The need for optical quality metrics that are correlated with visual performance (e.g., visual acuity) continues to grow in the face of existing and developing methods of applying wavefront error (WFE) correction, such as refractive surgery, custom contact and intraocular lenses, adaptive optics correction, and the general need to better understand how age-related optical change impacts visual performance as measured by visual acuity.^{1,2} For abrupt changes in aberrations, good progress has been made, demonstrating that change in acuity is well correlated with change in image quality.^{3–6} More specifically, research reveals that the visual Strehl (the optical Strehl ratio weighted by the neural contrast sensitivity function for interference fringes)^{5} is a particularly good metric, accounting for approximately 80% of variance in the resulting induced change in high-contrast logMAR acuity.^{4,7} Despite these gains, it is not known if the naturally occurring change in optical quality over the years^{8–14} within an individual is as well correlated with change in acuity and the extent such measures can help identify individuals on a fast track to an acuity loss.

Several factors and conditions are expected to impact the correlation between longitudinal change in optical quality and longitudinal change in acuity, including (1) adaptation^{15–18} to one’s slowly changing retinal image quality; (2) that the repeatability of both WFE^{19–21} and acuity measurements^{22} is not perfect; and (3) that changes in acuity may be related to other factors, such as neurological changes (e.g., neural cell loss or functional decline not measured by optical quality metrics calculated from WFE alone), that may subsequently be accounted for when age is included as a metric.^{23–26}

Several studies, including the Beaver Dam and the^{27} Blue Mountain Eye studies^{28} and the Smith-Kettlewell Eye Research Institute (SKI)^{29} study, have reported on the longitudinal change in acuity and its relationship to age. However, age is a catch-all factor that does not identify the cause of acuity loss. Because optical quality factors are expected to be related to visual performance and, on average, get worse with age,^{8–14} we seek here to determine to what extent change in acuity over time can be accounted for by change in any given optical quality metric or a combination of optical quality metrics and age for a population between 50 and 80 years during a 4-year period.

METHODS
Given that it is expected to take approximately 6 to 10 years for a sample population between 50 and 80 years to lose an average of 3 letters of acuity,^{30–35} a large number of subjects were enrolled to detect the anticipated average loss of one to two letters of acuity assuming a standard deviation of test-retest of two to three letters within the 4-year study period. Given the anticipated small change, we analyzed the data for the cohort as a whole and for a subset of the cohort who had a change in acuity of at least four letters, exceeding the two- to three-letter standard deviation for the test-retest measurement of acuity.^{22}

Subjects
One hundred sixty subjects (93 female, 67 male) between 50 and 80 years were recruited for a 4-year, five-visit Longitudinal Early Nuclear Cataract Study (LENCS). Subjects were included in the study if they had a best corrected acuity of 20/30 or better, a Lens Opacities Classification Systems III (LOCS III)^{36} grade for cortical cataracts of less than 2, no or trace amounts of posterior subcapsular cataract (P ), or mild nuclear cataract consistent with age. Subjects were excluded if they had any other ocular or systemic disease that would interfere with visual function. Of the 160 subjects, 2 dropped out for personal reasons unrelated to the study, 4 had cataract surgery on the study eye, and 2 passed away during the course of the study. At the end of 4 years, 152 subjects had completed all five visits, and 4 did not dilate to the 6 mm over which WFE and acuity were measured, leaving 148 Longitudinal Early Nuclear Cataract Study subjects meeting all analysis criteria. One eye of each subject was used, where the right or left eye was randomly chosen except when poorer visual function in one eye was the deciding factor, in which case the better eye was the study eye.

Protection of Human Subjects
The study followed the tenets of the Declaration of Helsinki and was approved by the institutional review board of the University of Houston. An informed consent was signed by each subject.

Eye Dilation
Tropicamide 1% and phenylephrine 2.5% ophthalmic solutions were used for pupil dilation and to minimize any residual accommodation.

