A Two-Stage Estimation Of Multiple-Response Accelerated Failure Time Model With Right-Censored Data

Survival analysis has a wide range of applications.The accelerated failure time(AFT)model is a commonly used survival model with strong interpretability.With the development of the information age,the number of covariates has increased significantly,and more and more survival data are high-dimensional.Additionally,an individual can experience several different events.Modeling multiple event times jointly is helpful to recover their underlying dependency.However,the problem about multiple event times and high-dimensional covariates is rarely discussed in the existing literature.In order to study the above problem,this article proposes a multiple-response AFT model that extends the AFT model to the multiple events case.It is assumed that the covariates are high-dimensional and the regression coefficient matrix is jointly lowrank and sparse,and all the multivariate event times are subject to right-censoring by a common censoring variable.Based on a unified estimation strategy for censored data,a two-stage procedure is proposed to estimate the coefficient matrix.The first step,weight the data with IPCW weights to obtain a sparse reduced-rank regression problem for censored data,which is equivalent to the one for full data in terms of the expected loss.The second step,use SESS algorithm to solve the new sparse reduced-rank regression problem for censored data to get the final estimator.The numerical simulation results in this article show the proposed method is far superior to other methods in estimation,prediction and variable selection in various settings.Especially when the dimension of covariates is low,the performance of the proposed method in the censored case is very close to that of SESS algorithm in the ideal uncensored case,which shows the proposed method can effectively recover most of the information lost due to censoring.The two-stage method is also applied to a real dataset of bone marrow transplant patients to predict the event times of the patients.On the test set,the predicting results of the proposed method are closer to the real values than baseline method,which further verifies the effectiveness of the method.