1 Department of Population Health Sciences, University of Wisconsin Medical School, Madison, WI.
2 Department of Biostatistics and Medical Informatics, University of Wisconsin Medical School, Madison, WI.
3 Department of Ophthalmology and Vision Sciences, University of Wisconsin Medical School, Madison, WI.
Received for publication December 28, 2001; accepted for publication October 1, 2002.
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ABSTRACT |
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cohort effect; cohort studies; generalized estimating equation; macular degeneration; risk adjustment
Abbreviations: Abbreviations: CI, confidence interval; OR, odds ratio.
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INTRODUCTION |
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There are two major challenges in analyzing the birth cohort effect on age-related maculopathy in the Beaver Dam Eye Study. First, in the Beaver Dam Eye Study, each participant was measured at three different time points. The association among measurements needs to be included in the model to yield efficient and correct inferences (4). Second, to better understand the reasons for a birth cohort effect, we want to adjust for known age-related maculopathy risk factors to see whether the birth cohort effect is attributable to them. Statistical methods, developed previously for investigating the birth cohort effect, focus on analyzing registry or survey data that are aggregated into a set of rates and arranged in a two-way table by age group and birth-year period. It is difficult to adjust for individual risk factors in these approaches (57).
To our knowledge, there have been no population-based studies conducted examining the relation of birth cohort effects with the prevalence of age-related maculopathy. The purpose of our report is to 1) examine this effect in the Beaver Dam Eye Study and 2) propose a strategy for handling the analytic challenges described above.
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MATERIALS AND METHODS |
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Population
Among eligible individuals, 4,926 participated in the baseline examination between March 1, 1988, and September 14, 1990; 3,722 (of whom 38 did not participate in the first examination) participated in the 5-year follow-up examination between March 1, 1993, and June 14, 1995; and 2,962 (of whom 198 did not participate in the first and/or second examination) participated in the 10-year follow-up examination between March 1, 1998, and June 9, 2000. Table 1 summarizes baseline characteristics of participants at the baseline examination, 5-year follow-up, and 10-year follow-up. There were no substantial differences among the three groups, although the average age was slightly younger and the percentage of hypertension was slightly lower for people that participated in the successive examination phases. The possible reasons for nonparticipation include death, moving out of the area, and refusal (911). Comparisons between participants and nonparticipants at all three examinations have been presented elsewhere (911).
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Detailed definitions for the presence and severity of specific lesions have appeared elsewhere (1, 2, 14, 15). For the purposes of this report, we put our focus to three lesions: soft drusen and early and late age-related maculopathy. Soft drusen was defined by the presence of either soft distinct or indistinct drusen in an eye. Early age-related maculopathy was defined as either the presence of soft indistinct drusen or the presence of any type of drusen with retinal pigment epithelial depigmentation or increased retinal pigment. Late age-related maculopathy was defined as the appearance of either exudative macular degeneration or pure geographic atrophy.
The birth cohort effect is defined as the variation in the prevalence of age-related maculopathy that arises from the different exposures of each birth cohort. Thus, if a birth cohort effect exists, individuals from different birth cohorts would have different chances of developing age-related maculopathy even if the same age. In this report, we are also interested in the "independent" birth cohort effect, adjusting for identified risk factors.
