Ординатура / Офтальмология / Английские материалы / Progress in Lens and Cataract Research_Hockwin_2002

Stratification of the SEE cohort by education produces the results shown in figure 7. Average annual exposures for persons having less than 5 years’ education are significantly higher (p 0.0001) than for those having more education. Median values for, respectively, those having less than 5 years’, 6–12 years’ and more than 12 years’ education were 0.017 (n 118), 0.009 (n 1,641), and 0.008 (n 691). These differences were not explained by race or gender.

We also stratified according to expressed photophobia (fig. 8). The wording of the interview form was whether or not the individual was sensitive to bright lights. No attempt was made to ascertain the time history of any sensitivity. Median values for individuals not expressing photophobia, 0.013 (n 1,626), were higher than for individuals who were photophobic, 0.010 (n 819). These differences were statistically significant (p 0.001).

Discussion

Estimation of ocular visible light exposures is important in the study of health effects of visible light. This is the first known study of such exposures in a population-based study.

Our approach, rather than using surrogate measures such as latitude, estimates exposures based on a synthesis of geographic, seasonal, and hourly ambient data as well as personal data on work and leisure habits (time out of doors, use of hats and/or sunglasses). With this model, we show exposure estimates for a population in Salisbury, Md. that would not have been revealed by an ecologic exposure model. Specifically, when we stratified the cohort by gender, race, level of education, and expressed photophobia, we found significant differences in average annual exposures. We found no statistically significant age-related differences, however. Given the sensitivity of the exposure estimates to self-reporting, a natural question is if there are any reporting differences that would produce these results. This is an interesting issue, but one that is beyond the scope of the current paper.

For estimation of UVB exposures, Sliney [20, 21] has suggested that a more realistic ocular exposure model should explicitly include features that account for brow shading. Additionally, it has been suggested that squinting [22] may be important in correctly estimating visible exposures. Such features are relevant to an ocular exposure model for the visible as well. Our model contains no such explicit parameters. Nevertheless, it produces exposure estimates for people expressing photophobia that are significantly lower than those for people that do not claim sensitivity to bright lights. Thus, while not explicitly modeled, exposure differences due to photophobia come about because of the general structure of the model. Specifically, these differences come about because of differences in time spent outdoors and eyewear use.

It is tempting to use exposure estimates made for a particular wavelength band and to generalize them to another. In other words to propose that they differ by a constant factor. As a counter example we show in figure 9 the average annual exposure estimates for the Salisbury cohort for the UVB [11] and the visible. Figure 9 clearly shows that the exposures are indeed linearly related, but that the proportionality factor is highly variable. This variable proportionality comes about because of several factors that differ between the two models. The OAERs in the two wavelength bands have an inverse seasonal relationship [10], glasses have a more profound effect in the UVB, and hats have no significant effect on the visible exposures. Additionally, the spatial character of UVB and visible light are different; visible light is more highly directional. Thus, although the global ambient exposures in the two wavelength bands are highly correlated, the relative ocular exposures in the two bands are highly variable.

In using our exposure model, there are some caveats that must be kept in mind. First, it addresses cumulative exposures rather than acute. In populationbased studies of the type discussed here, a model of acute exposures is clearly impractical. Recall of incidences of acute exposure are notoriously inaccurate. Second, it relies on the accuracy of individual recall of work and leisure activity over an extended time period. Finally, it estimates exposures to the plane of the face rather than to the interior of the eye.

This final caveat bears further discussion. A formal model of the amount of light reaching the retina would begin with a specification of the spectral radiance of a scene. A description of the sensor configuration (geometry of the

eye, orientation of the face) would then allow calculation of the retinal illumination. In a study of this kind, this formal approach clearly is unfeasible. A much simpler approach is to estimate facial exposure rather than retinal exposure, the assumption being that the two are highly correlated. Nevertheless, improvements in this model are desirable. For example, one could take account of facial physiognomy, pupillary constriction in response to visible light, and the increased absorption caused by yellowing of the lens. These augmentations should be included in future exposure models.

One important component of the model is the OAER. In a previous work [12], we found no relationship between job category for general population and the OAER. Other studies [19] have shown that the value of the OAER is sensitive to the reflectivity of the work surface. In a general population, this reflectivity may vary substantially. As surface reflectivity and time spent outdoors are major determining factors in the exposure, an individual’s true exposure may depart from his cohort’s exposure.

