Estimating marginal survival function by adjusting for dependent censoring using many covariates. (English) Zbl 1047.62092

Summary: One goal in survival analysis of right-censored data is to estimate the marginal survival function in the presence of dependent censoring. When many auxiliary covariates are sufficient to explain the dependent censoring, estimation based on either a semiparametric model or a nonparametric model of the conditional survival function can be problematic due to the high dimensionality of the auxiliary information.
We use two working models to condense these high-dimensional covariates in dimension reduction; then an estimate of the marginal survival function can be derived nonparametrically in a low-dimensional space. We show that such an estimator has the following double robust property: when either working model is correct, the estimator is consistent and asymptotically Gaussian; when both working models are correct, the asymptotic variance attains the efficiency bound.


62N02 Estimation in survival analysis and censored data
62N01 Censored data models
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
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[1] Andersen, P. K. and Gill, R. D. (1982). Cox’s regression model for counting processes: A large sample study. Ann. Statist. 10 1100–1120. JSTOR: · Zbl 0526.62026
[2] Bennett, S. (1983). Analysis of survival data by the proportional odds model. Statistics in Medicine 2 273–277.
[3] Bickel, P. J., Klaassen, C. A. J., Ritov, Y. and Wellner, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models . John Hopkins Univ. Press, Baltimore, MA. · Zbl 0786.62001
[4] Cox, D. R. (1972). Regression models and life-tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187–220. · Zbl 0243.62041
[5] Dabrowska, D. M. (1987). Nonparametric regression with censored survival time data. Scand. J. Statist. 14 181–197. · Zbl 0641.62024
[6] Gill, R. D., van der Laan, M. J. and Robins, J. (1997). Locally efficient estimation in censored data models with high-dimensional covariate vectors or time-dependent marker processes. Unpublished manuscript.
[7] Little, R. J. A. (1986). Survey nonresponse adjustments for estimates of means. Internat. Statist. Review 54 139–157. · Zbl 0596.62009
[8] Robins, J. M., Rotnitzky, A. and van der Laan, M. (2000). Comment on “On profile likelihood,” by S. Murphy and A. W. van der Vaart. J. Amer. Statist. Assoc. 95 477–482.
[9] Rotnitzky, A. and Robins, J. M. (1995). Semiparametric regression estimation in the presence of dependent censoring. Biometrika 82 805–820. · Zbl 0861.62030
[10] Rubin, D. B. (1976). Inference and missing data (with discussion). Biometrika 63 581–592. · Zbl 0344.62034
[11] Scharfstein, D. O. and Robins, J. M. (2002). Estimation of the failure time distribution in the presence of informative censoring. Biometrika 89 617–634. · Zbl 1036.62110
[12] Tibshirani, R. and Hastie, T. (1987). Local likelihood estimation. J. Amer. Statist. Assoc. 82 559–567. · Zbl 0626.62041
[13] van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes With Applications to Statistics . Springer, New York. · Zbl 0862.60002
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