Wavefront Sensing
Wavefront error was measured three times within 1 to 2 min, and the average of the three measurements was used as the best estimate of the eye’s WFE. All measurements were obtained using a custom Shack-Hartmann wavefront sensor, the design of which has previously been described in detail^{37} and quantified using the Z80.28–2004 ANSI standard for specifying the normalized Zernike expansion through the 10th radial order.^{38}

Optical Quality Metrics Calculated From WFE
The 4-year change in 31 optical quality metrics was calculated from WFE, each of which has been described in detail previously.^{5} Of these 31 metrics, 10 correspond to wavefront quality metrics measured in the pupil plane, and 21 correspond to image quality metrics measured in the retinal plane. In addition, high-order root mean square WFE (RMS WFE; calculated from the Zernike coefficients as the square root of the sum of the squares for coefficients in the third to tenth radial orders), coma (calculated from the Zernike coefficients as

, spherical aberration (calculated from the Zernike coefficients as

, and trefoil (calculated from the Zernike coefficients as

were included among optical quality metrics because they have been described to change with age and cataract development.^{8,39–42} All in all, 35 optical quality metrics based on WFE were calculated.

LOCS III Measurements
We used in our analyses the 4-year change in the LOCS III metrics^{36} for nuclear opalescence, nuclear color, cortical cataract, and P . For all five visits, the same four graders scored each LOCS III metric. The average score of the graders for each metric defined the final annual score for each metric.

Forward Scatter Metrics
The 4-year change in four forward scatter metrics (Max_SD, Max_Max, Max_Mean, and Mean_Mean) were used in our analyses. The four measures of forward scatter were extracted from the spot pattern of the Shack-Hartmann wavefront measurement and have been described previously.^{43} In short, metrics of forward scatter are derived by analyzing the individual lenslet point spread functions (PSF) within the Shack-Hartmann multiple-spot wavefront sensing image. More specifically, Max_SD is the maximum standard deviation of the pixel values of all PSFs in the Shack-Hartmann spot image, Max_Max is the maximum pixel value in the spot image, Max_Mean is the maximum mean pixel value of all PSFs in the spot image, and Mean_Mean is the mean of the mean pixel values of all PSFs in the spot image.

Measurement of Visual Acuity
Visual acuity was measured after a trial frame cycloplegic refraction viewing through a 6-mm artificial pupil at 12 ft. The chart was a high-contrast (96% Weber) logMAR chart as designed by Bailey-Lovie^{44,45} consisting of five letters per line and a 10^{0.1} change in letter size between lines. Charts were uniformly illuminated (285 cd/m^{2} as measured with a Minolta LS-110 luminance meter; Konica Minolta Inc., Osaka, Japan) in an Early Treatment Diabetic Retinopathy Study acuity display box. Subjects were instructed to begin reading at the smallest line of letters that they could read in full and to continue reading until five letters were missed. The total number of letters read up to the fifth miss was recorded and converted into logMAR acuity and used to calculate the 4-year change in acuity.

Data Analysis
First, for the 148 eye test population, the 95% confidence limit for the random inclination to lose or gain acuity was calculated (i.e., the limits on the binomial probability of either gaining or losing acuity). Second, the 148 eye test population was divided into two subgroups: eyes that did not have at least a four-letter change in acuity and those that did. Percent regression to the mean (P _{rtm} , i.e., the tendency for those at the extremes of the baseline distribution to regress toward the mean on subsequent measurement^{46–48} ) was calculated for each of these two subgroups using the following formula:

where r is the correlation between baseline and 4-year high-contrast acuity (HCA) for the two subgroups. As with the full population, the 95% confidence limit for the random inclination to lose or gain acuity was calculated for the two subgroups.

