Variable Selection Of CoX Model With The Heredity Constraint

In the research of biology,information and medical,we not only pay attention to the effect of main terms on the response,but also the interactions.The interaction term must satisfy the heredity constraints which means the interaction term exists only if the corresponding main term exists.This paper focuses on model selection and estimation of the Cox proportional hazards model with heredity constraints.First,We summarize the recent research on the Cox proportional hazard model.Introduce the idea of hierarchical interaction,and give a Cox model with heredity constraints.Moreover,we redefined the Cox model with heredity constraints by reparameterizing the coefficients of interactions,and use the adaptive LASSO method for variable selection and parameter estimation based on the penalized likelihood.We prove that the estimator has Oracle properties under regular conditions.Finally,numerical simulations and real data analysis verify the feasibility and practicability of the proposed method.In addition,we also simulate the performance under three different censoring rates.In this paper,the advantage of our method is that it automatically implements heredity constraints while doing variable selection,and it is more concise in algorithm implementation.