 850 ultrasound pachometer used in this study, the reader is referred to a recent techni- cal report by Gaisson & Forthomme (1992). Thus, as shown in a number of previous studies (Salz et al. 1983; Ling et al. 1986; Gaisson & Forthomme 1992), optical and ultrasound pachometry are equally accurate, with ultrasound pachometry being more precise.

3) Ultrasound velocity variation with age A further possible error in the current study is the assumption that the velocity of ultrasound in human cornea remains constant between the ages of 16 to 75 years. At present there is no specific data to suggest otherwise. Yet it is interesting to speculate on what would occur if corneal ultra- sound velocity did vary with age. Previous studies have reported a decrease in the central corneal thickness with increasing age (Alsbirk 1978; Olsen & Ehlers 1984; Sweeney & Holden 1990), inferring a decrease in corneal hydration (Hedbys & Dohlman 1963). Decreases in hydration are associ- ated with increases in ultrasound velocity (Cole- man et al. 1977). For example, it has been shown that the ultrasound velocity in the normal crystal- line lens is about 1% greater than that found in the more hydrated cataractous lens (Coleman et al. 1977). It is therefore possible to speculate that the previously reported decrease in central corneal

thickness could be associated with a slight de- crease in the hydration of the central cornea, and thus slight increase in ultrasound velocity. This in- crease in velocity would result in the ultrasound pulse returning to the probe more quickly, giving an artifactually thin corneal thickness reading. If the central cornea does thin with age, then the er- rors speculated above would tend to accentuate to any decrease in corneal thickness. This was not seen to occur in the current study, suggesting +at corneal ultrasound velocity remains constant with age. Another possibility is that variations in the density and distribution of the stromal collagen matrix, rather than changes in stromal hydration, may occur with age (Olsen 1982). At present it is uncertain whether the speculated changes in the collagen density in the ageing cornea would suffi- ciently influence the velocity of ultrasound to re- sult in a significant variation in measured corneal thickness. A rigorously designed experiment is necessary to confirm the assumption that corneal ultrasound velocity does not vary with age.

4) Power analysis It is also useful to examine the possible statistical errors associated with the hypothesis test (ANOVA) used in this experiment. For a general discussion of Type I error, Type I1 error, and power analysis in ANOVA the reader is referred to standard statistics texts such as Hays (1988) or Howell (1987). When testing the validity of the experimental null hypo- thesis it is possible that the researcher may falsely reject a correct null hypothesis (Type I error) or falsely accept an incorrect null hypothesis (Type 11 error). In most experimental paradigms the pro- bability of a Type I error (a) is set and minimized by the researcher at an arbitrary level of 0.05. Thus while the probability of a Type I error is tightly controlled, the probability of a Type I1 error (fi) is often ignored. Type 11 errors are dependent on the Type I error probability, the error variance and the sample size. It is possible to calculate the Type 11 error probability (fi) using standard formulae (Hays 1988; Howell 1987). Using the data from the current experiment examining the variation in central corneal thickness with age (Table l), it was calculated that the probability of making a Type 11 error (fJ) was approximately 0.90. The data from the mid-peripheral and cornea gave similar re- sults. Thus the low power (0.10) of the statistical hy- pothesis test resulted in a 90% chance of accepting

the null hypothesis when it was incorrect. To over- come this problem the researcher would have to either alter the alevel, decrease the variability in the data or increase the sample size. Of these three alternatives, the only practical solution would be to increase the sample size. What sample size would be needed to achieve a statistically useful re- sult? It is generally accepted (Howell 1987) that a useful statistical test has a power of 0.80 (i.e. fi = 0.20). Using standard formulae it can be calcu- lated that the minimum number of subjects re- quired to attain the required statistical power would be at least 80 in each group, in comparison to the 18 used in the present study.

What does this result infer? The ANOVA result of p = 0.64 suggests an acceptance of the null hypo- thesis (using a = 0.05). However, the unacceptably high Type 11 error rate (fi = 0.90) infers that there is insufficient data available to reliably accept the null hypothesis (Mendenhall 1987). Power analysis reveals that further data needs to be collected be- fore the null hypothesis can be reliably accepted or rejected. This data collection is currently under- way. Therefore this study illustrates the import- ance of determining the Type 11 error rate and power of the statistical hypothesis test when setting up an experimental paradigm. An unacceptably large Type 11 error rate resulting from measuring insufficient numbers of eyes in each age group is a common flaw in most studies in this area, and helps explain the wide range of conclusions presented. As yet there is no study in literature that answers the question of whether the cornea thins with age with sufficient statistical validity.

Conclusion

The data of the current study suggests that ageing has no significant effect on the thickness of the central, mid-peripheral or peripheral human cor- nea between the ages of 16 to 75 years. However, it should be noted that the current study, plus most of those previously reported in literature, is prone to an unacceptably high Type 11 error rate due to the s m a l l sample size used. It is therefore proposed that a large scale (over 80 subjects in each age group) study needs to be performed before the ex- perimental question can be answered with suffi- cient statistical rigor. This study is currently

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underway. The results of this study emphasize the importance of the researcher remaining aware of both the Type I and Type I1 error probabilities.

Acknowledgment

This study was supported by a grant from the New Zea- land Optometric Vision Research Foundation.

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462-466.

28-30.

Received on February 24th, 1992.

Author’s address:

Peter Herse, Department of Optometry, University of Auckland, Private Bag 92019, Auckland, New Zealand.

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