# Using the likelihood-ratio test as a Cochran-Armitage test for trend

Maybe this is a silly question, but I need to perform a test for trend in a 2x3 contingency table and I've been said to use the Cochran-Armitage test for trend with weights (0, 1, 2). Okay, that's fine, I can do that and I understand why that is a good approach. But then, I have the following doubt: if we know, by the Neyman-Pearson lemma, that the likelihood ratio test is a uniformly most powerful test, i.e., it has the highest power among all competitors, why not just use it comparing a constrained model that reflects the (0, 1, 2) nature of the Cochran-Armitage weights against the unconstrained model?