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Biostatistics Advance Access originally published online on April 18, 2008
Biostatistics 2008 9(4):750-764; doi:10.1093/biostatistics/kxn008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Estimating time-to-event from longitudinal ordinal data using random-effects Markov models: application to multiple sclerosis progression

Micha Mandel*

Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, Israel, msmic{at}mscc.huji.ac.il

Rebecca A. Betensky

Department of Biostatistics, Harvard School of Public Health, 665 Huntington Avenue, Boston, MA, USA

* To whom correspondence should be addressed.

Longitudinal ordinal data are common in many scientific studies, including those of multiple sclerosis (MS), and are frequently modeled using Markov dependency. Several authors have proposed random-effects Markov models to account for heterogeneity in the population. In this paper, we go one step further and study prediction based on random-effects Markov models. In particular, we show how to calculate the probabilities of future events and confidence intervals for those probabilities, given observed data on the ordinal outcome and a set of covariates, and how to update them over time. We discuss the usefulness of depicting these probabilities for visualization and interpretation of model results and illustrate our method using data from a phase III clinical trial that evaluated the utility of interferon beta-1a (trademark Avonex) to MS patients of type relapsing–remitting.

Keywords: Markov model; Ordinal response; Prediction; Transition model

Received July 3, 2007; revised November 16, 2007; revised January 23, 2008; accepted for publication February 15, 2008.


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M. Mandel
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