Statistics and Its Interface

Volume 16 (2023)

Number 3

Quadratic upper bound algorithms for estimation under Cox model in case-cohort studies

Pages: 459 – 474

DOI: https://dx.doi.org/10.4310/22-SII736

Authors

Jieli Ding (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Jiaqian Zhang (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Yanqin Feng (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Yuxuan Du (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Abstract

A case-cohort design is a cost-effective biased-sampling scheme in large cohort studies. Implementation of parameter estimators for case-cohort data requires numerical approaches. Using the minorization-maximization principle, which is a versatile tool for constructing optimization algorithms, we develop two quadratic-upper-bound algorithms for estimations in the Cox model under case-cohort design. The proposed algorithms are monotonic and reliably converge to the weighted estimators considered. These algorithms involve the inversion of the derived upper-bound matrix only one time in the whole process, and the upper-bound matrix is independent of both parameter and weight functions. These features make the proposed algorithms have simple update and low per-iterative cost, especially to large-dimensional problems. We conduct simulation studies and real data examples to illustrate the performance of the proposed algorithms, and compare them to Newton’s method.

Keywords

case-cohort design, minorization maximization algorithm, quadratic upper bounds, Cox model, estimating equations

Received 10 January 2022

Accepted 21 April 2022

Published 14 April 2023