Estimating Regression Parameters in Linear Regression Model with a Censored Response Variable
In this work we study the effect of several covariates X on a censored response variable T with unknown probability distribution. In this context, most of the studies in the literature can be located in two possible general classes of regression models: models that study the effect the covariates have on the hazard function; and models that study the effect the covariates have on the censored response variable. Proposals in this paper are in the second class of models and, more specifically, on least squares based model approach. Thus, using the bootstrap estimate of the bias, we try to improve the estimation of the regression parameters by reducing their bias, for small sample sizes. Simulation results presented in the paper show that, for reasonable sample sizes and censoring levels, the bias is always smaller for the new proposals.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081765Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1186
 D.R. Cox, Regression models and life-tables, J. R. Stat. Soc. Ser. B. 34, 1972, pp. 187-220.
 J.F. Lawless, Statistical Models and Methods for Lifetime Data, John Wiley and Sons, New York, 1982.
 D.R. Cox, Partial likelihood, Biometrika. 62, 1975, pp. 269-276.
 A.A. Tsiatis, Estimating regression parameters using linear rank tests for censored data, Ann. Statist. 18, 1990, pp. 354-372.
 T.L. Lai, and Z. Ying, Linear rank statistics in regression analysis with censored or truncated data, J. Multivariate Anal. 40, 1992, pp. 13-45.
 Z. Jin, D. Lin, L.J. Wei, and Z. Ying, Rank-based inference for the accelerated failure time model, Biometrika 90, 2003, pp. 341-353.
 R.G. Miller, Least squares regression with censored data, Biometrika 63, 1976, pp. 449-464.
 J.J. Buckley, and I.R. James, Linear regression with censored data, Biometrika 66, 1979, pp. 429-436.
 W. Stute, Consistent estimation under random censorship when covariables are present, J. Multivariate Anal. 45, 1993, pp. 89-103.
 J. Orbe, E. Ferreira, and V. N'u╦£nez-Ant'on, Censored partial regression, Biostatistics 4, 2003, pp. 109-121.
 W. Stute, Nonlinear censored regression, Statist. Sinica 9, 1999, pp. 1089-1102.
 E.L. Kaplan, and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53, 1958, pp. 457-481.
 W. Stute, Distributional convergence under random censorship when covariables are present, Scand. J. Stat. 23, 1996, pp. 461-471.
 R.D. Gill, Censoring and Stochastics Integrals. Math. Centre Tracts 124. Amsterdam: Math. Centrum, 1980.
 D. Mauro, A combinatoric approach to the Kaplan-Meier estimator, Ann. Statist. 13, 1985, pp. 142-149.
 W. Stute, The bias of Kaplan-Meier integrals, Scand. J. Stat. 21, 1994, pp. 475-484.
 B. Efron, and R.J. Tibshirani, An Introduction to the Bootstrap, Chapman and Hall, New York, 1993.