A likelihood approach to estimating sensitivity and specificity for binocular data: application in ophthalmology

Binocular data typically arise in ophthalmology where pairs of eyes are evaluated, through some diagnostic procedure, for the presence of certain diseases or pathologies. Treating eyes as independent and adopting the usual approach in estimating the sensitivity and specificity of a diagnostic test ignores the correlation between eyes. This may consequently yield incorrect estimates, especially of the standard errors. The paper proposes a likelihood-based method of accounting for the correlations between eyes and estimating sensitivity and specificity using a model for binocular or paired binary outcomes. Estimation of model parameters via maximum likelihood is outlined and approximate tests are provided. The efficiency of the estimates is assessed in a simulation study. An extension of the methodology to the case of several diagnostic tests, or the same test measured on several occasions, which arises in multi-reader studies, is given. A further extension to the case of multiple diseases is outlined as well. Data from a study on diabetic retinopathy are analysed to illustrate the methodology.