Variable selection in semiparametric hazard regression for multivariate survival data

This paper is concerned with how to select significant variables in the partially linear varying-coefficient hazard model for multivariate survival data. A new variable selection procedure is proposed to simultaneously estimate the parameters and select variables for the parametric parts. Compared to the profile pseudo-partial likelihood proposed by Cai et al. (2008), the advantage of our method is to be practically feasible and easily implemented. We show that the estimators of both the parametric and nonparametric parts achieve the best convergence rates and establish their asymptotic normality. Moreover, we demonstrate that proposed procedures perform as well as an oracle procedure. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed procedures and a real dataset from the Colon Cancer Study is analyzed for illustration.