The analysis of ophthalmological data pose unique challenges for the data analyst because the fundamental unit of analysis is not well defined. If the eye is used as the unit of analysis, then one must account for the correlation between fellow eyes in performing the analysis; otherwise one will underestimate p- values and widths of confidence intervals. There has been much interest in he past 15 years in the development of techniques for addressing this issue including GEE methods (Liang and Zeger, 1986) and generalized linear models (Rosner, 1984). Most of these methods are concerned with parametric statistical models such as linear or logistic regression. One gap in the literature that we intend to fill in this proposal is the incorporation of clustering effects for standard nonparametric tests. Many types of ophthalmologic data are not normally distributed (e.g. Humphrey visual field data), and require nonparametric methods for their analysis. If one wishes to use the eye as the unit of analysis, then it is important to incorporate clustering effects into these methods that take the correlation between fellow eyes into account. Many ophthalmologists prefer to use the person as the unit of analysis (e.g. using visual function in the better eye) rather than the eye. However, Olkin and Viana (1995) showed that the distribution of visual function in the better eye as a function of a person-specific covariate (e.g. age) is not normally distributed, and propose special methods for this type of analysis. We propose to extend this work to the case of eye specific covariates and the case of several covariates in the same model. Another issue is that some ophthalmic conditions (e.g. cataract) have subclassifications with possibly different etiologies (e.g. nuclear, cortical, PSC cataract). However, the important public health question is: what is the overall probability of any type of cataract as a function of risk factors (e.g., antioxidant use). We intent to generalize the standard logistic model, to be compound logistic model which accounts for the possibly differential risk factor profiles. Furthermore, there has been much work on censored survival data where the failure times occur only at specific visits. We intend to incorporate clustering effects in interval censored data. A final goal of our proposal is to perform an analysis of the natural course of retinitis pigmentosa over a 12 year period. This will allow estimation of the rates of decline of the ERG and visual field over a long period of time as well as provide estimates for an individual patient of the number of years of useful vision they can expect to have.
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