We identified the following as characteristics that could potentially influence the relation among age-related maculopathy, age at the examination, and birth cohort: gender, smoking status, history of heavy drinking, multivitamin use, cholesterol level, and hypertension status. These risk factors were chosen because of a strong relation with age-related maculopathy in previous studies. In the Beaver Dam Eye Study, smoking was related to the prevalence of age-related maculopathy (16), heavy drinking and hypertension were associated with exudative macular degeneration, a lesion that defined late age-related maculopathy (17, 18), and serum cholesterol was inversely associated with age-related maculopathy (19). Vitamin use was found to be associated with the incidence of age-related maculopathy in a clinical trial (20). Definitions of these confounding variables have been described in detail elsewhere (16, 17, 21, 22). In brief, a subject was classified as a current smoker if he/she had smoked more than 100 cigarettes in his/her lifetime and had not stopped smoking; as a former smoker if he/she had smoked more than this number but had not smoked within the last year prior to the examination; and as a nonsmoker if he/she had smoked fewer than 100 cigarettes in his/her lifetime. A current heavy drinker was defined as a person consuming four or more servings of alcoholic beverages daily, a former heavy drinker had consumed four or more servings daily in the past but not within the last year, and a non-heavy drinker had never consumed four or more servings daily on a regular basis. A person was classified as a current vitamin user if he/she had taken at least one vitamin per week in the month prior to the examination; as a past vitamin user if he/she had ever regularly taken vitamins at least once a week but not within the last month; and as never using vitamins if she/she never took vitamins regularly. Serum cholesterol levels were determined by enzymatic procedures (22). Hypertension was defined as a systolic blood pressure of 160 mmHg and/or a diastolic blood pressure of 95 mmHg and/or a history of hypertension using antihypertensive medication at the time of the examination.
We adjusted for these potential confounding variables in each model. Measurements of risk factors were taken at each examination; however, multivitamin use and cholesterol level were not available at the 10-year follow-up. In the following analysis, we use the 5-year multivitamin use and cholesterol level as the 10-year measurements.
Conventional approaches for the birth cohort effect: graphical displays and the age-cohort model
Previously developed statistical methods for the birth cohort effect focus on analyzing "rates." For the Beaver Dam Eye Study, we first aggregated data into a two-way table by year of birth and age group in 5-year intervals, and we calculated the prevalence of age-related maculopathy in each cell. Next, to display birth cohort patterns, we plotted the log odds of prevalent age-related maculopathy against age for each birth cohort and used the age-cohort model (57) to test the significance of birth cohort and age effects:
Here, ca is the prevalence of age-related maculopathy of the cth birth cohort and ath age group,
c represents the birth cohort effect of the cth birth cohort, and
a is the age effect of the ath age group. The statistical significance of each effect is determined by using the likelihood ratio statistic, which follows a chi-square distribution under the null hypothesis.
The age-cohort model is a direct application of Poisson regression (23); therefore, it can be easily implemented by existing statistical software. In addition, graphical presentations of the age-related maculopathy distribution can empirically display birth cohort patterns and provide a comparison with results from the regression approach. However, these methods suffer from significant limitations. First, the Beaver Dam Eye Study is a longitudinal study in which each participant was measured at three different time points (baseline and the 5th year and the 10th year), and thus the age-cohort model, which ignores the association among repeated measurements, would yield inefficient parameter estimates and incorrect inferences (4). Second, these approaches aggregate individual observations into a set of rates for analysis and therefore cannot adjust for individual-level risk factors. As described in the introduction, several risk factors other than age have been identified to be associated with age-related maculopathy. We need to adjust for the known risk factors in order to determine whether there is an independent effect of birth cohort.
A method proposal: Heagerty and Zegers model
Heagerty and Zeger (24) proposed a statistical model that utilized the generalized estimating equation (25) approach for analyzing repeated measures of categorical data, which is appropriate for this study. In Heagerty and Zegers model, two regression models are specified: one to describe the marginal means and another to describe the associations among repeated measurements. From the marginal mean model, we can estimate the odds ratio relating the response variable to risk factors. In our study, for example, the odds ratio between age-related maculopathy and birth year (i.e., birth cohort) can be estimated. The association model is used to describe the association among repeated measurements from the same participant. In our study, this model estimates the odds ratio that describes the degree to which developing age-related maculopathy is consistent among repeated measurements within each participant. For more details on Heagerty and Zegers model, readers can refer to the article by Huang et al. (26).
The endpoints soft drusen and early and late age-related maculopathy in the right, left, and either eye were used as the outcome variables. We fit Heagerty and Zegers model for each age-related maculopathy endpoint separately adjusting for participant age in 1987, age at the examination, and the risk factors identified in the procedures and definitions section of this report. To be more specific, let Yij be the indicator of developing age-related maculopathy for the ith participant at the jth examination (j = 1 (baseline), 2 (5-year follow-up), and 3 (10-year follow-up)):
where (risk factors)ij represents all the risk factors identified for the ith participant at the jth examination; (age in 1987)i is the ith participants age in year 1987 and is used to represent the birth cohort effect; and ageij is the age of the ith participant at the jth examination.
