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Semiparametric inference for the accelerated life model with time- dependent covariates. (English) Zbl 0812.62096
Summary: The accelerated life model assumes that the failure time associated with a multi-dimensional covariate process is contracted or expanded relative to that of the zero-valued covariate process. In the present paper, the rate of contraction/expansion is formulated by a parametric function of the covariate process while the baseline failure time distribution is unspecified. Estimating functions for the vector of regression parameters are motivated by likelihood score functions and take the form of log rank statistics with time-dependent covariates. The resulting estimators are proven to be strongly consistent and asymptotically normal under suitable regularity conditions.
Simple methods are derived for making inference about a subset of regression parameters while regarding others as nuisance quantities. Finite-sample properties of the estimation and testing procedures are investigated through Monte Carlo simulations. An illustration with the well-known Stanford heart transplant data is provided.

62N05 Reliability and life testing
62F12 Asymptotic properties of parametric estimators
62G07 Density estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI
[1] Andersen, P.K.; Gill, R.D., Cox’s regression model for counting processes: a large sample study, Ann. statist., 10, 1100-1120, (1982) · Zbl 0526.62026
[2] Begun, J.M.; Hall, W.J.; Huang, W.-M.; Wellner, J.A., Information and asymptotic efficiency in parametric-nonparametric models, Ann. statist., 11, 432-452, (1983) · Zbl 0526.62045
[3] Cox, D.R., Regression models and life tables (with discussion), J. roy. statist. soc. ser. B, 34, 187-220, (1972) · Zbl 0243.62041
[4] Cox, D.R.; Oakes, D., Analysis of surrival data, (1984), Chapman & Hall London
[5] Crowley, J.; Hu, M., Covariance analysis of heart transplant survival data, J. amer. statist. assoc., 72, 27-36, (1977)
[6] Cuzick, J., Asymptotic properties of censored linear rank tests, Ann. statist., 13, 133-141, (1985) · Zbl 0584.62069
[7] Kalbfleisch, J.D.; Prentice, R.L., The statistical analysis of failure time data, (1980), Wiley New York · Zbl 0504.62096
[8] Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P., Optimization by simulated anncaling, Science, 220, 671-680, (1983) · Zbl 1225.90162
[9] Lai, T.L.; Ying, Z., Stochastic integrals of empirical-type processes with applications to censored regression, J. multivariate anal., 27, 334-358, (1988) · Zbl 0684.62048
[10] Lai, T.L.; Ying, Z., Rank regression methods for left-truncated and right-censored data, Ann. statist., 19, 531-556, (1991) · Zbl 0739.62031
[11] Lin, D.Y.; Geyer, C.J., Computational methods for semiparametric linear regression with censored data, J. comput. and graph. statist., 1, 77-90, (1992)
[12] Prentice, R.L., Linear rank tests with right censored data, Biometrika, 65, 167-179, (1978) · Zbl 0377.62024
[13] Ritov, Y., Estimation in a linear regression model with censored data, Ann. statist., 18, 303-328, (1990) · Zbl 0713.62045
[14] Robins, J.M., Estimation of the time-dependent accelerated failure time model in the presence of confounding factors, Biometrika, 79, 313-334, (1992) · Zbl 0753.62076
[15] Robins, J.M.; Tsiatis, A.A., Semiparametric estimation of an accelerated failure time model with time-dependent covariates, Biometrika, 79, 311-319, (1992) · Zbl 0751.62046
[16] Rudin, W., Real and complex analysis, (1974), McGraw-Hill New York
[17] Shorack, G.R.; Wellner, J.A., Empirical processes with applications to statistics, (1986), Wiley New York · Zbl 1170.62365
[18] Tsiatis, A.A., Estimating regression parameters using linear rank tests for censored data, Ann. statist., 18, 354-372, (1990) · Zbl 0701.62051
[19] Wei, L.J.; Ying, Z.; Lin, D.Y., Linear regression analysis of censored survival data based on rank tests, Biometrika, 77, 845-851, (1990)
[20] Ying, Z., A large sample study of rank estimation for censored regression data, Ann. statist., 21, 76-99, (1993) · Zbl 0773.62048
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