Analysis of the time to sustained progression in Multiple Sclerosis using generalised linear and additive models

The course of multiple sclerosis (MS) is generally difficult to
predict. This is due to the great inter-individual variability with
respect to symptoms and disability status. An important prognostic
endpoint for MS is the expected time to sustained disease
progression. Using the Expanded Disability Status Scale (EDSS) this
endpoint is here defined as a rise of 1.0 or 0.5 compared to
baseline EDSS (5.5) which is confirmed for at least
six months. The goal of this paper was threefold. It aimed at
identifying covariates which significantly influence sustained
progression, determining size and form of the effect of these
covariates and estimating the survival curves for given predictors.
To this end a piecewise exponential model utilizing piecewise
constant hazard rates and a Poisson model were devised. In order to
improve and simplify these models a method for piecewise linear
parameterization of non-parametric generalized additive models
(GAMs) was applied. The models included fixed and random effects,
the posterior distribution was estimated using Markov Chain Monte
Carlo methods (MCMC) as well as a penalized likelihood approach and
variables were selected using Akaikes information criterium (AIC).
The models were applied to data of placebo patients from worldwide
clinical trials that are pooled in the database of the Sylvia Lawry
Centre for Multiple Sclerosis Research (SLCMSR). Only with a pure
exponential model and fixed effects, baseline EDSS and the number
of relapses in the last 12 month before study entry had an effect
on the hazard rate. For the piecewise exponential model with random
study effects there was no effect of covariates on the hazard rate
other than a slightly decreasing effect of time. This reflects the
fact that unstable patients reach the event early and are therefore
eliminated from the analysis (selection effect).