There are several key features of model 2. A significant positive ß2 means that, at the same age, participants born in the older cohort are exp(ß2) times as likely to develop age-related maculopathy as those from the cohort that is 1 year younger. The age effect exp(ß3) is the odds ratio of developing age-related maculopathy for every 1-year increase in age, comparing people from the same birth cohort. These two effects are adjusted for the identified risk factors. The reason that we centered (age in 1987)i and ageij at 65 years of age is for ease of interpretation and to avoid collinearity. Based on findings from figures 1 and 2, the decision was made not to put the quadratic term for ageij into the model; the figures showed a linear relation between the log odds of age-related maculopathy and age.
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A significant positive ß4 means that the odds ratio of developing age-related maculopathy per every 1-year decrease in birth year (the birth cohort effect) is higher for older people than younger people, and the odds ratio of developing age-related maculopathy on age (the age effect) is higher for people from older birth cohorts than for those from younger cohorts.
Implementing Heagerty and Zegers model for our data, we first fit model 3 to determine whether the parallel assumption described previously was met. For age-related maculopathy endpoints that had significant ß4 values, we calculated the birth cohort effect in each age group and the age effect for each birth cohort. For nonsignificant age-related maculopathy endpoints, we fit model 2 to estimate the overall birth cohort effect and age effect.
The software for fitting Heagerty and Zegers model can be downloaded from the Internet: http://www.biostat.jhsph.edu/biostat/research/software.shtml under the category "Estimating Equations for Dependent Ordinal Data." Example programs for implementing the software to analyze the birth cohort effect are available from the authors.
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RESULTS |
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Graphical displays and the age-cohort model
The prevalence of age-related maculopathy in either eye at baseline, 5-year follow-up, and 10-year follow-up was as follows: soft drusen: 25.3 percent, 32.7 percent, and 32.2 percent; early age-related maculopathy: 20.4 percent, 24.7 percent, and 22.8 percent; and late age-related maculopathy: 1.74 percent, 2.11 percent, and 2.78 percent, respectively. For use in graphical displays and the age-cohort model, nine birth cohorts and 11 age groups were constructed (birth cohort: 1907, 19081912, 19131917, 19181922, 19231927, 19281932, 19331937, 19381942,
1943; age groups:
44, 4549, 5054, 5559, 6064, 6569, 7074, 7579, 8084, 8589,
90 years). The left panels of figures 1 and 2 show the observed log odds of age-related maculopathy in either eye versus age for different birth cohorts. From the plots, we observed that, as people became older, the chances of developing age-related maculopathy increased. Those in older birth cohorts tended to have higher probabilities of developing early age-related maculopathy than did those from younger cohorts, even with the same age, suggesting a birth cohort effect on early age-related maculopathy. A birth cohort effect was not as apparent for soft drusen as it was for early age-related maculopathy. The prevalence of late age-related maculopathy was equal to zero for people born after 1937, and a less clear birth cohort effect was observed for people born before 1937. A linear relation between the log odds and age was apparent within each birth cohort for all three age-related maculopathy endpoints. This supported the exclusion of the quadratic age term in Heagerty and Zegers model.
Results from the age-cohort model are shown in table 2. We found that the overall birth cohort effect was significant for early age-related maculopathy but not for soft drusen or late age-related maculopathy. A strong age effect was found for all the endpoints. This was consistent with what we saw in the graphical displays.
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Because the prevalence of late age-related maculopathy was very low (or equal to zero) in younger birth cohorts, Heagerty and Zegers model did not converge. Therefore, we analyzed only "late age-related maculopathy in either eye" and included only those participants born before year 1937. Because of the results of risk factor adjustment for soft drusen and early age-related maculopathy endpoints, we fit the model without adjusting for the identified risk factors. The ß4 value of model 3 for late age-related maculopathy in either eye was not significant (p value = 0.66). The results of model 2 (table 3) showed that there were both a birth cohort effect and an age effect on late age-related maculopathy in the either eyes for participants born before 1937.
