A Product-Limit Estimator of the Conditional Survival Function When Cure Status Is Partially Known
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A Product-Limit Estimator of the Conditional Survival Function When Cure Status Is Partially KnownDate
2021-03-01Citation
Safari WC, López-de-Ullibarri I, Jácome MA. A product-limit estimator of the conditional survival function when cure status is partially known. Biometrical Journal. 2021; 63: 984–1005. https://doi.org/10.1002/bimj.202000173
Abstract
[Abstract] We introduce a nonparametric estimator of the conditional survival function in the mixture cure model for right-censored data when cure status is partially known. The estimator is developed for the setting of a single continuous covariate but it can be extended to multiple covariates. It extends the estimator of Beran, which ignores cure status information. We obtain an almost sure representation, from which the strong consistency and asymptotic normality of the estimator are derived. Asymptotic expressions of the bias and variance demonstrate a reduction in the variance with respect to Beran's estimator. A simulation study shows that, if the bandwidth parameter is suitably chosen, our estimator performs better than others for an ample range of covariate values. A bootstrap bandwidth selector is proposed. Finally, the proposed estimator is applied to a real dataset studying survival of sarcoma patients.
Keywords
Bootstrap bandwidth
Censoring
Cure model
Kernel estimator
Nadaraya-Watson weights
Censoring
Cure model
Kernel estimator
Nadaraya-Watson weights
Description
This is the peer reviewed version of the following article: Safari, W. C., López-de-Ullibarri, I., & Jácome, M. A. (2021). Correction: A product-limit estimator of the conditional survival function when cure status is partially known. Biometrical Journal, 63, 1544–1546. https://doi.org/10.1002/bimj.202000173, which has been published in final form at https://doi.org/10.1002/bimj.202000173. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
Editor version
ISSN
1521-4036
0323-3847
0323-3847