American Journal of Epidemiology Vol. 153, No. 2 : 184-187
Copyright © 2001 by The Johns Hopkins University School of Hygiene and Public Health
ORIGINAL CONTRIBUTIONS |
Observed versus Indirect Estimates of Incidence of Open-Angle Glaucoma
From the Department of Preventive Medicine, University Medical Center at Stony Brook, Stony Brook, NY.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Incidence data on open-angle glaucoma (OAG) are limited and difficult to obtain. To date, few studies have reported incidence directly measured from population-based cohorts. Other reported estimates have been derived indirectly from age-specific prevalence by using several assumptions, and their validity is unknown. To the authors' knowledge, this report presents the first comparison of observed versus indirect estimates of OAG incidence based on data from the population-based Barbados Incidence Study of Eye Diseases (1992–1997) (n = 3,427; 85% participation). The observed 4-year incidence of OAG was 1.2% (95% confidence interval (CI): 0.6, 2.1%) at ages 40–49 years, 1.5% (95% CI: 0.8, 2.5%) at ages 50–59 years, 3.2% (95% CI: 2.0, 4.8%) at ages 60–69 years, and 4.2% (95% CI: 2.6, 6.3%) in persons at ages 70 or more years. When incidence was calculated from the prevalence data, power function fitting achieved a closer approximation to observed incidence than did logistic curve fitting. Calculated incidence rates for each group were similar when assuming mortality that was equal (incidence rate = 0.7, 1.3, 2.3, and 4.8%) or differential (incidence rate = 0.7, 1.2, 2.4, and 4.8%). Other nonlogistic approaches also increased the resemblance of observed and calculated estimates. In the absence of longitudinal data, reasonably valid incidence estimates of OAG were obtained from available prevalence data. These estimation techniques can be useful when OAG incidence estimates are required for research or public health purposes.
glaucoma; incidence; prevalence
Abbreviations: BES, Barbados Eye Study; OAG, open-angle glaucoma
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Open-angle glaucoma (OAG) is a major cause of vision loss worldwide. Knowledge of the prevalence and incidence of OAG is important for public health planning as well as for understanding the patterns of occurrence of the disease. Prevalence is the proportion of a defined population affected by a particular disease at a specific point in time, whereas incidence is a measure of new cases of disease developing among previously unaffected individuals during a specific period of time. Since estimates of prevalence could be influenced by disease duration, estimates of incidence are more appropriate and relevant for etiologic studies and the planning of cohort studies or prevention trials. However, while prevalence can be measured by a one-time cross-sectional survey, incidence data require long-term follow-up of a cohort and are thus more difficult to obtain.
Several population-based studies have measured the prevalence of OAG (1
–7), but few cohort studies exist to provide direct observed estimates of incidence (8, 9). For this reason, most reported estimates of glaucoma incidence have been derived indirectly from available prevalence data by using a method based on several assumptions (10–13). Given the scarcity of actual incidence data, the validity of these estimates is unknown. Recently, both prevalence (7) and 4-year incidence (9) of major eye diseases have been reported by the Barbados Eye Studies. This report compares observed incidence estimates of OAG, measured in the Barbados Eye Studies cohort, with indirect theoretical estimates derived from age-specific prevalence from the study.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The Barbados Eye Studies comprise a series of large, population-based epidemiologic investigations of visual loss in Black populations and is funded by the National Eye Institute. The Barbados Eye Study (BES), conducted in 1988–1992, was a prevalence study based on a simple random sample of Barbadian-born citizens aged 40–84 years, with an 84 percent participation rate (7
). Of the 4,631 BES participants at baseline, 4,314 (93 percent) self-reported their race as Black, 184 (4 percent) as mixed (Black and White), and 133 (3 percent) as White or other (7). The distribution of this and other demographic variables closely paralleled the age-specific census results for the country (7), supporting good generalizability of the results. The BES cohort members were offered a 4-year reexamination in the Barbados Incidence Study of Eye Diseases (1992–1997) and 3,427 participated (85 percent of those eligible), with most losses to follow-up being due to mortality (9). The baseline and follow-up examinations had similar protocols, which included ophthalmic and other measurements, perimetry, tonometry, fundus stereophotography, an interview, and a standardized ophthalmologic examination (7, 9). The criteria for OAG required the presence of both visual field defects and optic disc damage in at least one eye after exclusion of other possible causes.
Observed incidence
Since incidence is the number of events occurring in a specified population within a given time period, the incidence rate at which new events occur can be calculated as follows. Let m denote the number of cases newly diagnosed between baseline and follow-up, and let n represent the number of persons at risk (that is, those who were disease free at baseline); then the incidence rate is given by m/n. In this report, the observed 4-year incidence of OAG was calculated as the number of individuals who developed OAG during the 4-year follow-up period divided by the number of persons free of OAG at baseline, based on those who participated both in baseline and follow-up examinations.
Indirect incidence estimates
Indirect estimates of incidence were derived from age-specific prevalence based on the methods of Leske et al. (10), which assumed equal mortality for persons with and those without OAG, and the methods of Podgor and Leske (12), which assumed differential mortality. We used various approaches to smooth the age-specific prevalence data. Assuming equal mortality, the incidence estimate was calculated by: Ix = (Px+4 – Px)/(1 – Px), where Ix is the 4-year incidence rate at age x, Px is the prevalence proportion at age x, and Px+4 is the prevalence proportion at age x+4. Curve-fitting approaches were applied to the data over the age subgroups, and the smoothed prevalence proportion for the beginning of the age interval was denoted by Px (10). Assuming differential mortality, incidence estimates were calculated by a complex formula presented in Podgor and Leske (12).