Third, for both the full complement of eyes and the faster changing subset, 4-year change in logMAR HCA (ΔHCA) was regressed against change in each optical quality metric calculated from WFE, change in the LOCS III metrics, change in the scatter metrics, and baseline age. For each regression, the coefficient of determination (r ^{2} ) was calculated and used to rank order all metrics and age to determine the individual regression variables that accounted for the most variability in ΔHCA. Finally, for both the full set and subset of eyes, the best variables were included in a stepwise regression analysis (alpha to enter/exit, 0.15; Minitab 15, Minitab Inc., State College, PA) to determine the combination of variables that accounted for the most variability in ΔHCA for 4 years using a Bonferroni correction for a large number of comparisons within multiple regression.

RESULTS
After 4 years, and of the 148 eyes of 148 subjects, 48 gained at least one letter of acuity, 89 lost at least one letter of acuity, and 11 had no change from base line. The 95% confidence limits for the random inclination to lose or gain acuity were 74 ± 12. The average 4-year change in acuity for all eyes was a loss of 1.6 letters, with a standard deviation of ±4.1 letters (t _{148} = 4.31, p < 0.001). The greater number of eyes losing acuity and the average loss of acuity are both consistent with the expected tendency for a population in this age group to be slowly losing acuity, as expected from prior literature.^{30–35}

Within the 148 eye sample population, there were 50 eyes that gained or lost at least four letters of acuity (a four-letter loss is approximately 1.5 times the reported standard deviation of repeated acuity measurement^{22} ). The average 4-year change in acuity in this faster changing subset was a loss of 3.4 letters, with a standard deviation of ±6.1 letters (t _{50} = 2.73, p = 0.008). Of these eyes, 38 lost and 12 gained at least four letters of acuity. The 95% confidence limit for the random inclination to lose or gain acuity was 25 ± 6.9. When evaluating smaller subsets within a larger sample, it is necessary to consider regression to the mean.^{46,47,49} The percent regression to the mean for those losing and gaining at least four letters was 17% and 16%, respectively. Figure 1 displays the number of subjects gaining or losing acuity as a function of the magnitude of the gain or loss for the entire group and the subset that gained or lost at least four letters of acuity.

FIGURE 1: Number of eyes that gained or lost four or more letters of acuity (n = 50, black bars ) or less than four letters of acuity (n = 98, gray bars ). Of those eyes gaining or losing four or more letters of acuity, 38 eyes lost acuity and 12 eyes gained acuity. Of those eyes that gained or lost three letters or less, 11 eyes had no change, and 51 lost and 36 gained letters of acuity. The 95% confidence limits for the random inclination for the loss or gain in the two subsets are 25 ± 6.9 and 49 ± 9.7, respectively. Positive kurtosis but not skew was significant for the full data set, failing Kolmogorov-Smirnov test for normalcy (KS = 0.095, p < 0.01).

For both the full set and faster changing subset of eyes, the 4-year change in acuity was regressed against the 4-year change for all 35 metrics of retinal image quality calculated from WFE, the four LOCS III lens opacification metrics, the four scatter metrics, and baseline age. In both cases, the top individual regression variables included seven image quality metrics calculated from WFE, three LOCS III lens quality metrics, two forward scatter metrics, and patient age. These variables are listed separately for the full set and faster changing subset in the top and bottom halves of Table 1 in rank order based on the coefficient of determination, r ^{2} , of the regression against change in visual acuity.

TABLE 1: Rank order of top individual regression variables

Notice in Table 1 for both the entire cohort of 148 eyes from 148 individuals and the subset of eyes where acuity changed four or more letters that change in image quality metrics are always high in the rank order compared with backscatter as measured by LOCS III scores or scatter metrics. However, all of the image quality metrics and the measures of high-order aberrations are calculated using Zernike coefficients of the measured WFE and are therefore likely to be highly correlated. To weed out the variables that best account for change in acuity, a stepwise multiple regression was performed to identify from the metrics listed in Table 1 those that uniquely account for the variance in change in acuity.

