I understand how to evaluate therapeutic studies: basically you compare the results of two groups that were chosen randomly. One group gets the new drug, the other group gets the placebo (or the drug against which the new drug should be tested). Neither the physicians nor the patients know in which group they are (double-blind testing). You can clearly see the results and test the statistical significance (e.g. with a t-test, depending on the study design).
I have a problem understanding diagnostic studies. My problem lies in the fact that you do not know "the truth", i.e. whether a patient really has the condition which should be diagnosed. Therefore you use the so-called "gold standard", i.e. the best diagnostic method so far. There is no problem when the new diagnostic method is worse than the gold standard. Yet I think there might be a problem when the new diagnostic method is better than the gold standard! Why? Because the results will be different which would be interpreted as inferior.
Let me give you an example: Let's assume that a patient really has some form of cancer, yet the gold standard is not able to detect it. The new method is able to detect it and therefore both tests disagree. Because the gold standard is taken as the reference the new method would get a minus point here... although it was right in the first place!
Is my thinking correct? If yes, how do handle this problem in practice? Is there a common term for this kind of problem? If no, where lies my misunderstanding?
Perhaps another (more extreme) example is in order: Let's say the gold standard has an accuracy of 50%, i.e. the toss of a coin. If you had a new method with an accuracy of 100% (so the results of this method and "the truth" are the same) and tested it against the gold standard this new method would get an accuracy of only 50% (i.e. the accuracy of the gold standard against "the truth").