Identifying Gene-Environment Interactions with A Least Relative Error Approach

TL;DR

This paper introduces a novel joint analysis method for gene-environment interactions using a least relative error approach, effectively handling multiple effects and censored data, with promising simulation and real data results.

Contribution

It proposes a new relative error-based loss function for joint gene-environment interaction analysis, accommodating multiple effects and censored responses, with an efficient algorithm for estimation.

Findings

The method performs well in simulations.

It successfully analyzes lung cancer prognosis data.

The approach offers an alternative to classic least squares methods.

Abstract

For complex diseases, the interactions between genetic and environmental risk factors can have important implications beyond the main effects. Many of the existing interaction analyses conduct marginal analysis and cannot accommodate the joint effects of multiple main effects and interactions. In this study, we conduct joint analysis which can simultaneously accommodate a large number of effects. Significantly different from the existing studies, we adopt loss functions based on relative errors, which offer a useful alternative to the "classic" methods such as the least squares and least absolute deviation. Further to accommodate censoring in the response variable, we adopt a weighted approach. Penalization is used for identification and regularized estimation. Computationally, we develop an effective algorithm which combines the majorize-minimization and coordinate descent. Simulation shows that the proposed approach has satisfactory performance. We also analyze lung cancer prognosis data with gene expression measurements.