The identification of predictive biomarkers from a large amount of biomarkers has attracted a lot of attention in clinical trials. It is crucial to yield an intepretable sparse model by enforcing the hierarchy structure between the prognostic and predictive effects such that a nonzero predictive effect must induce its ancestor prognostic effects being nonzero in the model. In this article, we propose an integrative algorithm by integrating the majorization-minimization (MM) and the alternating direction method of multipliers (ADMM) to solve a regularized objective function with an overlapped group penalty function, for the sake of enforcing the aforementioned hierarchy structure between prognostic and predictive effects. Our proposed method can deal with different types of response variable including continuous, categorical, and survival data. The simulation study and real data analysis prove that our algorithm is consistent and more powerful for discovering the true predictive effects.