Recently Perera et al. introduced two new binocular accuracy measures to evaluate diagnostic tests for paired organs. They adopted the Gaussian copula model to account for correlation between fellow eyes. As the measures are functions of several joint probabilities and due to the nature of the joint models, variations of the estimates for the two new measures were assessed via bootstrapping. We provide a different approach to inference about the two interesting and innovative measures. In our opinion, when patients are independent, the binomial models suffice for inference about the parameters of interest. Inference becomes simple and straightforward. We perform numerical studies and analyse the data set as of Perera et al. for illustration. Also, we investigate thru simulations the issue of robustness of the Gaussian copula and the binomial models under model misspecification.
Keywords: Gaussian copula; Ophthalmology; binocular sensitivity; binocular specificity; pairing.