For both the full set and the faster changing subset of eyes, the variables displayed in Table 1 were entered into forward stepwise regression analyses (alpha to enter/exit, 0.15) to determine the combination of variables that are most predictive of ΔHCA for 4 years. In both cases, the same four variables best explained the 4-year ΔHCA and are described in the order of importance according to the following equations:

For the entire cohort,

For the fast changing subset,

where ΔHCA′ is the predicted 4-year change in high-contrast acuity, Age is age at study entry, ENT is an optical quality metric describing the entropy of the PSF,^{5,48} P is a LOCS III lens quality metric quantifying the amount of P ,^{36} and Trefoil is the RMS WFE for the trefoil terms.

As indicated, equation 2 incorporates all subjects tested on the first and last visits (r ^{2} adjusted = 0.15, p = 2.37 × 10^{−5} ; significant after Bonferroni correction for a large number of comparisons within multiple regression), and equation 3 incorporates only those subjects whose acuity changed by four or more letters between the first and last visits (r ^{2} adjusted = 0.34, p = 1.48 × 10^{−4} ; significant after Bonferroni correction for a large number of comparisons within multiple regression). The sequential partial r ^{2} adjusted values with the addition of each factor to regression equation 2 are 0.07, 0.11, 0.13, and 0.15, and the sequential partial r ^{2} adjusted values with the addition of each factor to regression equation 3 are 0.19, 0.27, 0.32, and 0.34, respectively. Here, the partial r ^{2} values of the multiple regression analyses, unlike the full correlations, reflect the unique contribution of each factor in the regression. That these four variables are able to enter equations 2 and 3 suggests that ENT, P , trefoil, and age contain fundamentally different information from the other variables, the significance of which is addressed in the Discussion. For fast changing eyes, age is a least important variable adding 0.02 to the total r ^{2} adjusted value of 0.34. The increase in r ^{2} found for the faster changing subset relative to the full set of eyes is significant^{50} (two-tailed p-value = 0.02).

For the full and faster changing sets of eyes, panels A and C in Figure 2 linearly regress ΔHCA predicted by equations 2 and 3 (ΔHCA’) against the actual ΔHCA, and panels B and D plot the residuals. Given that there is no systematic trend revealed in the residuals in either case suggests that only noise remains.

FIGURE 2: (A) Baseline age and change in entropy of the point spread function (ENT), posterior subcapsular cataract, and trefoil (i.e., predicted 4-year change in high-contrast acuity [ΔHCA′] according to equation 2) are able to account for approximately 15% of the variance in the actual change in logMAR high-contrast acuity (ΔHCA) in the full set of eyes. (B) There are no systematic trends in the residuals revealed when the residuals are plotted as a function of actual ΔHCA. (C) Baseline age and change in ENT, posterior subcapsular cataract and trefoil (i.e., ΔHCA′ according to equation 3) are able to account for approximately 34% of the variance in actual ΔHCA in the faster changing subset of eyes. (D) There are no systematic trends in the residuals revealed when the residuals are plotted as a function of actual ΔHCA. The solid lines in panels B and D are the mean residual error (effectively zero), and the dashed lines are ±2 SD. Negative values in all panels refer to the loss of logMAR acuity, and positive values, a gain in logMAR acuity.

The impact of change in P on the change in acuity is emphasized by the fact that the study design attempted to control for P at enrollment because of its known impact on visual acuity.^{51–54} Nonetheless, P remained the third most important contributor to the change in visual acuity for the study cohort and the second most important variable in the subset that lost four or more letters of acuity. Posterior subcapsular cataracts are located close to the visual axis and are known for their impact on visual performance.^{51–54} Among all subjects completing the 4-year study, gradable P (above the minimum LOCS III score of 0.1) was found in 26 of 152 subjects on the first visit and 53 of 152 subjects on the final visit, a 104% increase compared with an 18% increase in gradable cortical cataracts (from 121 to 143 subjects).

