JSM 2005 - Toronto

Abstract #304781

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 102
Type: Contributed
Date/Time: Monday, August 8, 2005 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract - #304781
Title: Bayesian Hierarchical Model in Estimating Ordinal Data Nested in Categorical Data
Author(s): Xian Zhou*+ and Peter Mueller and Benjamin Neby Bekele
Companies: The University of Texas M. D. Anderson Cancer Center and The University of Texas M. D. Anderson Cancer Center and The University of Texas M. D. Anderson Cancer Center
Address: 1515 Holcombe Blvd, Houston, TX, 77584, United States
Keywords: mixture model ; Bayesian ; ordinal data ; categorical data
Abstract:

The multinomial probit (MNP) model is an alternative to the multinomial logit model for situations in which a finite number of outcomes are observed conditional on covariates. We extend the MNP model and develop a joint MNP and ordinal probit model to model the cell probabilities for multiple categorical outcomes with ordinal variables nested within each categorical outcome. We assume the latent variables associated with the ordinal data follow a mixture of normal distributions. This mixture probit model allows us to model the cell probabilities while holding the cut-point parameters fixed. Moreover, it is more flexible in estimating cell probabilities when compared to the Bayesian ordinal probit regression models introduced by Albert-Chib where the cut-point parameters are random. A hierarchical prior is imposed on the location parameters of the normal kernels in the mixture model associated with the ordinal outcomes. We apply our model to a randomized Phase III study to assess the relationship between treatments on the probability of observing toxicities of a given type and grade.

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Revised March 2005