Estimating Time to Event From Longitudinal Categorical Data: An Analysis of Multiple Sclerosis Progression.
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 of one point of EDSS (relative progression). Survival methods for time to progression are not adequate for such data since 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 of EDSS of at least one point, and time to two consecutive visits with EDSS greater than three 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 MS center in Boston, MA. We apply our approach to progression defined by time to two consecutive visits with EDSS greater than three, and calculate crude (without covariates) and covariate-specific curves.
Mandel
Micha
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Micha Mandel is a postdoctoral fellow, Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115 ( mmandel@hsph.harvard.edu ). Susan A. Gauthier is an 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 the Director of the Center for Neurological Imaging at Brigham and Women's Hospital and an Assistant Professor in Radiology at Harvard Medical School, Boston, MA 02115. Howard L. Weiner is the Director of the Partners Multiple Sclerosis Center and a co-director of the Center for Neurological Diseases at the Brigham and Womens Hospital, and the Robert L. Kroc Professor of Neurology, Harvard Medical School, Boston, MA 02115. Rebecca A. Betensky is an associate professor, Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115.
Gauthier
Susan A
SA
Guttmann
Charles R G
CR
Weiner
Howard L
HL
Betensky
Rebecca A
RA