Statistics and Its Interface

Volume 16 (2023)

Number 4

A pairwise pseudo-likelihood approach for the additive hazards model with left-truncated and interval-censored data

Pages: 553 – 563



Peijie Wang (School of Mathematics, Jilin University, Changchun, China)

Yichen Lou (School of Mathematics, Jilin University, Changchun, China)

Jianguo Sun (Department of Statistics, University of Missouri, Columbia, Mo., U.S.A.)


Left-truncated and interval-censored data occur commonly and some approaches have been proposed in the literature for their analysis. However, most of the existing methods are based on the conditional likelihood given left-truncation times, which can be inefficient since the information in the marginal likelihood of the truncation times is ignored. To address this, in this paper, a pairwise pseudo-likelihood augmented estimation approach is proposed under the additive hazards model that can fully make use of all available information. The derived estimator is shown to be consistent and asymptotically normal, and simulation studies suggest that the proposed method works well and provides a substantial efficiency gain over the conditional approach. In addition, the method is applied to a set of real data arising from an AIDS cohort study.


additive hazards model, bootstrap, interval-censored data, left truncation, pairwise pseudo-likelihood augmented estimation

This work was partially supported by the National Nature Science Foundation of China (Grant No. 11801212, Grant No. 12071176).

Received 21 March 2022

Accepted 25 May 2022

Published 14 April 2023