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For complex diseases, the interactions between genetic and environmental riskfactors can have important implications beyond the main effects. Many of theexisting interaction analyses conduct marginal analysis and cannot accommodatethe joint effects of multiple main effects and interactions. In this study, weconduct joint analysis which can simultaneously accommodate a large number ofeffects. Significantly different from the existing studies, we adopt lossfunctions 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 weightedapproach. Penalization is used for identification and regularized estimation.Computationally, we develop an effective algorithm which combines themajorize-minimization and coordinate descent. Simulation shows that theproposed approach has satisfactory performance. We also analyze lung cancerprognosis data with gene expression measurements.

Identifying Gene-Environment Interactions with A Least Relative Error Approach