  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.
