SUPER: a tuning-free procedure for subgroup analysis

Music City Center 

Subgroup analysis has gained considerable attention as heterogeneity becomes increasingly common in many contemporary applications. Without any prior information, current popular methods for subgroup identification typically rely on pairwise fusion penalized mechanisms for shrinkage estimation in clustering. However, these methods require the tuning of an optimal regularization parameter from a broad range of potential values, resulting in significant computational costs associated with certain information criteria. In this paper, we propose a new methodology called scaled fusion penalized regression (SUPER) which evaluates the noise level in the fusion penalized regression and incorporates it into the determination of penalty level in an automatic way, thus enjoying the tuning-free property and facilitating further statistical inferences. An algorithm of alternative direction method of multipliers (ADMM) is then developed to implement the proposed method. We also establish the consistency and asymptotic normality for the proposed estimator. Both computational and theoretical advantages of SUPER are demonstrated by simulation studies and a real data analysis.

Subgroup analysis

Heterogeneity

Scale-invariance

Tuning free

Penalized fusion

Statistical inference 

Section on Statistical Computing