Statistics and Its Interface

Volume 14 (2021)

Number 4

Constrained estimation in Cox model under failure-time outcome-dependent sampling design

Pages: 475 – 488

DOI: https://dx.doi.org/10.4310/21-SII667

Authors

Jie Yin (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Changming Yang (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

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

Yanyan Liu (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Abstract

The failure-time outcome-dependent sampling (ODS) design is a cost-effective sampling scheme, which can improve the efficiency of the studies by selectively including certain failures to enrich the observed sample. In modeling process, taking some prior constraints on parameters into account may lead to more powerful and efficient inferences. In this paper, we study how to fit the proportional hazards model with parameter constraints to data from a failure-time ODS design. We propose constrained weighted estimation by conducting an optimization problem on a working likelihood function. The asymptotic properties of the proposed estimator are established.We develop a restricted minorization-maximization (MM) algorithm for the numerical calculation of the proposed estimator. Simulation studies are conducted to evaluate the finite-sample performance of the proposed estimator. An application to a data set from a Wilms tumor study is illustrated for the utility of the proposed method.

Keywords

biased sampling, inverse probability weighted Cox model, Karush–Kuhn–Tucker conditions, minorization-maximization algorithm

Received 22 December 2019

Accepted 4 March 2021

Published 8 July 2021