For the faster changing subset of eyes, equation 3 showed that the same four variables remained in the multiple regression model. Importantly, equation 3 showed that, in this faster changing subset, age is now the least important variable remaining in the equation (adding only 2% to the total 34% of variance in acuity change accounted for), whereas ENT is the most important variable and accounts for 19% of the variance in acuity change. That age is a relatively weak predictor of faster changes in acuity is not particularly surprising given that individual changes in image quality metrics calculated from WFE are more likely to change in 4 years than the large collection of factors captured by age. Taken together, these results suggest that (1) image quality factors contributing to the 4-year change in this subset of faster changing eyes are the major driving force for the significant correlation found in the full set of eyes; (2) age is a poor predictor of fast change; and (3) an adverse, as opposed to, a positive change in the key optical factors (ENT, P , and trefoil) can be used to help identify patients at risk of being on the fast track to acuity loss.

The age-related change in acuity is not new, and the results reported here for all eyes (solid circles) are compared in Figure 3 to Beaver Dam^{27} (solid diamonds), Blue Mountain^{28} (open diamonds), and SKI^{29} data (open squares). The data of all four studies are similar and reveal an acuity loss with age that is well fit with an accelerating function. Unlike the Beaver Dam, Blue Mountain, and SKI studies, the results presented here shed light on the optical factors contributing to loss of acuity with age. Because the loss of acuity as a function of age is essentially identical in all four studies, the optical factors found here contributing to the acuity change are most likely generalizable to the population as a whole.

FIGURE 3: Four-year change in high-contrast acuity as a function of baseline age for all 152 subjects (solid circles ) is reported as letters gained (positive values) or lost (negative values) and compared with the 5-year change reported in the Beaver Dam^{27} (solid diamonds ) and Blue Mountain^{28} (open diamonds ) Eye studies, and an average of 4.4-year change reported in the Smith-Kettlewell Eye Research Institute (SKI)^{29} (open square ) study. Data points represent the average age per bin (LENCS) or the midpoint of the bin range (Blue Mountain, Beaver Dam, and SKI). Error bars are one standard error of the mean (LENCS). The solid curve is nonlinear least squares fit to all plotted data (i.e., LENCS, Beaver Dam, Blue Mountain, and SKI) and represents the expected change in acuity for 4 to 5 years as a function of age.

DISCUSSION
For eyes aged 50 to 80 years, where acuity has changed at least four letters in 4 years, optical metrics ENT, P , and trefoil account for 32% of the variance in acuity change with entry age adding an additional 2%. These findings suggest that change in quantifiable optical metrics can help identify suspect individuals on a fast track to an acuity change near the noise limits of the acuity measurement. For the cohort as a whole, the average loss in acuity in 4 years was small but significant (1.6 letters), largely driven by the fast changing subset given the average acuity change for eyes whose acuity changed less than four letters was a loss of 0.5 letters.

As noted in the introduction, studies examining the impact of sudden changes in image quality on acuity reveal that individual retinal image quality metrics can, by themselves, account for approximately 80% of the variance in acuity. This raises the question, why does change in retinal image quality metrics account for much less of the variance in a 4-year longitudinal study ? There are several factors that contribute. First, the abrupt change studies typically vary image quality over a range large enough to decrease acuity to at least 25 letters (5 lines). In the current longitudinal study , the logMAR acuity changes are much smaller (<1 line) for most patients. If we reanalyze the abrupt change data of the Ravikumar report^{7} limiting the range to 10 letters (2 lines, 97% of LENCS subjects reported here), the percentage of the variance in acuity that the retinal image quality metrics account for is on the order of 60%. If we limit the Ravikumar data to 5 letters (1 line, 86% of LENCS subjects reported here), the percentage of variance in acuity accounted for by their retinal image quality metrics is on the order of 40%. Here, for those eyes gaining or losing four or more letters of acuity, the single most significant optical quality metric (ENT) in the stepwise multiple regression accounts for 19% of the variance alone, with trefoil adding another 8%, age accounting for only 2%, and P making up the remaining 5%.

