I have previously used McNemar's test to compare PCR and bacterial culture using the same sample. I now have two different samples from the same patient taken from tonsills and quincy. So I now have 4 results from 4 different tests. Does there exist a statistical test to compare all of my data? Using McNemar's test I can only compare 2 of the tests against each other.
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Cochran's Q test is a generalization of the McNemar test when outcomes are binary, as they seem to be in your case (positive/negative infection assessment by either PCR or bacterial culture).
Whether that's a wise choice in this circumstance is a separate question. That might tell you whether there are any differences but it won't provide much more information. It also would tend to ignore systematic differences between tonsil and quinsy, which are of a different nature than a simple difference between test results on the same type of sample.
I suspect that a mixed logistic regression model would be more informative. For each combination of sample type and test you would have a separate data row, having 0/1 as the test result along with annotations for sample type, test type, and an ID for the clinical case. Fixed effects would be sample type, test type, and their interaction. A random intercept for ID would account for the within-patient correlations.
