Extension of the EM-algorithm using PLS to fit linear mixed effects models for high dimensional repeated data

International audienceIn studies where individuals contribute more than one observations, such as longitudinal or repeated measures studies, the linear mixed model provides a framework to take correlation between these observations into account. By introducing random effects, mixed models allow to take into account the variability of the response among the different individuals and the possible within-individual correlation. In addition, recent studies have collected high-dimensional data, which involve new statistical issue as the sample size is relatively small compared to the number of covariates. To deal with high dimensional data, reduction dimension method can be used which aims at summarizing the numerous predictors in form of a small number of new components (often linear combinations of the original predictors). The traditional approach is the Principal Component Regression which is an application of Principal Component Analysis (PCA) to regression model. PCA is applied without considering of the link between the outcome and the independent variables. An alternative method is the Partial Least Square (PLS) that takes this link into account. To solve the high-dimensional issue in the repeated/longitudinal data context, we propose an approach adapted from the Expectation-Maximization (EM) algorithm for linear mixed models by incorporating a PLS step to reduce the high-dimensional data to low-dimensional features. Under this algorithm framework, we use simulation studies to investigate the performance and computational properties of this extension of EM-algorithm using PLS (EM-PLS) and compare it with other reduction dimension approaches. To illustrate the practical usefulness of the approach, we apply the EM-PLS algorithm developed in this work to fit real data sets including for instance cell-cycle gene expression data observed over several time points or brain images collected during repeated sessions