Abstract: This study proposes a maximum penalized likelihood procedure for simultaneous estimation and variable selection in the context of Cox proportional hazards models with informative right-censored data. A copula function is adopted to model the dependence between censoring and event times. Moreover, two penalty functions are introduced to accommodate the sparsity of regression coefficients and smooth the baseline hazard estimate. Since the baseline hazard function is nonnegative, we propose a specific algorithm comprising a modified Newton algorithm for updating regression coefficients and a multiplicative iterative algorithm for updating baseline hazard at each iteration. Furthermore, we establish the asymptotic properties of the proposed estimators. Simulation studies show that the proposed method performs satisfactorily. Finally, we apply the proposed method to investigate the potential risk factors of AIDS for HIV-1-infected patients from the AIDS Clinical Trials Group Protocol 175 study.

Key words and phrases: Copulas, informative censoring, maximum penalized likelihood, variable selection.