Subgroup Analysis Of Fusion Penalty Survival Data Based On Proportional Hazard Regression Model

The application of subgroup identification in social life has widely aroused the research interest of many scholars in statistics,precision medicine and precision marketing,etc.The subgroup analysis can provide better solutions for precision medicine and precision marketing.In this paper,a partial likelihood subgroup identification method based on the right censored data for proportional risk regression model.This method can effectively identify the group members of each subgroup while determining the number of subgroups.Firstly,the classical Cox proportional risk regression model is extended to be the individual proportional risk regression model.Secondly,using local linear polynomial approximation,the penalty is approximated as quadratic form and then we get the smooth penalized partial likelihood function.Then we obtain the parameter estimate by maximizing such loss function with proper value of tunning parameter.Some of parameter estimates are fused.So the partition of group is obtained.BIC is used to select the tunning parameters.At the same time,we also propose a Newton iteration algorithm.Finally,numerical simulations and example analysis show that the subgroup analysis method proposed is effective in the case of moderate sample size and censoring rate.