  Model-based recursive partitioning (MOB) is a semi-parametric statistical
approach allowing the identification of subgroups that can be combined with a
broad range of outcome measures including continuous time-to-event outcomes.
When time is measured on a discrete scale, methods and models need to account
for this discreetness as otherwise subgroups might be spurious and effects
biased. The test underlying the splitting criterion of MOB, the M-fluctuation
test, assumes independent observations. However, for fitting discrete
time-to-event models the data matrix has to be modified resulting in an
augmented data matrix violating the independence assumption. We propose MOB for
discrete Survival data (MOB-dS) which controls the type I error rate of the
test used for data splitting and therefore the rate of identifying subgroups
although none is present. MOB-ds uses a permutation approach accounting for
dependencies in the augmented time-to-event data to obtain the distribution
under the null hypothesis of no subgroups being present. Through simulations we
investigate the type I error rate of the new MOB-dS and the standard MOB for
different patterns of survival curves and event rates. We find that the type I
error rates of the test is well controlled for MOB-dS, but observe some
considerable inflations of the error rate for MOB. To illustrate the proposed
methods, MOB-dS is applied to data on unemployment duration.
