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Bernard Rosner, Gui-Shuang Ying, Robert Glynn, Maureen G Maguire; Statistical Analysis for Correlated Binary Ophthalmologic Data. Invest. Ophthalmol. Vis. Sci. 2017;58(8):1529. doi: https://doi.org/.
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© ARVO (1962-2015); The Authors (2016-present)
To describe and demonstrate methods of analysis for ophthalmologic data with a binary outcome using the eye as the unit of analysis.
We describe marginal models to perform two-eye analyses to assess associations between binary eye-specific outcome variables and either person or eye-specific exposure or treatment variables. We compare these methods to each of single eye analyses and two-eye analyses that ignore inter-eye correlations. These methods are applied to: (1) ETROP (Early Treatment for Retinopathy of Prematurity) which includes infants affected bilaterally with one eye treated conventionally and the fellow eye treated early and unilateral affected infants with treatment assigned randomly, (2) AREDS (Age-Related Eye Disease Study) where treatment was systemic and the outcome was incidence of geographic atrophy (GA) in individual eyes over a 5-year follow-up period.
In ETROP (see Table 1), standard logistic regression model provided both larger and smaller p-values than models accounting for inter-eye correlation. Specifically, the treatment effect on unfavorable vision outcome was not significant with standard logistic regression (OR = 0.67, 95% CI = 0.44 – 1.03, p = 0.07) but was significant with a marginal model (generalized estimating equations (GEE) approach) with a working independence correlation structure (OR = 0.67, 95% CI = 0.50 – 0.90, p = 0.008).In AREDS (see Table 2), although there was no significant treatment effect with either one-eye or two-eye analyses for GA, there were significant effects in GEE models for both current smoking (OR = 1.77, 95% CI = 1.08 – 2.89 , p = 0.02) and BMI (30 vs 22 kg/m2) (OR = 1.38, 95% CI = 1.18 – 1.61, p < 0.001), ordinary logistic regression yielded inappropriately low p-values, while variable results were obtained with single-eye analyses for both risk factors.
Ignoring inter-eye correlation can lead to inappropriately large p-values for paired designs and inappropriately small p-values for parallel designs when both eyes are in the same group. Marginal models using the eye as the unit of analysis provide valid inference compared with two-eye analyses that ignore inter-eye correlation and enhanced power compared with one-eye analyses.
This is an abstract that was submitted for the 2017 ARVO Annual Meeting, held in Baltimore, MD, May 7-11, 2017.
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