One aspect of the model not discussed previously is the fact that it is strictly valid only for the northern hemisphere. Further, it contains no explicit latitudinal dependence on the extent of daylight hours. There is, however, implicit latitudinal dependence on the geographical modification factor and on the OAER, which is parameterized on season. To generalize the model, latitudinal dependence must be incorporated into the global ambient exposure table. To see how this could be done, consider the mean hourly exposure for midday (hours 10 through 16 of table 1), and its complement (hours 5 through 9 and 17 through 19). These data are displayed in figure 10 along with their corresponding raised cosine approximations. For example, the model for the midday is the following:

where 0 9.04 and 1 4.52. These two-parameter models for the midday and off midday periods are good approximations of the seasonal dependence of table 1. From this point it is very straightforward to incorporate the latitude dependence into the coefficients ( 0 and 1) of the raised cosine models. Such a more complete description would manifest itself as a flattening of the curves of figure 10 as one approaches the equator and a reversal of phase (minimum in June) for the southern hemisphere.

With these caveats in mind, the model represents an advancement over those that employ surrogate measures of exposure. It represents a generalization to a general population of concepts that previously had been applied to a narrowly defined group of individuals. It directly estimates visible exposures. The mathematical formalism is such that exposure estimates (with the appropriate

Fig. 10. Ground level global spectral irradiances for various solar zenith angles [redrawn from 23].

changes to the values of the various empirical parameters) can be made easily for other bodily locations. It allows exploration of accuracy of various factors that contribute to estimating exposures. Finally, it encompasses environmental as well as personal factors.

We have demonstrated the use of our model in discerning interpersonal exposure differences that would not have been predicted by ecologic models. These results, therefore, establish the utility of our model for studies of the relationship between sunlight exposure and incidence and progression of eye disease.

Acknowledgments

This effort was supported by National Institutes of Health Grant 5P01AG10184-05. Field site facilities were provided by the Foundation for Advanced Research in the Medical Sciences (FARMS). We wish to thank Dr. Rachael T. Pinker of the University of Maryland, College Park, Md. for supplying the global PAR data sets from which the geographic correction factors were derived. Dr. S.K. West is a Senior Scientific Investigator in the Research to Prevent Blindness.

Appendix A: Geographic Correction Factor

We wish to explore the impact upon the geographic correction factor of a particular instrument spectral response function. We express the measured fluence (energy density) as

where the limits of integration are set by the instrument function, W( ), and E( ) is the spectral irradiance at a particular geographical location. We define the geographic correction factor as the ratio

where the corresponding spectral irradiance functions have been assumed. We further assume that these spectral irradiance functions may not have a fixed relationship to each other, but may have a wavelength dependence:

An upper bound on the effect due to the action spectrum is obtained by invoking the generalized first mean value theorem:

where lies somewhere within the wavelength band of the instrument function.

To derive an estimate of the impact of this spectral effect, we inspect the zenith angle dependence of the global spectral irradiance. Shown in figure 11 is such a dependence for atmospheres of (m 1) and 4(m 1/cos z). For all geographic locations that we consider, the factor R will show no greater spectral variation than the ratio of spectral irradiances for (m 4) and (m 1) (corresponding zenith angles are 0° and 75.5°). For this range of atmospheres, the factor R varies no more than 11% from its mean value over the interval 0.4–0.7 m. What this result suggests is that the instrument function, W, is relatively unimportant in establishing the value of the geographic modifier and that at most, its effect could be to alter the value of the ratio by 11%. Note that this is a very conservative estimate. In fact, the PAR and photopic action spectra values of the geographic modifier (equation a4) for this spectral ratio differ by less than 2%.

Appendix B: Statistical Variations of Model Parameters

We now address the issue of reliability of the exposure estimates. A full error analysis is beyond the scope of this paper, because a number of the parameters in the model have interrelated error sources. In most cases, however, we can enumerate the sources of statistical variation and estimate bounds on their effects. We group the discussion of the sources of statistical fluctuations into two broad categories: those that are ecologic in nature, and those that are personal. Included in the former class are the ambient exposures and the geographic modifier. Examples from the latter group are the effect of recall in establishing estimates of time spent outdoors, and the numerical value of the OAER.

As an initial approach to evaluating variability due to ambient exposure levels, we choose the simplest possible estimate of personal exposure. This is basically an ecologic model

UVB geographic correction factor

Fig. 11. Comparison of UVB and visible band geographic modifiers.

that assumes unity value for all multiplicative parameters. Thus, the personal exposure for a single day, D, is

t 1

As an example of typical data, we take the month of August 1996. For this period, we calculate a total ambient exposure of 438 V h, and therefore an average daily exposure of 14.1 V h. The standard deviation calculated from these data is 3.57 V h. Therefore, the standard error of the daily mean is 0.641 V h, or 4.5%. For purposes of following discussions, the covariance matrix for the two daily intervals is as follows:

The geographic correction factor is interesting because there are two general issues associated with its value: accuracy and statistical fluctuations. The question of accuracy comes about because of the fact that this parameter is based on ground level estimates of visible exposures that are created using measured satellite data and semiempirical radiation transport models [13–18]. Statistical fluctuations arise from the intrinsic variability of the integrated exposure at a given geographic location, and variability associated with an individual’s reporting of his whereabouts in past years. Here we deal only with the intrinsic statistical variability of this parameter.

