Modelling Repeated-Series Longitudinal Data

We present a model for describing repeated-series longitudinal data, that is, longitudinal data where each unit may yield multiple series of the same variable. Such data arise commonly in ophthalmologic studies, where one obtains measurements on the same variable for the right and left eyes at each clinic visit. We model the mean as a linear function of predictors, and assume that the error term is a sum of a random subject effect and a vector AR(1) process. We fit the model by maximum likelihood and assess the adequacy of the error assumptions by an extension of the empirical semivariogram. We apply our model for data from a clinical trial comparing two treatments for ocular hypertension and glaucoma, with intra-ocular pressure as the primary endpoint. Results suggest that autocorrelation within and between eyes is a significant feature of the variance model. Standard errors depend critically on the variance assumption.