Adaptive lasso for the Cox regression with interval censored and possibly left truncated data

We propose a penalized variable selection method for the Cox proportional hazards model with interval censored data. It conducts a penalized nonparametric maximum likelihood estimation with an adaptive lasso penalty, which can be implemented through a penalized EM algorithm. The method is proven to enjoy the desirable oracle property. We also extend the method to left truncated and interval censored data. Our simulation studies show that the method possesses the oracle property in samples of modest sizes and outperforms available existing approaches in many of the operating characteristics. An application to a dental caries data set illustrates the method's utility.