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Weighted least squares method for the accelerated failure time model with auxiliary covariates. (English) Zbl 1420.62424

Summary: This paper deals with the analysis of accelerated failure time model when the primary covariate is subject to missing. We assume that the true covariate is measured precisely on a randomly chosen validation set, whereas auxiliary information for primary covariate is available to all study subjects. The asymptotic properties for the proposed estimator are developed and the simulation studies show that the efficiency gain is remarkable compared to the method using only the validation sample. A real example is also provided as an illustration.

MSC:

62N02 Estimation in survival analysis and censored data
62J05 Linear regression; mixed models
62G20 Asymptotic properties of nonparametric inference
62N05 Reliability and life testing

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References:

[1] Buckley, J. D., James, I.: Linear regression with censored data. Biometrika, 66(3), 429-436 (1979) · Zbl 0425.62051 · doi:10.1093/biomet/66.3.429
[2] Buckley, J. D.: Additive and multiplicative models for relative survival rates. Biometrics, 40(1), 51-62 (1984) · doi:10.2307/2530743
[3] Cerami, E., Gao, J., Dogrusoz, U., et al.: The cbio cancer genomics portal: An open platform for exploring multidimensional cancer genomics data. Cancer Discovery, 2(5), 401-404 (2012) · doi:10.1158/2159-8290.CD-12-0095
[4] Cox D. R., Oakes D.: Analysis of Survival Data. Chanman and Hall, London, 1984
[5] Efron, B., Tibshirani, R. J.: An Introduction to the Bootstrap. Chanman and Hall, London, 1993 · Zbl 0835.62038 · doi:10.1007/978-1-4899-4541-9
[6] Granville, K., Fan, Z.: Accelerated failure time models with auxiliary covariates. Journal of Biometrics & Biostatistics, 3(6), 1-8 (2012) · doi:10.4172/2155-6180.1000152
[7] Granville, K., Fan, Z.: Buckley-James estimator of aft models with auxiliary covariates. PloS one, 9(8), e104817 (2014) · doi:10.1371/journal.pone.0104817
[8] He, W., Yi, G. Y., Xiong, J.: Accelerated failure time models with covariates subject to measurement error. Statistics in Medicine, 26(26), 4817-4832 (2007) · doi:10.1002/sim.2892
[9] Hu, P., Tsiatis, A. A., Davidian, M.: Estimating the parameters in the cox model when covariate variables are measured with error. Biometrics, 54(4), 1407-19 (1998) · Zbl 1058.62557 · doi:10.2307/2533667
[10] Huang, J., Ma, S., Xie, H.: Regularized estimation in the accelerated failure time model with high dimensional covariates. Biometrics, 62(3), 813-820 (2006) · Zbl 1111.62090 · doi:10.1111/j.1541-0420.2006.00562.x
[11] Jiang, J., Zhou, H.: Additive hazard regression with auxiliary covariates. Biometrika, 94(2), 359-369 (2007) · Zbl 1132.62091 · doi:10.1093/biomet/asm016
[12] Jin, Z., Lin, D. Y., Ying, Z.: On least-squares regression with censored data. Biometrika, 93(1), 147-161 (2006) · Zbl 1152.62068 · doi:10.1093/biomet/93.1.147
[13] Kaplan, E., Meyer, P.: Nonparametric estimation for incomplete observation. Journal of the American Statistical Association, 53, (1958)
[14] Kulich, M., Lin, D. Y.: Additive hazards regression with covariate measurement error. Journal of the American Statistical Association, 95(449), 238-248 (2000) · Zbl 0996.62038 · doi:10.1080/01621459.2000.10473917
[15] Lai, T. L., Ying, Z.: Large sample theory of a modified buckley-james estimator for regression analysis with censored data. Annals of Statistics, 19(3), 1370-1402 (1991) · Zbl 0742.62043 · doi:10.1214/aos/1176348253
[16] Lin, D. Y., Ying, Z.: Cox regression with incomplete covariate measurements. Journal of the American Statistical Association, 88(424), 1341-1349 (1993) · Zbl 0794.62073 · doi:10.1080/01621459.1993.10476416
[17] Liu, Y., Wu, Y., Zhou, H.: Multivariate failure times regression with a continuous auxiliary covariate. Journal of Multivariate Analysis, 101(3), 679-691 (2010) · Zbl 1181.62159 · doi:10.1016/j.jmva.2009.09.008
[18] Liu, Y., Zhou, H., Cai, J.: Estimated pseudo-partial-likelihood method for correlated failure time data with auxiliary covariates. Biometrics, 65(4), 1184-1193 (2009) · Zbl 1180.62177 · doi:10.1111/j.1541-0420.2009.01198.x
[19] Pepe, M. S., Fleming, T. R.: A nonparametric method for dealing with mismeasured covariate data. Journal of the American Statistical Association, 86(413), 108-113 (1991) · doi:10.1080/01621459.1991.10475009
[20] Prentice, R. L.: Amendments and corrections: “linear rank tests with right censored data”. Biometrika, 70(1), 304-304 (1978) · doi:10.1093/biomet/70.1.304-a
[21] Ritov, Y.: Estimation in a linear regression model with censored data. Annals of Statistics, 18(1), 303-328 (1990) · Zbl 0713.62045 · doi:10.1214/aos/1176347502
[22] Shi, X., Liu, Y., Wu, Y.: Continuous auxiliary covariate in additive hazards regression for survival data. Journal of Systems Science and Complexity, 27(6), 1247-1262 (2014) · Zbl 1310.62087 · doi:10.1007/s11424-014-3010-3
[23] Stute, W.: Consistent estimation under random censorship when covariables are present. Journal of Multivariate Analysis, 45, 89-103 (1993) · Zbl 0767.62036 · doi:10.1006/jmva.1993.1028
[24] Stute, W.: Distributional convergence under random censorship when covariables are present. Scandinavian Journal of Statistics, 23(4), 461-471 (1996) · Zbl 0903.62045
[25] Tsiatis, A. A.: Estimating regression parameters using linear rank tests for censored data. Annals of Statistics, 18(1), 354-372 (1990) · Zbl 0701.62051 · doi:10.1214/aos/1176347504
[26] Tsiatis, A. A., Davidian, M.: A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error. Biometrika, 88(2), 447-458 (2001) · Zbl 0984.62078 · doi:10.1093/biomet/88.2.447
[27] Vaart, A. W. van der: Asymtotic Statistics, Cambridge University Press, United Kingdom, 1998 · Zbl 0943.62002 · doi:10.1017/CBO9780511802256
[28] Wei, L. J.: The accelerated failure time model: a useful alternative to the cox regression model in survival analysis. Statistics in Medicine, 11(14-15), 1871-1879 (1992) · doi:10.1002/sim.4780111409
[29] Wei, L. J., Ying, Z., Lin, D. Y.: Linear regression analysis of censored survival data based on rank tests. Biometrika, 77(4), 845-851 (1990) · doi:10.1093/biomet/77.4.845
[30] Ying, Z.: A large sample study of rank estimation for censored regression data. Annals of Statistics, 21(1), 76-99 (1993) · Zbl 0773.62048 · doi:10.1214/aos/1176349016
[31] Yu, M., Nan, B.: Regression calibration in semiparametric accelerated failure time models. Biometrics, 66(2), 405-414 (2009) · Zbl 1192.62123 · doi:10.1111/j.1541-0420.2009.01295.x
[32] Zhou, H., Pepe, M. S.: Auxiliary covariate data in failure time regression. Biometrika, 82(1), 139-149 (1995) · Zbl 0823.62100 · doi:10.1093/biomet/82.1.139
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