Robust likelihood inference for diagnostic accuracy measures for paired organs

Paired data arise naturally in Ophthalmology where pairs of eyes undergo diagnostic tests to predict the presence of certain diseases. The common correlation model is popular for modeling the joint probabilities of responses from fellow eyes for inference about accuracy measures. One of the assumptions underlying the model is exchangeability of fellow eyes that stipulates the accuracy measures such as sensitivities/specificities of fellow eyes be equal. We propose a parametric robust likelihood approach to testing the equality of accuracy measures of fellow eyes without modeling correlation. The robust likelihood procedure is applicable for inference about diagnostic accuracy measures in general paired designs. We provide simulations and analyses of a data set in Ophthalmology to demonstrate the effectiveness of the parametric robust procedure.