On least-squares regression with censored data
1 Department of Biostatistics, Columbia University, New York, New York 10032, U.S.A. zjin{at}biostat.cpmc.columbia.edu, 2 Department of Biostatistics, CB 7420, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A. lin{at}bios.unc.edu, 3 Department of Statistics, Columbia University, New York, New York 10027, U.S.A. zying{at}stat.columbia.edu
The semiparametric accelerated failure time model relates the logarithm of the failure time linearly to the covariates while leaving the error distribution unspecified. The present paper describes simple and reliable inference procedures based on the least-squares principle for this model with right-censored data. The proposed estimator of the vector-valued regression parameter is an iterative solution to the Buckley–James estimating equation with a preliminary consistent estimator as the starting value. The estimator is shown to be consistent and asymptotically normal. A novel resampling procedure is developed for the estimation of the limiting covariance matrix. Extensions to marginal models for multivariate failure time data are considered. The performance of the new inference procedures is assessed through simulation studies. Illustrations with medical studies are provided.
Key Words: Accelerated failure time model; Buckley-James estimator; Gehan statistic; Linear model; Linear programming; Rank estimator; Resampling; Semiparametric model; Survival data; Variance estimation
Received July 2004. Revised July 2005.
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