Bayesian Test of Homogeneity in Transition Model for Longitudinal Ordinal Response Data with Missing Values

M Ganjali,S Noorian

doi:10.2991/jsta.2013.12.2.6

Abstract

For analyzing longitudinal ordinal response data, many methods are available to take into account the correlations between responses of the same individual where different methods use different approaches. One of the methods to consider this correlation is the transition (Markov) model. In this paper, we present a Bayesian test of homogeneity of a transition model for analyzing longitudinal ordinal response data. In other words we test whether the transition probabilities πmabt’s, which are probabilities of moving to state b from state a of mth individual at time t, are the same for any given time t, i.e., πmabt = πmab . A cumulative logistic regression model and the Bayesian method, using MCMC, are implemented for testing the null hypothesis of homogeneity. We also define what a specific homogeneous covariate is. Our approach is applied on three-period longitudinal Fluvoxamine (a treatment for deregulation of serotonin in brain) data.

Highlights

In many areas of medical research, longitudinal ordinal response data are often collected where the response of interest for each individual is recorded on an ordinal scale and is observed on several regular or irregular time points
In this paper we propose a Bayesian test of homogeneity of transition probabilities in longitudinal ordinal response data with random dropout
In other words, If we have an ordinal variable with J levels, the form of the transition model for T response variables, is: K

Summary

Introduction

In many areas of medical research, longitudinal ordinal response data are often collected where the response of interest for each individual is recorded on an ordinal scale and is observed on several regular or irregular time points. Since in longitudinal study there is a sequence of responses measured for the same individual, we should take into account the correlation between these responses For handling such correlation between responses, some approach are proposed such as marginal modelling, random effects modelling and transition (Markov) modelling. 1984; Verbeke and Lesaffre, 1996; Tutz and Hennevogl, 1996; Verbeke and Molenberghs, 1997; Diggle et al, 2002; Tutz, 2005) Both of these approaches are generally appropriate for long sequences of measurements. Using the terminology of Diggle and Kenward (1994), the dropout mechanism is called completely random dropout if the probability of dropping out is independent of both responses (observed and unobserved). In this paper we propose a Bayesian test of homogeneity of transition probabilities in longitudinal ordinal response data with random dropout.

Fluvoxamine Data Study and Transition Model

Fluvoxamine Data

Transition Models

Bayesian Analysis

Findings

Conclusion