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Chapter 2

Assessing Toxicities in a Clinical

TTrial: Bayesian Inference for

Multivariate Ordinal Data

2.1 Overview

We address modeling and inference for data that include ordinal outcomes nested
within categories. The data format can alternatively be seen as multivariate ordinal
data with each dimension of the multivariate outcome corresponding to one level of a
categorical variable. The motivating application is to model adverse event (toxicity)
data in clinical trials. Toxicity type and severity are usually recorded as categorical
and ordinal outcome, respectively. In a randomized phase III study, in addition to the
efficacy of the study agent, investigators and regulators are also interested in learning
about the toxicity profile of the study agent. Traditionally, simple descriptive statis-
tics such as cross-tabulations have been provided. However, this purely descriptive
approach fails to offer an in-depth understanding of how the treatment affects both
the toxicity type and the severity associated with a specific type of toxicity.

The multinomial probit (MNP) model (Aitchison and Bennett, 1970) and the

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