It is instructive to inspect the difference between the geographic correction factor for visible exposures and that for the UVB [10]. Such a comparison is shown in figure 12. As seen in this figure, the correction factors are very highly correlated. The range from maximum to minimum correction, however, are quite different. While the UVB correction factor displays a variation (for the sites included in the model) of approximately 3.5:1, the visible varies only by 2.3:1. The specific

Fig. 12. Mean hourly exposures for midday and off midday periods along with raisedcosine approximations. MSY Maryland sun years.

relationship between the geographic correction factors in these two wavelength bands is

This result has important implications for the sensitivity of an ecologic-type exposure model for the visible. Specifically, it predicts that such a model, which uses geographic location as a surrogate for exposure, is less likely to elucidate relationships between cumulative exposure and ocular disease, than is a similar ecologic-based model for UVB exposures.

Following the procedures reported in Duncan et al. [10], we look at example correction factors for a nearby location (Washington, D.C.), a case of a large correction factor (San Juan, P.R.), and of a small correction factor (Berlin). On the basis of equation b3, we expect the standard deviations for each of these geographic correction factors to be reduced by the factor 0.491 from those calculated for the UVB (respectively, 0.034, 0.056, and 0.055) [10]. Expressed as a percentage of the particular geographic correction factor, these are 1.7% for Washington, D.C., 1.3% for San Juan, P.R. and 4.8% for Berlin.

Next, we take up a discussion of some of the personal parameters of the exposure model. The effect of the OAER assigned an individual is an important question because it appears as a multiplicative constant outside the summation over time (see equation 1). Thus the impact of variabilities in the value of this parameter will have a direct effect on the exposure estimate.

In an ideal situation, the numerical value of an OAER would be established for each individual by means of an extended observation period. In other words, this OAER would be computed by means of a temporal average. Since this is obviously impractical, we resorted [10] to observing a number of individuals, calculating an OAER for each, and then attempting to associate the numerical value with the job function. In other words, we used an ensemble averaging operation. As detailed in this work, we found no such statistically significant difference between job categories.

Generally the most important factor in establishing the value of the OAER is the reflectivity of the surface over which an individual is situated. For persons that work outside, and to the extent that this work surface is characteristic of the job, this ratio will be less variable over time. However, the interperson variability may be expected to be larger than the intraperson variability. (The ensemble standard deviation may be larger than a particular temporal standard deviation.) On the other hand, for people that do not work outdoors, the time they spend outdoors is likely to be over a wide variety of surface reflectivities. In this case, one could easily invoke ergodicity to claim that the ensemble average was interchangeable with the temporal average.

In any case, however, we have derived ensemble average OAERs and then assigned these means to each member of the cohort. Therefore, we must ask ourselves, to what extent this numerical value is truly representative of a given individual. By the argument above for nonoutdoor workers, this is probably a reasonable estimate. In this case, the standard error of the mean for these OAERs (see table 3) represents a reliable estimate of the OAER variability, and thus directly an estimate of the variability of the exposure estimate. For outdoor workers, the conclusion is not so clear-cut. Here, the standard deviation of the estimate of the value of the OAER (see table 3) may be a better estimate of the fluctuation. For each of the three OAERs listed in table 3, the standard deviation is the same order as the OAER itself. In the absence of retest data on OAERs for individual people, however, one cannot say whether the standard deviation or the standard error of the mean is more realistic. Despite the obvious noise in the data, the fact that we were able to discern exposure estimates that would not have been captured by an ecologic model suggests that the model has analytic value.

We next take up the effect of variability in reporting times upon the estimate of the personal exposure. Thus the generalization of equation b1 becomes

t 1

where F is a variable equal to unity when the individual is outdoors and zero otherwise. Using the procedures detailed in Duncan et al. [10] along with equation b2 and the expected values for the ambient exposures for the 10 a.m. to 4 p.m. interval and its complement:

we find that the standard deviation of the exposure estimate is 0.416 V h (12.5% of the expected value of 3.32 V h). The uncertainty in the personal exposure estimate is nearly tripled by the statistical fluctuations in the reporting of time out of doors.

We conclude that uncertainty in the estimate of an individual’s personal exposure is engendered more by uncertainties in factors associated with the individual (OAER and personal reporting) rather than by those of the ecologic-type parameters of the model (geographic modifier and ambient exposures).

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Donald D. Duncan, Johns Hopkins University, Applied Physics Laboratory, Johns Hopkins Road, Laurel, MD 20723–6099 (USA)

Tel. 1 240 228 6568, Fax 1 240 228 6779, E-Mail donald.duncan@jhuapl.edu