  The problem of dynamic prediction with time-dependent covariates, given by
biomarkers, repeatedly measured over time, has received much attention over the
last decades. Two contrasting approaches have become in widespread use. The
first is joint modelling, which attempts to jointly model the longitudinal
markers and the event time. The second is landmarking, a more pragmatic
approach that avoids modelling the marker process. Landmarking has been shown
to be less efficient than correctly specified joint models in simulation
studies, when data are generated from the joint model. When the mean model is
misspecified, however, simulation has shown that joint models may be inferior
to landmarking.
  The objective of this paper is to develop methods that improve the predictive
accuracy of landmarking, while retaining its relative simplicity and
robustness. We start by fitting a working longitudinal model for the biomarker,
including a temporal correlation structure. Based on that model, we derive a
predictable time-dependent process representing the expected value of the
biomarker after the landmark time, and we fit a time-dependent Cox model based
on the predictable time-dependent covariate. Dynamic predictions based on this
approach for new patients can be obtained by first deriving the expected values
of the biomarker, given the measured values before the landmark time point, and
then calculating the predicted probabilities based on the time-dependent Cox
model.
  We illustrate the approach in predicting overall survival in liver cirrhosis
patients based on prothrombin index.
