Integrative sparse partial least squares.

Partial least squares, as a dimension reduction technique, has become increasingly important for its ability to deal with problems with a large number of variables. Since noisy variables may weaken estimation performance, the sparse partial least squares (SPLS) technique has been proposed to identify important variables and generate more interpretable results. However, the small sample size of a single dataset limits the performance of conventional methods. An effective solution comes from gathering information from multiple comparable studies. Integrative analysis has essential importance in multidatasets analysis. The main idea is to improve performance by assembling raw data from multiple independent datasets and analyzing them jointly. In this article, we develop an integrative SPLS (iSPLS) method using penalization based on the SPLS technique. The proposed approach consists of two penalties. The first penalty conducts variable selection under the context of integrative analysis. The second penalty, a contrasted penalty, is imposed to encourage the similarity of estimates across datasets and generate more sensible and accurate results. Computational algorithms are developed. Simulation experiments are conducted to compare iSPLS with alternative approaches. The practical utility of iSPLS is shown in the analysis of two TCGA gene expression data.