**Fei Zhou 1, Jie Ren 1, Gengxin Li 2, Yu Jiang 3, Xiaoxi Li 1, Weiqun Wang <sup>4</sup> and Cen Wu 1,\***


Received: 7 November 2019; Accepted: 26 November 2019; Published: 3 December 2019

**Abstract:** Lipid species are critical components of eukaryotic membranes. They play key roles in many biological processes such as signal transduction, cell homeostasis, and energy storage. Investigations of lipid–environment interactions, in addition to the lipid and environment main effects, have important implications in understanding the lipid metabolism and related changes in phenotype. In this study, we developed a novel penalized variable selection method to identify important lipid–environment interactions in a longitudinal lipidomics study. An efficient Newton–Raphson based algorithm was proposed within the generalized estimating equation (GEE) framework. We conducted extensive simulation studies to demonstrate the superior performance of our method over alternatives, in terms of both identification accuracy and prediction performance. As weight control via dietary calorie restriction and exercise has been demonstrated to prevent cancer in a variety of studies, analysis of the high-dimensional lipid datasets collected using 60 mice from the skin cancer prevention study identified meaningful markers that provide fresh insight into the underlying mechanism of cancer preventive effects.

**Keywords:** GEE; lipid–environment interaction; longitudinal lipidomics study; penalized variable selection
