Variable selection for multivariate failure time data
1 Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A. cai{at}bios.unc.edu, 2 Department of Operation Research and Financial Engineering, Princeton University, New Jersey 08544, U.S.A. jqfan{at}princeton.edu, 3 Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania 16802-2111, U.S.A. rli{at}stat.psu.edu, 4 Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A. zhou{at}bios.unc.edu
In this paper, we propose a penalised pseudo-partial likelihood method for variable selection with multivariate failure time data with a growing number of regression coefficients. Under certain regularity conditions, we show the consistency and asymptotic normality of the penalised likelihood estimators. We further demonstrate that, for certain penalty functions with proper choices of regularisation parameters, the resulting estimator can correctly identify the true model, as if it were known in advance. Based on a simple approximation of the penalty function, the proposed method can be easily carried out with the Newton–Raphson algorithm. We conduct extensive Monte Carlo simulation studies to assess the finite sample performance of the proposed procedures. We illustrate the proposed method by analysing a dataset from the Framingham Heart Study.
Key Words: Cox's model; Marginal hazards model; Penalised likelihood; Smoothly clipped absolute deviation; Variable selection
Received March 2004. Revised October 2004.
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