Nonparametric estimation for competing risks survival data subject to left truncation and interval censoring

• Published in: Computational statistics Vol. 37; no. 1; pp. 29 - 42
• Main Author: Shen, Pao-sheng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022; Springer Nature B.V
• Subjects: Bias; Calendars; Economic Theory/Quantitative Economics/Mathematical Methods; Failure; HIV; Human immunodeficiency virus; Mathematics and Statistics; Maximum likelihood estimators; Nonparametric statistics; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Random variables; Statistics; Survival analysis; Left truncation; NPMLE; Cumulative incidence function; EM algorithm
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-021-01111-5

In this article, we consider nonparametric estimation of the cumulative incidence function (CIF) for left-truncated and interval-censored competing risks (LT-ICC) data. To reduce the bias of the pseudo-likelihood estimator (PLE) of CIF in the literature, we proposed two alternative estimators. The first estimator, called the modified PLE (MPLE), is obtained based on the modified NPMLE of F ( t ). The second estimator, called the modified maximum likelihood estimator (MMLE), is derived using modified likelihood functions for LT-ICC data, where the left endpoints of the intervals for left-censored observations with failure type j are the maximum of left-truncated variables and the estimated left endpoint of the support of the observations. Simulation studies show that the MPLE and MMLE are less biased than the PLE for most of the cases considered and their standard deviations are significantly smaller than that of the PLE.