30
Figure 2.4: Estimated mixture of normal distribution of the latent variable ι⅛∙ con-
ditioned on τi — 0 for j = 1,..., 7. Shaded curve corresponds to placebo (x = — 1)
and dashed to isotretinoin (τ = 1). Darkly and lightly shaded areas represent, re-
spectively, the probability of no toxicity (πj∙0) and toxicity at grade 1 (π7∙1) under
placebo.
2.7 Discussion
We have proposed a Bayesian hierarchical model to analyze ordinal data nested within
categories. Our model characterizes the ordinal∕categorical data structure by a varia-
tion of the ordinal probit model. We provide posterior summaries to assess treatment
effects. In the phase III clinical trial example, traditional analysis might simply group
the toxicities levels into two: no toxicity (0) and some toxicity (1+2+3+4), and then,
apply a Chi-squared test or Fisher’s exact test to compare the two treatment groups
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