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Semiparametric estimation of survival function when data are subject to dependent censoring and left truncation

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  • Shen, Pao-sheng

Abstract

Satten et al. (2001) proposed an estimator of the survival function (denoted by S(t)) of failure times that is in the class of survival function estimators proposed by Robins (1993). The estimator is appropriate when data are subject to dependent censoring. In this article, we consider the case when data are subject to dependent censoring and left truncation, where the distribution function of the truncation variables is parameterized as G(x;[theta]), where [theta][set membership, variant][Theta][subset of]Rq, and [theta] is a q-dimensional vector. We propose two semiparametric estimators of S(t) by simultaneously estimating G(x;[theta]) and S(t). One of the proposed estimators, denoted by , is represented as an inverse-probability-weighted average (Satten and Datta, 2001). The other estimator, denoted by , is an extension of the estimator proposed by Satten et al.. The asymptotic properties of both estimators are established. Simulation results show that when truncation is not severe the mean squared error of is smaller than that of . However, when truncation is severe and censoring is light, the situation can be reverse.

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  • Shen, Pao-sheng, 2010. "Semiparametric estimation of survival function when data are subject to dependent censoring and left truncation," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 161-168, February.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:3-4:p:161-168
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    References listed on IDEAS

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    1. van der Laan, Mark J., 1996. "Nonparametric Estimation of the Bivariate Survival Function with Truncated Data," Journal of Multivariate Analysis, Elsevier, vol. 58(1), pages 107-131, July.
    2. Asgharian M. & MLan C.E. & Wolfson D. B., 2002. "Length-Biased Sampling With Right Censoring: An Unconditional Approach," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 201-209, March.
    3. James M. Robins & Dianne M. Finkelstein, 2000. "Correcting for Noncompliance and Dependent Censoring in an AIDS Clinical Trial with Inverse Probability of Censoring Weighted (IPCW) Log-Rank Tests," Biometrics, The International Biometric Society, vol. 56(3), pages 779-788, September.
    4. Satten, Glen A. & Datta, Somnath & Robins, James, 2001. "Estimating the marginal survival function in the presence of time dependent covariates," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 397-403, October.
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