Glaucoma may be diagnosed on the basis of longitudinal data collected using Standard Automated Perimetry (SAP). We consider the application of several joint modeling approaches to longitudinal data obtained via SAP along with both correlated binary and correlated survival outcomes. In each case the outcome consists of a diagnosis of glaucoma or glaucomatous progression. We propose and investigate logistic and multinomial models for the binary data, which use simple linear random effects models for the SAP data. We investigate in particular how our proposed models account for the correlation between fellow eyes of a subject. For our survival data we investigate a joint model which combines a frailty model with a hierarchical nonparametric model for the SAP data through the use of B-splines. In our research we demonstrate how our joint modeling approach can be used to improve upon existing methods of diagnosis, where improvement is determined by comparing rates of sensitivity and specificity. In addition we show that, in the case of binary outcome data, our approach allows for the estimation of the probability of glaucoma given longitudinal data, while also accounting for the correlation between the fellow eyes of a patient. We lastly demonstrate that we can obtain novel and statistically significant risk factors when modeling the longitudinal data nonparametrically within a joint modeling framework.
