Tutorial on Biostatistics: Longitudinal Analysis of Correlated Continuous Eye Data

ABSTRACT

Purpose: To describe and demonstrate methods for analyzing longitudinal correlated eye data with a continuous outcome measure.

Methods: We described fixed effects, mixed effects and generalized estimating equations (GEE) models, applied them to data from the Complications of Age-Related Macular Degeneration Prevention Trial (CAPT) and the Age-Related Eye Disease Study (AREDS). In CAPT (N = 1052), we assessed the effect of eye-specific laser treatment on change in visual acuity (VA). In the AREDS study, we evaluated effects of systemic supplement treatment among 1463 participants with AMD category 3.

Results: In CAPT, the inter-eye correlations (0.33 to 0.53) and longitudinal correlations (0.31 to 0.88) varied. There was a small treatment effect on VA change (approximately one letter) at 24 months for all three models (p = .009 to 0.02). Model fit was better with the mixed effects model than the fixed effects model (p < .001).

In AREDS, there was no significant treatment effect in all models (p > .55). Current smokers had a significantly greater VA decline than non-current smokers in the fixed effects model (p = .04) and the mixed effects model with random intercept (p = .0003), but marginally significant in the mixed effects model with random intercept and slope (p = .08), and GEE models (p = .054 to 0.07). The model fit was better with the fixed effects model than the mixed effects model (p < .0001).

Conclusion: Longitudinal models using the eye as the unit of analysis can be implemented using available statistical software to account for both inter-eye and longitudinal correlations. Goodness-of-fit statistics may guide the selection of the most appropriate model.

KEYWORDS:

• Linear regression models
• correlated data
• inter-eye correlation
• longitudinal correlation
• fixed effects model
• mixed effects model
• generalized estimating equations

Disclosure statement

All authors have no conflict of interest disclosure to disclose.

Additional information

Funding

Supported by grants [R01EY022445 and P30 EY01583-26] from the National Eye Institute, National Institutes of Health, Department of Health and Human Services.