The smooth integration of counting and absolute deviation （SICA） penalized variable selection procedure for high-dimensional linear regression models is proposed by Lv and Fan （2009）. In this article, we extend their idea to Cox＇s proportional hazards （PH） model by using a penalized log partial likelihood with the SICA penalty. The number of the regression coefficients is allowed to grow with the sample size. Based on an approximation to the inverse of the Hessian matrix, the proposed method can be easily carried out with the smoothing quasi-Newton （SQN） algorithm. Under appropriate sparsity conditions, we show that the resulting estimator of the regression coefficients possesses the oracle property. We perform an extensive simulation study to compare our approach with other methods and illustrate it on a well known PBC data for predicting survival from risk factors.
Case-cohort design usually requires the disease rate to be low in large cohort study,although it has been extensively used in practice.However,the disease with high rate is frequently observed in many clinical studies.Under such circumstances,it is desirable to consider a generalized case-cohort design,where only a fraction of cases are sampled.In this article,we propose the inference procedure for the additive hazards regression under the generalized case-cohort sampling.Asymptotic properties of the proposed estimators for the regression coefcients are established.To demonstrate the efectiveness of the generalized case-cohort sampling,we compare it with simple random sampling in terms of asymptotic relative efciency.Furthermore,we derive the optimal allocation of the subsamples for the proposed design.The fnite sample performance of the proposed method is evaluated through simulation studies.
Multivariate failure time data are frequently encountered in biomedical research.In this article,we model marginal hazards with accelerated hazards model to analyze multivariate failure time data.Estimating equations are derived analogous to generalized estimating equation method.Under certain regular conditions,the resultant estimators for the regression parameters are shown to be asymptotically normal.Furthermore,we also establish the weak convergence of estimators for the baseline cumulative hazard functions.
