Recently many of the researchers use logistic regression predicted value probability for finding the combined effect of two or more diagnostic test [Test Variable] in ROC analysis. Is it a good idea?.
It is a good idea to do that, provided that helps you answer the research question. Otherwise not necessarily.
If you want only to compare different tests and you don't want to use them together there is no need for that.
If you want to harness the power of several diagnostic tests then it helps.
If you want to see how much more a test helps in reclassifying a group of other tests/markers, then you might use integrated discrimination improvement (IDI) and net reclassification improvement (NRI). http://www.ncbi.nlm.nih.gov/pubmed/22679181
Yes, it is a good idea. What you can also do is determine the added diagnostic value that a second test brings. You can run one logisitic model with a single test and compare the AUC value of its ROC curve to that of the second model which would include both tests. I use a program called MedCalc which allows you to run a statistical test comparing AUC values to determine if they are significantly different. You can also compare the pseudo R-squared values of the two models to see how much more variance is accounted for. I've attached one of my publications that provides an example of what I just described.
Leucata raises important points about depending on the question. The papers by Pencina and colleagues introducing the NRI and IDI are worth a read if you don't mind the statistics theory. The most recent is particularly good: Leening, M. J. G., Steyerberg, E. W., Van Calster, B., D'Agostino, R. B., Sr, & Pencina, M. J. (2014). Net reclassification improvement and integrated discrimination improvement require calibrated models: relevance from a marker and model perspective. Statistics in Medicine, 33(19), 3415–3418. doi:10.1002/sim.6133
I've attached a link to some R code for comparison of AUCs, and calculation of NRIs, IDIs, and the Risk Assessment Plot which I described in the attached publication.
Article New Metrics for Assessing Diagnostic Potential of Candidate Biomarkers
Data R function for Risk Assessment Plot & reclassification metri...