Multiple comparisons of treatments with skewed ordinal responses

In clinical studies, treatment responses are frequently measured with an ordinal scale. To compare the efficacy of these treatments, one could employ either the proportional odds model or the latent normal model. However, these two models are inadequate for comparing treatments with highly skewed ordinal responses, due to the possibility of yielding an inflated type I error rate. To overcome this problem, the latent Weibull model has been suggested for investigating the efficacy difference between two treatments. For more general applications, this model is extended to include clinical trials with more than two treatments. Two testing procedures are derived: one for multiple comparisons with a control and the other for pairwise treatment comparisons. The testing procedures are also demonstrated with two clinical examples.