Diagnostic and screening studies in ophthalmology frequently involve binocular data where pairs of eyes are evaluated, through some diagnostic procedure, for the presence of certain diseases or pathologies. It is usually sufficient in practice that at least one eye is positively diagnosed for the patient to be sent for further and more extensive eye examination. More relevant diagnostic accuracy measures in these cases are therefore the probability of at least one correct positive diagnosis in patients with one or both eyes truly diseased and the probability of two correct negative diagnoses for patients with both eyes truly un-diseased. The former is analogous to sensitivity and the latter to specificity. Predictive values may be similarly re-defined.
The thesis proposes these new sensitivity and specificity measures as alternatives to conventional ones for paired binocular binary diagnostic data arising from screening studies with cross-sectional sampling. The measures are defined for flexible models based on copulas and extensions of existing models for correlated binary data. The proposed methodology is illustrated with data from a study on diabetic retinopathy.