Estimating time to event from longitudinal categorical data: An analysis of multiple sclerosis progression

Micha Mandel*, Susan A. Gauthier, Charles R.G. Guttmann, Howard L. Weiner, Rebecca A. Betensky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

The expanded disability status scale (EDSS) is an ordinal score that measures progression in multiple sclerosis (MS). Progression is defined as reaching EDSS of a certain level (absolute progression) or increasing EDSS by one point (relative progression). Survival methods for time to progression are not adequate for such data because they do not exploit the EDSS level at the end of follow-up. Instead, we suggest a Markov transitional model applicable for repeated categorical or ordinal data. This approach enables derivation of covariate-specific survival curves, obtained after estimation of the regression coefficients and manipulations of the resulting transition matrix. Large-sample theory and resampling methods are employed to derive pointwise confidence intervals, which perform well in simulation. Methods for generating survival curves for time to EDSS of a certain level, time to increase EDSS by at least one point, and time to two consecutive visits with EDSS greater than 3 are described explicitly. The regression models described are easily implemented using standard software packages. Survival curves are obtained from the regression results using packages that support simple matrix calculation. We present and demonstrate our method on data collected at the Partners Multiple Sclerosis Center in Boston. We apply our approach to progression defined by time to two consecutive visits with EDSS greater than 3 and calculate crude (without covariates) and covariate-specific curves.

Original languageAmerican English
Pages (from-to)1254-1266
Number of pages13
JournalJournal of the American Statistical Association
Volume102
Issue number480
DOIs
StatePublished - Dec 2007

Bibliographical note

Funding Information:
Micha Mandel is Lecturer, Department of Statistics, Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel (E-mail: msmic@huji.ac.il). Susan A. Gauthier is Associate Neurologist, Partners Multiple Sclerosis Center, Brigham and Women’s Hospital, and Instructor of Neurology, Harvard Medical School, Boston, MA 02115. Charles R. G. Guttmann is Director of the Center for Neurological Imaging, Brigham and Women’s Hospital, and Assistant Professor in Radiology, Harvard Medical School, Boston, MA 02115. Howard L. Weiner is Director of the Partners Multiple Sclerosis Center and a co-director of the Center for Neurological Diseases, Brigham and Women’s Hospital, and Robert L. Kroc Professor of Neurology, Harvard Medical School, Boston, MA 02115. Rebecca A. Betensky is Professor, Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115. This research was supported in part by NIH CA075971, the Harvard Center for Neurodegeneration and Repair (HCNR), the Nancy Davis Center Without Walls, and the Partners Multiple Sclerosis Center. The authors thank Brent Coull, the editor, the associate editor, and three anonymous referees for helpful comments and suggestions.

Keywords

  • Markov model
  • Multistate model
  • Ordinal response
  • Pointwise confidence interval
  • Survival curve
  • Time series
  • Transition model

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