Since your response is binary (positive vs negative), PROC MIXED is definitely not what you want to use since it expects a normal response. Cochran's Q tests that the marginal probabilities (probability of positive in each sample) are equal, but since you seem to really be after assessing conditional probabilities (such as probability of positive in sample 4 given result in sample3), I don't think it is what you want either. One thing you could consider are transition models as described in this note.
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