Sensitivity and specificity of a subset of items

I have a list of 60 stimuli and for each one of them, I have their sensitivity, specificity and ji value for the detection of demented vs. nondemented participants. I am using 20 of these stimuli in an abbreviated version of this battery, and I would like to be able to calculate a sensitivity-specificity for a given cut-off of this 20-item version based on the individual info of each item. Is this possible? I'm thinking maybe there's a way to weigh-average their sensitivities and specificities or something. Please help!