Multiple comparisons with a control for a latent variable model with ordered categorical responses

Ordered categorical data are frequently encountered in clinical studies. A popular method for comparing the efficacy of treatments is to use logistic regression with the proportional odds assumption. The test statistic is based on the Wilcoxon–Mann–Whitney test. However, the proportional odds assumption may not be appropriate. In such cases, the probability of rejecting the null hypothesis is much inflated even though the treatments have the same mean efficacy. An alternative approach that does not rely on the proportional odds assumption is to conceptualize the responses as manifestations of some underlying continuous variables. However, statistical procedures were developed only for the comparison of two treatments. In this article, we derive testing procedures that compare several treatments to a control, utilizing a latent normal distribution with the latent variable model. The proposed procedure is useful because multiple comparisons with a control is very frequently an objective of a clinical study. Data from clinical trials are used to illustrate the proposed procedures.