Invariance property of the latent weibull test for comparing ordinal data

The latent Weibull model has recently been reported to be a superior testing tool for comparing two treatments with ordinal responses. Response-adaptive procedures were also developed for the design of these clinical studies. The test statistic is constructed on the basis of the latent Weibull model. Due to the need for model identification, the estimation procedure relies on the selection of one of the treatments as a reference, which is modeled by a standard Weibull distribution. However, it is unclear whether the choice of the reference affects the test procedure. The objective of this short paper is to provide a theoretical proof of this crucial invariance property, under which the test conclusion is invariant to the choice of the reference. A clinical example is also used to illustrate the invariance property.