Help with diagnostic test analysis


I’m doing a project with a physician in a hospital and I am hoping to run some statistics on a data set I have, and I’m realizing now how little I know about statistics (it made more sense to me when I was planning the project). I don't know if this is the right place to ask this or not, but if anyone has some tips to tell me if I’m doing this right or not, that would be awesome.

Basically I have a data set with about 5000 patients who were each given two different diagnostic tests, each for the same disease. I also have the sensitivity and specificity of each test for the disease. So what I want to do is use statistics to compare the concordance between the two tests in patients (i.e. the proportion of patients with the disease who were either positive for both tests, or negative for both tests), vs. what I would expect it to be by multiplying the sensitivities (sensitivity 1 x sensitivity 2 is the proportion that should be positive for both, if I’m doing it right, and (1-sensitivity 1)(1-sensitivity 2) is the proportion that should be negative for both).

I calculated that 52% would be expected to be concordant, but 79% actually were. So what I have been doing is going in to STATA, clicking one sample proportion test calculator, entering 5000 for sample size, 0.79 for sample proportion, and 0.52 for expected proportion, and it gives me p=0.0000. I expected it to be significant, so I’m not surprised, but I just want to make sure I’m actually doing the statistics right (I have no experience with this, besides a stats course I took some time ago). Any help would be awesome.