  Longitudinal and high-dimensional measurements have become increasingly
common in biomedical research. However, methods to predict survival outcomes
using covariates that are both longitudinal and high-dimensional are currently
missing. In this article, we propose penalized regression calibration (PRC), a
method that can be employed to predict survival in such situations. PRC
comprises three modeling steps: First, the trajectories described by the
longitudinal predictors are flexibly modeled through the specification of
multivariate mixed effects models. Second, subject-specific summaries of the
longitudinal trajectories are derived from the fitted mixed models. Third, the
time to event outcome is predicted using the subject-specific summaries as
covariates in a penalized Cox model. To ensure a proper internal validation of
the fitted PRC models, we furthermore develop a cluster bootstrap optimism
correction procedure that allows to correct for the optimistic bias of apparent
measures of predictiveness. PRC and the CBOCP are implemented in the R package
pencal, available from CRAN. After studying the behavior of PRC via
simulations, we conclude by illustrating an application of PRC to data from an
observational study that involved patients affected by Duchenne muscular
dystrophy, where the goal is predict time to loss of ambulation using
longitudinal blood biomarkers.
