Correlated data are the norm in ophthalmologic data, due to correlated response for paired eyes. An abundance of methods are now available that enhance standard models by incorporating clustering effects (Rosner, 1984; Liang and Zeger, 1986). These methods are limited usually to either normally distributed or binary outcomes. However, many scales used in ophthalmology are continuous, but non-normally distributed (e.g. visual field area). Other scales are ordinal and non-normally distributed, but are sometimes treated as normally distributed as well (e.g. diabetic retinopathy grade). Nonparametric methods are a natural approach for such scales. In this proposal, we propose a model for incorporating clustering effects for ranked data and use this model to extend tests such as the Mann-Whitney U test for the clustered data situation. In addition, we propose extensions to allow for tied values and to adjust for other covariate effects. Another issue in ophthalmologic data is that some endpoints are composite in nature (e.g. nuclear cataract, cortical cataract, PSC cataract, control). An interesting issue is that the risk factor profile for some risk factors may be different for different types of cataract, while for other risk factors it may be the same. (Marshall & Chisholm, 1985). We propose to use a flexible type of polytomous regression model in this setting and to enhance it by considering matched designs as well as outcome categories that are not mutually exclusive. Furthermore, we propose to develop a user-friendly software package to easily fit such models including use of stepwise regression strategies. A third area of interest is the use of correlated data methods in a small sample setting. Most previous methods developed have good asymptotic properties but depend on at least a moderately sized sample for their validity .We propose to extend existing methods of exact inference by incorporating clustering effects and making these methods available by exportable software. Finally, the area under the ROC curve is frequently used as a measure of goodness-of-fit for logistic regression models. However, its use is problematic if separate logistic models are fit for the right and left eyes of an individual in ophthalmologic studies. We propose to extend traditional ROC curve methods (Hanley and McNeil, 1982) to the clustered data situation where outcome on fellow eyes may be either concordant (bilateral cases) or discordant (unilateral cases).
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