  Random forests is a state-of-the-art supervised machine learning method which
behaves well in high-dimensional settings although some limitations may happen
when $p$, the number of predictors, is much larger than the number of
observations $n$. Repeated measurements can help by offering additional
information but no approach has been proposed for high-dimensional longitudinal
data. Random forests have been adapted to standard (i.e., $n > p$) longitudinal
data by using a semi-parametric mixed-effects model, in which the
non-parametric part is estimated using random forests. We first propose a
stochastic extension of the model which allows the covariance structure to vary
over time. Furthermore, we develop a new method which takes intra-individual
covariance into consideration to build the forest. Simulations reveal the
superiority of our approach compared to existing ones. The method has been
applied to an HIV vaccine trial including 17 HIV infected patients with 10
repeated measurements of 20000 gene transcripts and the blood concentration of
human immunodeficiency virus RNA at the time of antiretroviral interruption.
The approach selected 21 gene transcripts for which the association with HIV
viral load was fully relevant and consistent with results observed during
primary infection.