This report includes only Black participants, due to the small number of other study participants. Information on 4-year mortality, according to OAG status, was obtained from the follow-up data on the cohort.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Table 1 presents the age-specific prevalence of OAG among BES Black participants. Prevalence increased with age, reaching 17 percent for those aged 70 years or older. As expected, the mortality observed during the 4-year interval also increased with age. Mortality for age groups 40–49, 50–59, 60–69, and 70 or more years, respectively, was 1.54, 2.46, 6.88, and 19.08 percent for persons without OAG and 5.56, 0, 7.04, and 19.88 percent for persons with OAG.
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Four different curve-fitting approaches to smooth the prevalence proportion were determined from logistic, power, quadratic, and cubic functions (by regression analyses). Figure 1 depicts the observed versus estimated prevalences. Table 2 presents the age-specific observed 4-year incidence, which increased from 1.2 percent in persons 40–49 years of age to 4.2 percent in those aged 70 years or older. This table also shows the indirect 4-year incidence estimates based on a logistic fit, using the equal mortality assumption, which ranged from 0.6 percent for persons aged 40–49 years to 7.5 percent for the oldest age group. Based on the power function fit, the incidence estimates were 0.7, 1.3, 2.3, and 4.8 percent for the successive age groups, with similar results obtained by quadratic and cubic approaches. Table 3 indicates that indirect estimates, using the differential mortality assumption, essentially remained the same as those presented in table 2.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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In the absence of observed incidence data, investigators have used the methods of Leske et al. (10
) and Podgor and Leske (12) to derive theoretical incidence estimates (13, 14). While it is important to know the validity of predicting incidence from prevalence, the evaluation of the estimation approach requires incidence rates. This investigation presents the first comparison of observed OAG incidence versus indirect estimates, calculated from the prevalence data. The evaluation is based on a study cohort that provides a unique opportunity to verify the validity of these indirect OAG incidence estimates. Both the original prevalence study and the follow-up study had high rates of participation (84 and 85 percent of those eligible, respectively), thus increasing the overall representativeness of the results and minimizing potential biases resulting from nonparticipation. Losses to follow-up were mainly due to mortality, with such data being available to the study. Thus, the incidence data on the cohort provide an excellent source for evaluating the effectiveness of the incidence-estimation techniques. Comparison of the theoretical estimates with the directly measured 4-year incidence rates showed that close estimates can be obtained, with reasonable fit of the prevalence data. Indirect estimates calculated using equal or differential mortality assumptions were very similar (tables 2 and 3), as participants with and those without OAG had similar mortality rates at older ages. Mortality rates were not as similar at younger ages, but OAG was infrequent in these age groups. Therefore, the incidence estimates for OAG were not affected by the assumption of differential mortality.
Different approaches to curve fitting of the prevalence data resulted in various incidence estimates. The R2 values indicated that approaches such as power, quadratic, and cubic techniques provided a better fit to the prevalence data than the logistic curve and led to incidence estimates that were closer to the observed incidence, especially for the older age group. Although all of the approaches used in this report tended to underestimate incidence for the youngest age group, the effect of such underestimation may be small, since OAG incidence in this age group is uncommon. The low prevalence of the disease among younger persons may have contributed to the less precise estimates in the age group 40–49 years. The logistic fitting overestimated incidence for persons aged 70 or more years, whereas the non-logistic approaches closely approximated the incidence for the older age group. Although our evaluations do not include estimation for ages younger than 40 years, it is possible that the cubic and quadratic fits may overestimate incidence for ages younger than 40 years (figure 1).
Although the increase in OAG with age is well established, the pattern of increase may vary for different populations (1–7). Additionally, OAG prevalence is higher in populations of African descent (3, 5–7) than in White populations (1–4). Therefore, each population may have a different rate of increase. The model that best fits any particular age-specific prevalence curve may depend on the prevalence in that particular population. Although all models presented here provide good estimates for our data, these models may or may not be appropriate for other populations. When applying this methodology, several curve-fitting approaches should be tested to determine the best fit for the data.
In the absence of longitudinal data, reasonably valid incidence estimates of OAG can be derived from available prevalence data by indirect methods. These indirect approaches can provide useful estimates of incidence when direct observations cannot be obtained, thus assisting in research or public health applications.
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ACKNOWLEDGMENTS |
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Supported by grants EYO7625 and EYO7617 from the National Eye Institute, Bethesda, MD.
The authors thank the Barbados Eye Studies Group, the participants, and the Ministry of Health, Barbados, West Indies, for their role in the study.
The Barbados Eye Studies Group: Principal investigator: Dr. M. Cristina Leske; Coordinating Center, University at Stony Brook, Stony Brook, NY: Dr. M. Cristina Leske, Dr. Leslie Hyman, Dr. Barbara Nemesure, Suh-Yuh Wu, Dr. Xiaowei Li, Shu-Hong Xie, Lixin Jiang, Kasthuri Sarma, Barbara Springhorn, and Koumudi Manthani. Data Collection Center, Ministry of Health and the Environment, Bridgetown, Barbados, West Indies: Dr. Anthea M. S. Connell, Dr. Anselm Hennis, Dr. Ann Bannister, Dr. Muthu A. Thangaraj, Coreen Barrow; Patricia Basdeo, Kim Bayley, and Anthanette Holder. Fundus Photography Reading Center, The Johns Hopkins University, Baltimore, MD: Dr. Andrew P. Schachat, Judith A. Alexander; Noreen B. Javornik, Cheryl J. Hiner, Deborah A. Phillips, Reva Ward, and Terry W. George.
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NOTES |
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Reprint requests to Dr. M. Cristina Leske, Department of Preventive Medicine, University Medical Center at Stony Brook, HSC L3 086, Stony Brook, NY 11794–8036 (e-mail: cleske{at}uhmc.sunysb.edu).
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