Promoting sign consistency in the cure model estimation and selection

In survival analysis, when a subset of subjects has extremely long survival, the two-part cure rate model has been commonly adopted. In the two-part model, the first part is for a binary response and describes the probability of cure. The second part is for a survival response and describes the probability of survival. Despite their intuitive interconnections, most of the existing works estimate the two parts without any constraint. The existing works on proportionality promote similarity in magnitudes (i.e. quantitative similarity) and can be too restrictive. In this study, for the two-part cure rate model, we propose imposing a sign-based penalty to promote similarity in signs (i.e. qualitative similarity). The proposed strategy can be more informative than those that neglect the two-part interconnections and be less restrictive than the existing proportionality works. Penalty is also imposed to select relevant variables and accommodate high-dimensional data. Numerical studies, including simulation and two data analyses, demonstrate the advantageous performance of the proposed approach.