Evaluation of the sensitivity and specificity of qualitative diagnostic test under normal assumption

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Sensitivity and specificity of an investigational qualitative diagnostic test are conventionally estimated by comparing with an existing qualitative reference test which is often imperfect and hence introduces misclassification biases to sensitivity and specificity estimates. In many situations, both tests measure an underlying continuous trait associated with a specific disease/virus and report binary results by comparing the measurement to a pre-determined cutoff point. The maximum likelihood estimates of the sensitivity and specificity are established under independent normal assumption between the underlying trait and measurement errors for both investigational test and reference test. This allows us to avoid misclassificiation biases caused by imperfect reference test without retesting any subjects.