Statistics and Its Interface

Volume 13 (2020)

Number 3

Semiparametric Accelerated Failure Time Modeling for Multivariate Failure Times under Multivariate Outcome-Dependent Sampling Designs

Pages: 373 – 383



Tsui-Shan Lu (Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan)

Sangwook Kang (Department of Applied Statistics, Yonsei University, Seoul, South Korea)

Haibo Zhou (Department of Biostatistics, University of North Carolina, Chapel Hill, N.C.,


Researchers working on large cohort studies are always seeking for cost-effective designs due to a limited budget. An outcome-dependent sampling (ODS) design, a retrospective sampling scheme where one observes covariates with a probability depending on the outcome and selects supplemental samples from more informative segments, improves the study efficiency while effectively controlling for the budget. To take the advantage of the ODS scheme when multivariate failure times are main response variables, relevant study designs and inference procedures need to be studied.

In this paper, we consider a general multivariate-ODS design for multivariate failure times under the framework of a semiparametric accelerated failure time model. We develop a weighted estimating equations approach, based on the induced smoothing method, for parameter estimation. Extensive simulation studies show that our proposed design and estimator are more efficient than other competing estimators based on simple random samples. The proposed method is illustrated with a real data set from the Busselton Health Study.


Biased sampling, Induced smoothing, Rank-based estimation, Resampling, Weighted estimating equations, Sandwich variance estimation

This research was partly supported by the Ministry of Science and Technology in Taiwan grant (108-2118-M-003-001-MY2) for Dr. Lu, the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2017R1A2B4005818) for Dr. Kang and US National Institutes of Health grants (P01-CA142538 and P30-ES010126) for Dr. Zhou.

Received 20 May 2019

Accepted 11 February 2020

Published 22 April 2020