For all age-related maculopathy endpoints, the measurements from the same participant were very highly correlated. For example, measurements of early age-related maculopathy in either eye from the same participant were 109.69 (95 percent CI: 73.45, 163.80) times as likely to be consistent than to be different. Comparing the results between the simple logistic regression without Heagerty and Zegers longitudinal correction and Heagerty and Zegers model, we found that both approaches produced similar regression coefficient estimates but that the standard error estimates were different. The two approaches, therefore, provided different conclusions about the birth cohort effect: 1) The birth cohort effect on soft drusen disappeared with logistic regression but was still significant under Heagerty and Zegers model; and 2) for early age-related maculopathy, the interaction between age and birth cohort was not significant in the logistic regression approach, but Heagerty and Zegers model gave a significant interaction. These pieces of evidence showed the importance of taking the longitudinal effect into account.
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DISCUSSION |
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The birth cohort effect that we observed remained strong after adjusting for known risk factors. This might suggest that earlier "unmeasured" exposures (e.g., diet) may, in part, explain the birth cohort effect. It is also possible that the effect is due to the limitations of the measurement of risk factors. A major concern is underreporting of smoking and drinking history. Underreporting of alcohol consumption or cigarette smoking in people at risk for developing age-related maculopathy would lead to an underestimate of the association between them. If there is differential underreporting by different age cohorts because of the perceived social acceptability of smoking, for example, this might lead to more residual confounding in some groups compared with others.
In contrast to the age-cohort model, Heagerty and Zegers approach can take the longitudinal effect into account and adjust for individual-level risk factors. However, all these come at the price of requiring a larger sample size to obtain parameter estimations. Comparing results from both models, we found that the age-cohort model tends to give more conservative estimations than does Heagerty and Zegers model. Possible interpretations for this difference are the following: first, repeated measurements in the Beaver Dam Eye Study were highly correlated; the age-cohort model ignores this strong correlation and thus results in less efficient parameter estimates (larger variances for estimated parameters). Second, the age-cohort model aggregates individual observations into group data, and therefore this analysis may combine individuals that had different associations with birth cohorts and mask this relation. Our recommendation for using these two models is to use the age-cohort model and graphical displays first for basic findings. Then, Heagerty and Zegers model can be implemented to ensure that the age-cohort model has not masked the relation between age-related maculopathy and birth cohorts.
In exploring our longitudinal data for the cohort effect, we are concerned with the potential influence of mortality or nonparticipation on our findings. Although age-related maculopathy is not associated with mortality in our population, smoking, age, and birth cohort year are. The weight of these three forces could counter our ability to find evidence of a cohort effect on age-related maculopathy. In addition, we anticipate that the protective effect of higher serum total cholesterol found in our analyses might be obscured because of the relation of that variable to mortality. A protective effect of multivitamin use on either mortality or age-related maculopathy is unlikely to bias our findings of a cohort effect. We cannot infer which specific component(s) of the multivitamin supplement might be protective; it is also possible that vitamin use is simply a marker of a "healthy lifestyle."
In this report, we found a significant difference in the birth cohort effect across age groups only for early age-related maculopathy. It is possible that the presence of soft drusen is genetically or "constitutionally" determined, where more advanced lesions may be more influenced by the effects of environment on an aging or otherwise compromised retina. The lack of a significant difference in late age-related maculopathy may be related to the small number of cases of these lesions.
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ACKNOWLEDGMENTS |
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The authors thank the Beaver Dam Scientific Advisory Board (Dr. Mae Gordon, Dr. Lee Jampol, Dr. Natalie Kurinij, Dr. Daniel Seigel, and Dr. Robert Wallace) and the primary care physicians and optometrists of Beaver Dam and their staffs for their contributions.
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NOTES |
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REFERENCES |
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