Which test should be used to estimate a p-value for trend when the outcome (dependent) variable is multinomial (with multiple unordered categories like race) and the independent variable is an ordered categorical variable say BMI with 3 categories (say <30 kg/m2, 30-40, >=40). And, how do you implement it in SAS and/or R. Any example code/reference would be helpful.

I believe we can use the Jonckheere–Terpstra trend test for continuous variables and Cochran–Armitage trend test for binary variables. But, I am not sure what the appropriate test is when it comes to multinomial variables.