A Transition Model for Analysis of Repeated Measure Ordinal Response Data to Identify the Effects of Different Treatment
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M. Ganjali Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran, Iran Z. Rezaee Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran, Iran
Key Words Longitudinal ordinal response data; Cumulative logit model; Transition model; Pseudo-R2; Insomnia Correspondence Address M. Ganjali Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran, Iran (e-mail: [email protected])
A Transition Model for Analysis of Repeated Measure Ordinal Response Data to Identify the Effects of Different Treatments
INTRODUCTION Many studies observe the response of interest for each subject repeatedly, at several times or under various conditions. In health-related applications (eg, in longitudinal studies), repeated ordinal response data commonly occur. For example, a physician might evaluate patients at baseline and at weekly intervals regarding whether a new drug treatment is successful. In some cases, explanatory variables may vary also over time. Because in these studies there is a sequence of ordinal responses for the same individual, we have to consider not only the fact that responses are ordinal in nature but also the possibility of correlations between responses given by the same individual. Different models can be used to handle such correlations. Agresti (1) and Lall et al. (2) conducted a comprehensive survey of models for ordered categorical data in which the need for model interpretation in medical science applications was emphasized. One possibility is marginal modeling, which can be used to make inferences about parameters averaged over the whole population (3–5). A second possibility is random effects modeling, which makes inferences about variability between respondents (6–10). However, both of these procedures are generally appropriate for longer sequences of measurements than those examined
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A first-order transition model is used to analyze repeated measurement or longitudinal ordinal response data to compare several treatments for which measurements for each subject occur both at baseline and at follow-up. The likelihood function is partitioned to make possible the use of existing software for estimating model parameters. Data from a clinical trial illustrate the application of the transition model. Nagelkerke’s pseudo-R2 is used for the goodness of fit of the model.
in this article. For the data considered here, the primary question of interest is the degree of change, or improvement, among treatments or how transitions are made between consecutive time points. For such a scientific question, a more appropriate approach would be to use Markov (transition) models (see Ref. 11 for using multinomial logit for nominal responses and Ref. 12 for a log-linear approach). For reviews of transition and other models for ordinal longitudinal responses, see the work of McCullagh (13), Diggle et al. (14), and Agresti (15). In this article, we use a first-order transition model for repe
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