The proposed project is a two year study to develop inferential and study design aspects of a linear statistical model appropriate to the analysis of longitudinal ophthalmologic data and to apply the improved model in a re-analysis of a data set obtained from the Early Treatment Diabetic Retinopathy Study (ETDRS). The relevant statistical model is the repeated-measures random effects/AR(l) model for continuous data due to Heitjan and Sharma. This model incorporates cross-correlation between eyes and longitudinal correlation among measurements obtained from a single eye. The re-analysis of the ETDRS data set will consider the effects of aspirin on visual acuity measured continuously. A previously published analysis (ETDRS Report Number 8) analyzed a categorical version of visual acuity, ignoring longitudinal correlation and handling cross-correlation between eyes by analyzing eyes separately. The repeated measures random effects /AR(l) model has already been utilized by Heitjan and Sharma in a published study of intraocular pressure, using the expected information to perform statistical inference. Simulation studies have shown that it performs well in the balanced data case. Our first objective is to develop better inferential methods so as to 1) handle unbalanced (i.e., missing) data such as that arising when only one eye of two has the disease of interest and/or when the number of follow-up visits varies with subject, 2) control for the use of a possibly mis-specified variance structure, and 3) compensate for the use of estimated variance parameters in the standard error of the fixed effects, a procedure that may result in an underestimation of the standard error. This objective will be accomplished by the following: 1) replacing the expected information with the observed information, the observed information being a more reliable method of performing statistical inference in the presence of missing data, 2) using the robust (sandwich) variance estimator, a method that can control for a possibly mis-specified variance structure, and 3) approximating the degrees of freedom so as to control for the possibility of underestimated standard errors. Methodological advances will be incorporated into a computer package to be made available on the World Wide Web. Our second objective is to carry out power and sample size calculations for several different longitudinal ophthalmologic study designs, under various assumptions about the prevalence of bi-ocular versus uni-ocular disease, differential treatment allocation, loss-to-follow-up, and expected adherence to study treatment(s). The implications of treatments applied at the eye-level (e.g., photocoagulation) as well as systemically applied treatments (e.g., aspirin) on sample size, frequency of evaluation, and power will be considered.
