Maximum likelihood estimation for length-biased and interval-censored data with a nonsusceptible fraction

Pao-sheng Shen, Yingwei Peng, Hsin-Jen Chen and Chyong-Mei Chen ()
Additional contact information
Pao-sheng Shen: Tunghai University, Xitun District
Yingwei Peng: Queen’s University
Hsin-Jen Chen: National Yang Ming Chiao Tung University
Chyong-Mei Chen: National Yang Ming Chiao Tung University

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2022, vol. 28, issue 1, No 4, 68-88

Abstract: Abstract Left-truncated data are often encountered in epidemiological cohort studies, where individuals are recruited according to a certain cross-sectional sampling criterion. Length-biased data, a special case of left-truncated data, assume that the incidence of the initial event follows a homogeneous Poisson process. In this article, we consider an analysis of length-biased and interval-censored data with a nonsusceptible fraction. We first point out the importance of a well-defined target population, which depends on the prior knowledge for the support of the failure times of susceptible individuals. Given the target population, we proceed with a length-biased sampling and draw valid inferences from a length-biased sample. When there is no covariate, we show that it suffices to consider a discrete version of the survival function for the susceptible individuals with jump points at the left endpoints of the censoring intervals when maximizing the full likelihood function, and propose an EM algorithm to obtain the nonparametric maximum likelihood estimates of nonsusceptible rate and the survival function of the susceptible individuals. We also develop a novel graphical method for assessing the stationarity assumption. When covariates are present, we consider the Cox proportional hazards model for the survival time of the susceptible individuals and the logistic regression model for the probability of being susceptible. We construct the full likelihood function and obtain the nonparametric maximum likelihood estimates of the regression parameters by employing the EM algorithm. The large sample properties of the estimates are established. The performance of the method is assessed by simulations. The proposed model and method are applied to data from an early-onset diabetes mellitus study.

Keywords: Interval censoring; Left truncation; Length-biased sampling; Mixture cure model; Nonparametric maximum likelihood estimation (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10985-021-09536-2 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:28:y:2022:i:1:d:10.1007_s10985-021-09536-2

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

DOI: 10.1007/s10985-021-09536-2

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 ().