Conditional Variable Screening for Ultra-High Dimensional Longitudinal Data With Time Interactions

Abstract

In recent years, we have been able to gather large amounts of genomic data at a fast rate, creating situations where the number of variables greatly exceeds the number of observations. In these situations, most models that can handle a moderately high dimension will now become computationally infeasible or unstable. Hence, there is a need for a prescreening of variables to reduce the dimension efficiently and accurately to a more moderate scale. There has been much work to develop such screening procedures for independent outcomes. However, much less work has been done for high-dimensional longitudinal data in which the observations can no longer be assumed to be independent. In addition, it is of interest to capture possible interactions between the genomic variable and time in many of these longitudinal studies. In this work, we propose a novel conditional screening procedure that ranks variables according to the likelihood value at the maximum likelihood estimates in a marginal linear mixed model, where the genomic variable and its interaction with time are included in the model. This is to our knowledge the first conditional screening approach for clustered data. We prove that this approach enjoys the sure screening property, and assess the finite sample performance of the method through simulations.

Keywords: interactions; linear mixed models; longitudinal analysis; sure screening property; ultra‐high dimensionality; variable screening.