Abstract
In real applications, we may be confronted with the problem of informative censoring. Koziol-Green model is commonly used to model the possible information contained in the informative censoring. However the proportionality assumption cast by Koziol-Green model (see (1.2) below) is “too restrictive in that it limits the scope of the Cox model in practice” (see Subramanian, 2000). In this paper, we try to relax the proportionality condition of Koziol-Green model by modeling the censorship semiparametrically. It is shown that our suggested semiparametric censoring model is an applicable extension of the Koziol-Green model. Through a close connection with the logistic regression, our model assumptions are readily to be checked in paractice. We also propose estimation for both the regression parameter and the cumulative baseline hazard function which can incorporate the additional information contained in the semiparametric censorship model. Simulations and the analysis of a real dataset confirm the applicability of the suggested model and estimation.
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References
Aerts, M., Cleaskens, G., andHart, J. D. (1999). Testing the fit of a parametric function.Journal of the American Statistical Association, 94:869–879.
Andersen, P. K. andGill, R. D. (1982). Cox's regression model for counting processes: A large sample study.The Annals of Statistics, 10:1100–1120.
Bickel, P. J., Klaassen, C. A. J., Ritov, Y., andWellner, J. A. (1993).Efficient and Adaptive Estimation for Semiparametric Models, The John Hopkins University Press, Baltimore and London.
Cox, D. R. (1972). Regression models and life tables (with discussion).Journal of the Royal Statistical Society. Series B, 34:187–220.
Dabrowska, D. M. (1989). Uniform consistency of the kernel conditional Kaplan-Meier estimate.The Annals of Statistics, 17(3): 1157–1167.
de Uña Álvarez, J. andGonzález-Manteiga, W. (1998). Distributional convergence under proportional censorship when covariates are present.Statistics & Probability Letters, 39:305–315.
de Uña Álvarez, J. andGonzález-Manteiga, W. (1999). Strong consistency under proportional censorship when covariates are present.Statistics & Probability Letters, 42:283–292.
Dikta, G. (1998). On semiparametric random censorship models.Journal of Statistical Planning and Inference, 66:253–279.
Dikta, G. (2000). The strong law under semiparametric random censorship models.Journal of Statistical Planning and Inference, 83(1):1–10.
Escobar, L. A. andMeeker, W. Q. (1992). Assessing influence in regression analysis with censored data.Biometrics, 48:507–528.
Foutz, R. V. (1977). On the unique consistent solution to the likelihood equations.Journal of the American Statistical Association, 72:147–148.
Gather, U. andPawlitschko, J. (1998). Estimating the survival function under a generalized Koziol-Green model with partially informative censoring.Metrika, 48:189–207.
Hart, J. D. (1997).Nonparametric Smoothing and Lack-of-fit Tests. Springer-Verlag, New York.
Jensen, U. andWiedmann, J. (2001). Estimation of a survival curve with randomly censored data in the presence of a covariate.Metrika, 53(3):223–244.
Koziol, J. A. andGreen, S. B. (1976). A Cramer-von Mises statistic for randomly censored data.Biometrika, 63:465–474.
Lin, D. Y. andSpiekerman, C. F. (1996). Model checking techniques for parametric regression with censored data.Scandinavian Journal of Statistics. Theory and Applications, 23(2):157–177.
Sasieni, P. D. (1992). Non-orthogonal projections and their application to calculating the information in a partly linear Cox model.Scandinavian Journal of Statistics. Theory and Applications, 19(3):215–233.
Subramanian, S. (2000). Efficient estimation of regression coefficients and baseline hazard under proportionality of conditional hazard.Journal of Statistical Planning and Inference, 84(1–2):81–94.
Veraverbeke, N. andCadarso-Suárez, C. (2000). Estimation of the conditional distribution in a conditional Koziol-Green model.Test, 9(1):97–122.
White, H. (1994).Estimation, Inference and Specification Analysis. No. 22 in Econometric Society Monographs. Cambridge University Press, Cambridge.
Zhu, L. X., Yuen, K. C. andTang, N. Y. (2002). Resampling methods for testing a semiparametric random censorship model.Scandinavian Journal of Statistics. Theory and Applications, 29(1):111–123.
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This research is partially supported by NSF Grant DMS-0772292
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Yuan, M. Semiparametric censorship model with covariates. TEST 14, 489–514 (2005). https://doi.org/10.1007/BF02595415
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DOI: https://doi.org/10.1007/BF02595415