Adaptive LASSO for general transformation models with right censored data

In this paper, we consider variable selection for general transformation models with right censored data and propose a unified procedure for both variable selection and estimation. We conduct the proposed procedure by maximizing penalized log-marginal likelihood function with Adaptive LASSO penalty (ALASSO) on regression coefficients. Two main advantages of this procedure are as follows: (i) the penalties can be assigned to regression coefficients adaptively by data according to the importance of corresponding covariates; (ii) it is free of baseline survival function and censoring distribution. Under some regular conditions, we show that the penalized estimates with ALASSO are n-consistent and enjoy oracle properties. Some simulation examples and Primary Biliary Cirrhosis Data application illustrate that our proposed procedure works very well for moderate sample size.