What other factors can account for this discrepancy between studies examining abrupt acuity change and our study? Subjects in the abrupt change studies are asked to read letters distorted by aberrations with which they are not familiar and with essentially no time to adapt, whereas in the longitudinal study , subjects are constantly adapting to their slowly changing aberration structure. As described in the introduction, it has been reported that subjects tend to adapt to their own slowly changing aberrations.^{15–18} For example, Artal et al.^{15} demonstrated simply rotating an individual’s aberration structure without changing its magnitude-decreased visual performance, suggesting that we are each adapted to our own unique aberration structure. Thus, any neural adaptation will act to increase the time to detect significant changes in acuity.

Another factor limiting the measurement of acuity change in a longitudinal study is noise. After accounting for baseline age and change in ENT, posterior subcapsular cataract and trefoil, the residual error (Figure 2 A) shows no systematic tendencies, that is, the residual error is likely the sum of different sources of nonsystematic measurement noise. Here, the average 4-year change in acuity of 1.6 letters is within the noise limits for the measurement of acuity, and the average magnitude of change of 3.4 letters for the faster changing group is near the noise limits in measuring acuity reported in the literature.^{22} Similarly, there is noise in WFE measurements^{19–21} which, in combination with the noise in acuity measurements, further reduces the ability to predict change when the change is small. Given these two factors (adaptation and measurement noise), we looked also at those variables accounting for 4-year change in acuity among those subjects who lost or gained at least 4 letters of acuity. For this smaller subgroup, the same four metrics remained in the final regression model accounting for acuity change. However, 34% of the variance in change in acuity is now accounted for, and age is the least important factor (only accounting for 2% of the variance in change in acuity), and retinal image quality measures became the most important factors. This makes sense given that the collective factors captured by age are not anticipated to change quickly during a short time span, whereas optical qualities can. Accounting for 34% of the change in acuity near the noise limits of measuring acuity is impressive. Such sensitivity suggests that the correlation will only increase as both the change in acuity and the metrics of retinal image quality increase with age.

CONCLUSIONS
For 50- to 80-year olds that had a change in acuity of four or more letters in a 4-year time span, change in entropy of the PSF (ENT), P , trefoil, and study entry age accounted for 34% of the variance in change in acuity. For the entire cohort of 148 eyes, change in the same variables accounted for 15%, with age entering first, and with the optical quality metrics otherwise entering in the same order. The different roles age plays in each analysis makes sense given that, unlike individual optical qualities, factors captured by age are not anticipated to change quickly over short periods of time. Correlations like those found here in fast changing eyes allow the identification of those at risk of being on a fast track to acuity loss. In the data set presented here, the significant correlations were found at or near the test-retest limits of acuity measurement, which suggests that the correlations will increase as the change increases.

Darren E. Koenig

University of Houston

College of Optometry

4901 Calhoun Rd

Houston, TX 77204

e-mail: [email protected]

ACKNOWLEDGMENTS
This study is supported by NIH/NEI R01 EY08520 (RAA), NIH/NEI R01 EY019105 (RAA), NIH/NEI P30 EY07551 (Core Grant to the College of Optometry), and the Borish Endowment funding for the Chair of Optometry (RAA).

The authors thank Hope Queener and Chris Kuether for the software and mechanical support and the study subjects for their graciousness and commitment.

R. A. A. has patent interest in retinal image quality metrics through the University of Houston and scatter metrics through the University of Texas Health Science Center San Antonio. No other author has a proprietary interest in any material or method mentioned.

Received August 30, 2012; accepted March 27, 2013.

APPENDIX
The Appendix (Table A1, a summary of individual regression variables) is available online at https://links.lww.com/OPX/A126 .

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