In two-armed randomized clinical trials (RCTs) designed to compare a new treatment with a control, a key endpoint is often measured and analyzed both at baseline and after treatment for two groups. More powerful and precise statistical inferences are possible once the between-group comparisons have been adjusted for covariates. In this thesis we propose a new method for ordered categorical outcomes which adjusts for baseline without relying on any specific assumptions on the data generating process. Based on baseline and post-treatment values, data are composed of counts of patients who have improved from one category to another, stayed the same or deteriorated. Not all patterns are comparable. Hence, the ordering is only partial. We develop an approach to test the treatment effects based on comparing each observation in one group to each observation in the other group to which it is comparable. The power comparisons of this test with four common approaches are conducted in our simulation study.