Hello, I was wondering if I could get some help. Lets say you have a group of patients who are positive for a disease based on the gold standard diagnosis (i.e. blood culture, biopsy, etc) or in other words a group of True Positives. Now you want to take these patients and for each one, look back at the screening test to see if it was positive or negative. Not only do you want to know if it was positive or negative, but you want to know the likelihood that it would be positive or that you would have a positive screen in a known diseased cohort of patients. Its a little tricky because you can only calculate true positives and false negatives. Lets also say that you are trying to compare two new screening tests and wanted to compare the old screening test and the new screening test against the cohort of known diseased patients. So in summary, here are my questions.
1. What is the best test or method to look back at the likelihood that a group of diseased patients (true positives) will have a positive screen? And how would you determine if this likelihood is good or bad?
2. Assume you would just repeat the calculation for Question #1 for a second type of screening test, how would you compare the two screening tests?