Nonparametric estimators of survival function under the mixed case interval-censored model with left truncation

Pao-Sheng Shen ()
Additional contact information
Pao-Sheng Shen: Tunghai University

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2020, vol. 26, issue 3, No 9, 624-637

Abstract: Abstract It is well known that the nonparametric maximum likelihood estimator (NPMLE) can severely underestimate the survival probabilities at early times for left-truncated and interval-censored (LT-IC) data. For arbitrarily truncated and censored data, Pan and Chappel (JAMA Stat Probab Lett 38:49–57, 1998a, Biometrics 54:1053–1060, 1998b) proposed a nonparametric estimator of the survival function, called the iterative Nelson estimator (INE). Their simulation study showed that the INE performed well in overcoming the under-estimation of the survival function from the NPMLE for LT-IC data. In this article, we revisit the problem of inconsistency of the NPMLE. We point out that the inconsistency is caused by the likelihood function of the left-censored observations, where the left-truncated variables are used as the left endpoints of censoring intervals. This can lead to severe underestimation of the survival function if the NPMLE is obtained using Turnbull’s (JAMA 38:290–295, 1976) EM algorithm. To overcome this problem, we propose a modified maximum likelihood estimator (MMLE) based on a modified likelihood function, where the left endpoints of censoring intervals for left-censored observations are the maximum of left-truncated variables and the estimated left endpoint of the support of the left-censored times. Simulation studies show that the MMLE performs well for finite sample and outperforms both the INE and NPMLE.

Keywords: Left truncation; Interval censoring; NPMLE; EM algorithm (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10985-020-09493-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:lifeda:v:26:y:2020:i:3:d:10.1007_s10985-020-09493-2

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10985

DOI: 10.1007/s10985-020-09493-2

Access Statistics for this article

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data is currently edited by Mei-Ling Ting Lee

More articles in Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().