Random forests are one of the state-of-the-art supervised machine learning methods and achieve good performance in high-dimensional settings where p, the number of predictors, is much larger than n, the number of observations. Repeated measurements provide, in general, additional information, hence they are worth accounted especially when analyzing high-dimensional data. Tree-based methods have already been adapted to clustered and longitudinal data by using a semi-parametric mixed effects model, in which the non-parametric part is estimated using regression trees or random forests. We propose a general approach of random forests for high-dimensional longitudinal data. It includes a flexible stochastic model which allows the covariance structure to vary over time. Furthermore, we introduce a new method which takes intra-individual covariance into consideration to build random forests. Through simulation experiments, we then study the behavior of different estimation methods, especially in the context of high-dimensional data. Finally, the proposed method has been applied to an HIV vaccine trial including 17 HIV-infected patients with 10 repeated measurements of 20,000 gene transcripts and blood concentration of human immunodeficiency virus RNA. 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.
Asymptotic for Lasso Estimator in High-Dimensional Repeated Measurements Model
