Sensitivity, specificity and other diagnostic measures with multiple sites per unit

Medical researchers often study the performance of diagnostic tools. The performance of the diagnostic tool is evaluated by calculating sensitivity, specificity and similar measures. Sensitivity is defined as the probability of a positive diagnostic test in a patient with the illness or injury for which the test serves as a diagnostic tool. Specificity is the probability of a negative diagnostic test in a patient free of the disease or injury. For some conditions, the test is applied to several anatomic locations or at different times in a patient and each test can be positive or negative. The findings of the tests performed on the same patient are correlated and any summary measure should account for this correlation. We propose a summary measure for the subject that combines the results from all tests performed on the same patient while accounting for the correlation. The measure is easily calculated and requires no specific statistical software. We also provide an estimate of the standard error and confidence intervals. The method is illustrated with a study, conducted at the University of California, Davis School of Medicine, of the sensitivity of magnetic resonance (MR) imaging and plain film (PF) radiography in detecting injuries in the cervical spine, such as fractures and soft tissue injuries.