TY - JOUR

T1 - Simultaneous confidence bands for survival functions from twice censorship

AU - Subramanian, Sundarraman

N1 - Funding Information:
The author wishes to offer his sincere thanks to Co-Editor-in-Chief Yimin Xiao and two anonymous referees whose comments were largely responsible for the improved final version.
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/7

Y1 - 2022/7

N2 - When a failure time observation is right censored, it is not observed beyond a random right threshold. When a possibly right censored observation is further susceptible to a random left threshold, a twice censored observation results. Patilea and Rolin have proposed product limit estimators for survival functions from twice censored data. Simultaneous confidence bands (SCBs) for survival functions from twice censored data are constructed in a way that mimics the approach that Hollander, McKeague and Yang pursued for random right censoring. Their nonparametric likelihood ratio function is adjusted, providing the basis for constructing the SCBs. The critical value needed for the SCBs is obtained using the bootstrap, for which asymptotic justification is provided. The SCBs align nicely as “neighborhoods” of the Patilea–Rolin nonparametric survival function estimator, in much the same way the likelihood ratio SCBs under random censoring are the “neighborhoods” of the Kaplan–Meier estimator. A simulation study supports the effectiveness of the proposed method. An illustration is given using synthetic data.

AB - When a failure time observation is right censored, it is not observed beyond a random right threshold. When a possibly right censored observation is further susceptible to a random left threshold, a twice censored observation results. Patilea and Rolin have proposed product limit estimators for survival functions from twice censored data. Simultaneous confidence bands (SCBs) for survival functions from twice censored data are constructed in a way that mimics the approach that Hollander, McKeague and Yang pursued for random right censoring. Their nonparametric likelihood ratio function is adjusted, providing the basis for constructing the SCBs. The critical value needed for the SCBs is obtained using the bootstrap, for which asymptotic justification is provided. The SCBs align nicely as “neighborhoods” of the Patilea–Rolin nonparametric survival function estimator, in much the same way the likelihood ratio SCBs under random censoring are the “neighborhoods” of the Kaplan–Meier estimator. A simulation study supports the effectiveness of the proposed method. An illustration is given using synthetic data.

KW - Continuous mapping theorem

KW - Empirical coverage probability

KW - Glivenko–Cantelli theorem

KW - Integrated hazard measure

KW - Lagrange multiplier

KW - Weak convergence

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U2 - 10.1016/j.spl.2022.109494

DO - 10.1016/j.spl.2022.109494

M3 - Article

AN - SCOPUS:85127653142

VL - 186

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

M1 - 109494

ER -