I am planning my Master thesis project in Neuropsychology and I am currently facing a statistical/mathematical challenge.

Here is what it is about:

Three patient groups will be administered a cognitive screenind instrument with seven subtests. Originally, the scores of the subtests are simply summarized and the total sum score is 30. This procedure ignores that different subtests have different power to detect cognitive dysfunction (i.e. different sensitivities and specificities).

I intend to develop a weighting in which subtests with a higher sensitivity and specificity will receive more weight in the total score.

My question is: Is there a statistical/mathematical way to decide how much weight the subtests should be assigned?

A simplified example to illustrate the problem.

Suppose I have three subtests. I collect the data and get the following sensitivities and specificities (using either ROC analyses or discriminant analysis):

Subtest 1: 68% sens / 78% spec

Subtest 2: 85%/91%

subtest 3: 95%/98%

The total sum score is 30.

It is obvious that subtest 3 should receive a higher weight because it seems better in detection dysfunction, but HOW MANY points should it get exactly? (12 points, 13 points, ...?)

Is there any statistical/mathematical procedure that might be worth looking at?

I hope I made the situation clear, please let me know if you need more information!

I have done quiet some research about it, but so far I am still pretty much in the dark...

I am thankful for ANY suggestion, idea, comment...

Sophie