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 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.